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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses .
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as we know , atoms that have the same number of protons and electrons but different # neutrons are known as isotopes.but if the # electrons are different at the same time , are they still isotopes ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ?
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so expanding on mass spectrometry ... if we were to look at the fragmentation of a molecule after it has been ionised how do we know which fragments would be produced ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . ''
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is ch+ possible for any organic compound ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law .
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if protons all have a positive charge , then why does n't the nucleus fly apart ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ?
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for example , if you run stable copper through a mass spectrometer , could the sample consist mostly of cu-63 ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % .
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how do scientists know that the sample of isotopes inserted into a mass spectrometer accurately reflects the relatively abundances of those isotopes in the entire earth ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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but is it not possible that a different sample of the same element may have different isotopes and different relative abundances of said isotopes ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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any idea why scientists do n't simply use a mass spectrometer ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field .
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also how would one insert a sample into the vacuum without letting gas in ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons .
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how does one know how many extra neutrons an isotope has ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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also how do you know the range of isotopes an element has ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . ''
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can atoms bond with each other and possibly create enough power as a supernova star ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes .
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so what exactly is a spectrum ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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as superscript of an element ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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using the approximated values of the mass numbers of isotopes is correct , is n't it ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge .
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are neutrons , protons , and electrons spherical or are they just portrayed like that ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge .
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why does potassium have 20 neutrons but only 19 protons ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument .
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if the answer is that potassium-38 is unstable , why is it unstable ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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one ion has a mass of 2 and a charge of 1 , while another has a mass of 4 and charge of 2 , while both have a m/z of 2 ) ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number .
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magnesium-24 has a net charge of zero correct ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses .
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is the higgs boson discovered ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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how is possible to have a `` sample '' with all the isotopes of 1 element and in the perfect proportions of the amounts in the earth ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element .
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y amu is given as 1\12 of carbon only and y not any other ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more .
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could the bend in the curve be just a change in the speed ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected .
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what energy is used to accelerate cations ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron .
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too many queries : ( 1 ) why only ions are affected by magnetic fields although electrically neutral ones are n't ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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2 ) why mass spectrometers work with positive ions ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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and how is atomic mass calculated ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % .
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how do we calculate percentage abundance ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element .
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how do i find the atmoic mass of a specific isotope ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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does mass spectrometry always work ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) .
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also , what are quarks , gluons , mesons and bosons ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element .
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what does the ~ mean in ~0u ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example .
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what is the point of neutrons ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ?
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meaning , should n't the calculated result of 2.685424 be rounded `` up '' to 2.69 , instead of being rounded down to 2.68 as set out in the example above ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law .
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ok forgive me if this is a stupid question but since the protons have a positive charge and the electrons have a negative charge does n't that mean they will be drawn towards each other like the opposite ends of a magnet ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge .
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could there ever be less neutrons in an atom , because do n't opposites attract , and if there were , would n't the protons repel from each other , leaving it with less protons , making it a different atom ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom .
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so does a electron have a volume or not ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element .
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if 1u is equal exactly 1/12 of the mass of a single neutral atom of carbon-12 , the ecuation to know the equivalence would be 1/12*12.01= 1.001 grams/mole ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % .
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why is there a 0 always before the relative abundance when solving and not when being written in the table ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field .
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how do scientists choose sample ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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where do you find mass spectrometers , and how do scientists agree on what results from the spectrometers to use ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element .
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should n't proton be slightly less than 1 u to make it exactly 12 ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ .
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but is it possible that more chlorine-37 can be found inside the earth ( that is , when we have the right technology or methods ) ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry .
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inside the earth in the future ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit .
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are atoms use only for things ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . ''
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i thought cells are used for humans , not atoms ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected .
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is an isotope like an ion ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis .
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why does the high energy electron beam strip away electrons rather than add them ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis .
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would a low energy electron beam add electrons ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % .
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does relative abundance of elements not vary at all from one extraction location to another ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge .
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before the spectrometer , how did a chemist know how many protons and neutrons and electrons an element had ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ?
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is radioactive dating the same as carbon dating ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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what is the simplified or basic key points on the difference between atomic mass and relative atomic mass ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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where do we get that the atomic mass for chlorine-35 is 34.969 ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ?
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i read a comment below about how you need to take into account the weight of the electrons and the binding energy , but how will it end up being less than 35 ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section !
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atomic weight and atomic mass are different ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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what is the difference between atomic mass , atomic weight , and mass number ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine .
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what 's the z-like sign in the first part of the atomic weight formula ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element .
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so far i have seen that only the lighter isotopes are more abundant due to its lower mass to charge ratio and being deflected more easily but what if the heavier isotope is more abundant but because of its higher mass and consequently its higher momentum , it does not get frequently deflected leading to a misconception that the lighter isotope is more abundant ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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at speeds near c , mass approaches infinity-so would n't the electon then be a significant fraction of the atom 's mass-not 1/2000 or less ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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this is more out of curiosity ; but how are the ions accelerated through the disks in the mass spectrometry ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected .
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what causes the ions to accelerate in the first place ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses .
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what are the muon and the tau ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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sir what is the meaning of atomic mass number when it is given in decimal form or in point ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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is m referring to the atomic mass `` ionic in this case '' or is it the mass number ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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how do we calculate atomic mass ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge .
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what are `` cations '' ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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also , to determine the total isotopes possible for an element , this is something to be looked up ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values .
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when , say , finding the percent abundances of isotopes , do i prioritize significant figures or making sure that my percents add up to 100 % ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % .
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and what is relative abundance ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ?
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how in the world can i do percent abundances the easiest way ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ?
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under section `` calculating the atomic weight of chlorine '' how did you get the numbers 34.969u and 36.96u ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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in the first section it talks about isotopes , is there a limit to the possible number of isotopes for each element ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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is the number of isotopes for a given element is constant ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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means cl has only three isotopes in any sample taken in the universe ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium .
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how an electron can pick another electron ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ .
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how accurate is relative abundance using mass spectrometry ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry .
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for example , maybe no samples were taken from the bottom of the ocean , deep within the earth , or in some other remote area of the earth ... so how can we be sure our sample accurately represents the entire earth ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms .
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if there are more than one proton in all atoms except hydrogen , why does n't the atom rip apart because like charges repel ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element .
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hi in the section of particle masses and unified atomic mass units its says that 1 u represent 1/12 of the mass of a single neutral atom of carbon-12 does that mean that 1 u represent 1 proton and neutron or am i wrong ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons .
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how do you predict how heavy is an atom ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine .
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when calculating atomic weight , where do the relative abundance numbers come from ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass .
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1.how many isotopes that one element have ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus .
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2.what is a net charge also how to work out for one element ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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in the chlorine example above , how did you find the atomic mass to be 34.969 and 34.966 ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball .
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if a heavier isotope is deflected less , why are some heavier isotopes more abundant than the lighter ones ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % .
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how would you even find the percent relative abundance ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine .
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what are the names of symbols used in equation for atomic weight ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . ''
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how does the study of atoms and molecular studies constitute to future jobs ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes .
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what purpose do the studies of invisible specs have in our already complex world ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . ''
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if we send more electro negative atoms like fluorine , oxygen then what happens ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis .
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what is the meaning of high energy electron beam ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field .
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how do these electrons in mass spectro meter ionizes atoms by picking electrons ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields .
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is there any video in ka explaining the working of cathode ray tube ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field .
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how a cathode ray tube produces electrons ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ .
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is it not violating the law of conservation of mass ?
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key points : atoms that have the same number of protons but different numbers of neutrons are known as isotopes . isotopes have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . introduction : dissecting an atom everything is made out of atoms . your computer or phone screen , the chair you are sitting on , you , and i are all made out of atoms . if we were to zoom in further using our very technologically advanced and imaginary chemistry goggles , we 'd be able to see that the atom itself is made out of subatomic particles with specific properties . an atom is composed of protons , neutrons , and electrons . a proton carries a $ 1 $ $ + $ charge , an electron carries a $ 1 $ $ - $ charge , and a neutron carries $ 0 $ charge . the nucleus is made up of protons and neutrons , and electrons are localized outside the nucleus . since electrons have a negative charge , they are attracted to the positively charged protons in the nucleus . this gives an atom its stability , and we can think about this mathematically using coulomb 's law . on a very simplistic level , we can represent an atom using figure 1 : we count two protons in the nucleus of this atom , which means that our atom has an atomic number ( $ \text z $ ) of $ 2 $ . since the identity of an element is determined by the atomic number , we can deduce that our atom must be an atom of helium . in order for the atom to be neutral , we have $ 2 $ electrons to balance out the positive charge from the protons . but what about the neutrons , which have no charge ? this particular atom of helium happens to have two neutrons . does that mean all helium atoms must have two neutrons ? we know that if the nucleus had a different atomic number , then the atom would be a different element . however , the same is not true of the number of neutrons in the nucleus . it is possible that atoms of the same element may contain different numbers of neutrons ; such atoms are known as isotopes . this comes from greek : iso- meaning `` same , '' and -tope meaning `` place . '' thus , isotopes—because they contain the same number of protons—occupy the same place on the periodic table . they differ , however , in the number of neutrons in their nuclei , which causes them to have different masses . particle masses and unified atomic mass units atoms are extremely tiny , and the particles within atoms are even tinier . while we can talk about the masses of atoms and particles in terms of everyday units such as grams and kilograms , it is much more convenient to use a very tiny unit of mass to discuss such very tiny things . that unit is known as $ \text { u } $ , which stands for unified atomic mass unit . by definition , $ 1\text { u } $ is equal to exactly $ \dfrac { 1 } { 12 } $ of the mass of a single neutral atom of carbon-12 . the number after the hyphen , 12 , is the sum of the protons and neutrons for that specific isotope of the element . the reason carbon-12 was chosen as the isotope to define the unit $ \text { u } $ is because it is the most common isotope of carbon . concept check : how many protons are in the nucleus of an atom of carbon-12 ? as we will now examine in more detail , the bulk of an atom 's mass is located in its nucleus . this is because protons and neutrons are much more massive than electrons . for example , a proton has a mass of $ 1.673\times10^ { -27 } \text { kg } $ , or $ 1.007\text { u } $ . a neutron is slightly heavier , with a mass of $ 1.675\times10^ { -27 } \text { kg } $ , or $ 1.009\text { u } $ . an electron , on the other hand , has a mass of only $ 9.109\times10^ { -31 } \text { kg } $ , or $ 5.486\times10^ { -4 } \text { u } $ . we can summarize this information in the following table : name | charge | symbol | mass $ ( \text { kg } ) $ | mass $ ( \text { u } ) $ | location : - : | : - : | : - : | : - : | : - : | : - : proton | $ 1 $ $ + $ | $ _1^1\text { p } ^+ $ | $ 1.673\times10^ { -27 } $ | $ 1 $ | inside nucleus neutron | $ 0 $ | $ ^1\text { n } $ | $ 1.675\times10^ { -27 } $ | $ 1 $ | inside nucleus electron | $ 1 $ $ - $ | $ \text { e } ^- $ | $ 9.109\times10^ { -31 } $ | $ 0 $ | outside nucleus there are a few things that we should conclude from this table . the first is that protons and neutrons have masses that are about 2,000 times greater than the mass of an electron . as such , electrons are considered to have a negligible effect upon the overall mass of an atom . this is a fancy way of saying that when we calculate the mass of atoms and molecules , we ignore the mass of electrons . this fact is illustrated further in the column listing the masses of these particles in $ \text { u } $ . the masses have been rounded to the nearest integer ; thus , protons and neutrons are considered to have identical masses of 1 $ \text { u } $ . while we know that neutrons are ever-so-slightly heavier than protons , this very small difference in mass is insignificant for many purposes , and we can simplify things greatly by assuming that protons and neutrons have equal mass . we should also note that electrons are considered to have a mass of ~ 0 $ \text { u } $ . again , this is not technically true . keep in mind , however , that the masses of the electrons are so small in comparison to the masses of the protons and neutrons in the nucleus that we can simply ignore the electrons ' masses altogether . mass number and isotope notation now that we have an understanding of the different masses and charges of protons , neutrons , and electrons , we can discuss the concept of mass number . by definition , the mass number is simply equal to the number of protons plus the number of neutrons in the nucleus . $ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows . we can rearrange the equation for mass number to solve for the number of neutrons : $ \begin { align } \text { # neutrons } & amp ; = \text { mass number } - ( \text { # protons } ) \ \ & amp ; =12-6 \ \ & amp ; =6\ , \text { neutrons in carbon- } 12 \end { align } $ therefore , we see that an atom of carbon-12 has 6 neutrons in the nucleus . let 's try another example . concept check : chromium-52 is the most stable isotope of chromium . how many neutrons are contained in a single atom of chromium-52 ? we have now seen that isotopes are defined by their mass number , which is equal to the sum of the number of protons and neutrons . to show this most simply , chemists commonly use the following notation to indicate atomic number , mass number , and charge—all in one symbol : in figure 2 , we have the isotopic notation for neutral hydrogen-3 and the magnesium-24 cation . in the center of each is the chemical symbol for each element . on the lower left is the atomic number , which corresponds to the number of protons in the atom 's nucleus . above the atomic number is the mass number , which is equal to the sum of the number of protons and the number of neutrons in the atom . to the upper right of the chemical symbol is the net charge on the species , if any . keep in mind that for neutral atoms , the net charge is zero , and nothing will be written in this space . atomic mass vs. mass number atomic mass is a concept that is very closely related to mass number . the atomic mass is the mass of a specific isotope of an element expressed in units of $ \ , \text { u } $ or $ \text { amu } $ . since the mass of a neutron and the mass of a proton are both very , very close to 1 $ \text { amu } $ , the atomic mass of an isotope is often very close to the mass number . however , they are different ! the mass number is an integer , since we always count whole numbers of protons and neutrons ( that is , you ca n't have 1.05 protons , or 0.27 neutrons ) . the mass number is also , usually , written as being unitless . in comparison , the atomic mass is only a whole number if you round to the nearest integer , and atomic mass has units of mass ( $ \text { u } $ ) . another term that students often might find confusingly similar to atomic mass and mass number is atomic weight , which is also a related but different term . do n't worry , though , we will discuss atomic weight in the following section ! relative abundance and atomic weight there are two stable isotopes of chlorine : chlorine-35 , and and chlorine-37 . and yet , if you look on the periodic table , you 'll find that the mass of an atom of chlorine is given as 35.45 $ \text { u } $ . where do the numbers after the decimal come from ? if you guessed that this number might be the mass of an average atom of chlorine , you would be correct . in fact , all of the masses that you see on the periodic table are averages that are based on the masses and abundances of all the stable isotopes of each element . these average masses are referred to as atomic weights . in comparison , atomic mass refers to the mass of a specific isotope . we use atomic masses to calculate the atomic weight of a given element . let 's now further consider the atomic weight of chlorine . as we said before , chlorine has two stable isotopes : chlorine-35 and chlorine-37 . the atomic weight of chlorine given on the periodic table is 35.45 $ \text { u } $ . this begs the question , why is n't the atomic weight of chlorine simply the average of 35 and 37 , which would be 36 $ \ , \text u $ ? the answer has to do with the fact that different isotopes have different relative abundances , meaning that some isotopes are more naturally abundant on earth than others . in the case of chlorine , chlorine-35 has a relative abundance of 75.76 % , whereas chlorine-37 has a relative abundance of 24.24 % . note that relative abundances are percentages , and thus the relative abundances of all the different stable isotopes of an element will add up to 100 % . the atomic weight that you find on the periodic table is actually a weighted average calculated from these values . to better illustrate this , let 's calculate the atomic weight of chlorine . example : calculating the atomic weight of chlorine when we want to calculate a weighted average , we multiply the value of every item in our set—in this case , the atomic mass of each isotope of chlorine—by its relative abundance expressed as a fraction , and then sum up all of our products . this can be written as follows : $ \text { atomic weight } =\sum\limits_ { i=1 } ^n ( \text { relative abundance } \times\text { atomic mass } ) _i $ if we apply this formula for chlorine , we get the following : $ \begin { align } \text { atomic weight of chlorine } & amp ; = ( 0.7576\times34.969\text { u } ) + ( 0.2424\times36.966\text { u } ) \ \ & amp ; = 26.49 \ , \text u+8.960\ , \text u \ \ & amp ; = 35.45\text { u } \end { align } $ we can see that because chlorine-35 is about 3 times more abundant than chlorine-37 , the weighted average is closer to 35 than to 37 . concept check : bromine has two stable isotopes—bromine-79 and bromine-81 . the relative abundance of each isotope is 50.70 % and 49.30 % , respectively . is the atomic weight of bromine closest to 79 , 80 , or 81 $ \text { u } $ ? mass spectrometry we now know how to find atomic weights by calculating weighted averages using relative abundances . but , where do these relative abundances come from ? for example , how do we know that 75.76 % of all chlorine on earth is chlorine-35 ? the answer is that these relative abundances can be determined experimentally using a technique called mass spectrometry . in a mass spectrometer , a sample containing the atoms or molecules of interest is injected into the instrument . the sample—typically in an aqueous or organic solution—is immediately vaporized by a heater , and the vaporized sample is then bombarded by high-energy electrons . these electrons are powerful enough to knock electrons off atoms in the sample , which creates cationic versions of the sample . these cations are then accelerated through electric plates and subsequently deflected by a magnetic field . once the ions reach the magnetic field , they are deflected different amounts depending on their speed and charge . ions that are moving more slowly , the heavier ions , are deflected less , and ions that are moving more quickly , the lighter ions , are deflected more . think of the force you need to apply to accelerate a bowling ball versus the force necessary to accelerate a tennis ball . it 's much easier to accelerate the tennis ball ! also , the higher the charge on the ion , the more it will be deflected . the amount that the ions are deflected is inversely proportional to their mass-to-charge ratio , $ \dfrac { m } { z } $ , where $ m $ is equal to the mass of the ion and $ z $ is equal to the charge . the detector records the $ \dfrac { m } { z } $ values for each ion , as well how many of each ion it sees . the relative abundance for a specific ion within the sample can be calculated by dividing by the number of ions of that type by the total number of ions detected . the instrument then generates a mass spectrum for the sample , which plots relative abundance against the mass-to-charge ratio , $ \dfrac { m } { z } $ . concept check : a sample of copper is injected into a mass spectrometer . after the sample is vaporized and ionized , the ions $ ^ { 63 } \text { cu } ^ { 2+ } $ and $ ^ { 65 } \text { cu } ^ { 2+ } $ are detected . which ion is deflected more inside the spectrometer ? analyzing the mass spectrum of zirconium let 's suppose we analyzed a sample of elemental zirconium , atomic number 40 , using mass spectrometry . after putting the sample through the instrument , we would get a mass spectrum that looks like figure 4 , where the height of a peak is roughly proportional to the relative abundance for a given value of $ \dfrac { m } { z } $ : concept check : based on this spectrum , what is the most common isotope of zirconium in our sample ? based on the relative height or intensity of the peaks at a given mass-to-charge ratio , we can find the relative abundances of the isotopes . the peaks are labeled in the simulated mass spectrum assuming a charge of $ +1 $ for the ions pictured , which allows us to calculate the atomic mass of each isotope . using this information , we can calculate the atomic weight of zirconium by finding a weighted average of the atomic masses for each isotope . to try this calculation yourself , see the practice problem below ! nowadays , we already know the atomic weights for all the most common elements , and so it is not often necessary to analyze individual elements using mass spectrometry—except to teach students ! most of the time , working chemists use mass spectrometry in the lab in order to help them determine the structure or identity of unknown molecules and compounds . in today 's world , mass spectrometry is an invaluable analytical tool , not only in chemistry , but also in medicine , forensics , environmental science , and other important fields . summary atoms that have the same number of protons and electrons but different numbers of neutrons are known as isotopes . isotopes of a given element have different atomic masses . the relative abundance of an isotope is the fraction of a single element that exists on earth with a specific atomic mass . atomic weights are weighted averages calculated by multiplying the relative abundance of each isotope by its atomic mass and then summing up all the products . the relative abundances of each isotope can be determined using mass spectrometry . a mass spectrometer ionizes atoms and molecules with a high-energy electron beam and then deflects the ions through a magnetic field based on the mass-to-charge ratio of the ion , $ \dfrac { m } { z } $ . the mass spectrum of a sample shows relative abundance of each ion on the y-axis and $ \dfrac { m } { z } $ along the x-axis . try it !
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$ \text { mass number } = ( \text { # protons } ) + ( \text { # neutrons } ) $ just as the atomic number defines an element , we can think of the mass number as defining the specific isotope of a particular element . in fact , a common way of specifying an isotope is to use the notation `` element name-mass number '' such as in carbon-12 , which is a carbon atom with a mass number of 12 . using that information , we can calculate the number of neutrons in an atom of carbon-12 as follows .
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what are two differences between carbon-12 and carbon-14 ?
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introduction so far , we ’ ve spent a lot of time describing the pathways used to break down glucose . when you sit down for lunch , you might have a turkey sandwich , a veggie burger , or a salad , but you ’ re probably not going to dig in to a bowl of pure glucose . how , then , are the other components of food – such as proteins , lipids , and non-glucose carbohydrates – broken down to generate atp ? as it turns out , the cellular respiration pathways we ’ ve already seen are central to the extraction of energy from all these different molecules . amino acids , lipids , and other carbohydrates can be converted to various intermediates of glycolysis and the citric acid cycle , allowing them to slip into the cellular respiration pathway through a multitude of side doors . once these molecules enter the pathway , it makes no difference where they came from : they ’ ll simply go through the remaining steps , yielding nadh , fadh $ _2 $ , and atp . in addition , not every molecule that enters cellular respiration will complete the entire pathway . just as various types of molecules can feed into cellular respiration through different intermediates , so intermediates of glycolysis and the citric acid cycle may be removed at various stages and used to make other molecules . for instance , many intermediates of glycolysis and the citric acid cycle are used in the pathways that build amino acids $ ^1 $ . in the sections below , we ’ ll look at a few examples of how different non-glucose molecules can enter cellular respiration . how carbohydrates enter the pathway most carbohydrates enter cellular respiration during glycolysis . in some cases , entering the pathway simply involves breaking a glucose polymer down into individual glucose molecules . for instance , the glucose polymer glycogen is made and stored in both liver and muscle cells in our bodies . if blood sugar levels drop , the glycogen will be broken down into phosphate-bearing glucose molecules , which can easily enter glycolysis . non-glucose monosaccharides can also enter glycolysis . for instance , sucrose ( table sugar ) is made up of glucose and fructose . when this sugar is broken down , the fructose can easily enter glycolysis : addition of a phosphate group turns it into fructose-6-phosphate , the third molecule in the glycolysis pathway $ ^2 $ . because it enters so close to the top of the pathway , fructose yields the same number of atp as glucose during cellular respiration . how proteins enter the pathway when you eat proteins in food , your body has to break them down into amino acids before they can be used by your cells . most of the time , amino acids are recycled and used to make new proteins , not oxidized for fuel . however , if there are more amino acids than the body needs , or if cells are starving , some amino acids will broken down for energy via cellular respiration . in order to enter cellular respiration , amino acids must first have their amino group removed . this step makes ammonia $ ( \text { nh } _3 ) $ as a waste product , and in humans and other mammals , the ammonia is converted to urea and removed from the body in urine . once they ’ ve been deaminated , different amino acids enter the cellular respiration pathways at different stages . the chemical properties of each amino acid determine what intermediate it can be most easily converted into . for example , the amino acid glutamate , which has a carboxylic acid side chain , gets converted into the citric acid cycle intermediate α-ketoglutarate . this point of entry for glutamate makes sense because both molecules have a similar structure with two carboxyl groups , as shown below $ ^3 $ . how lipids enter the pathway fats , known more formally as triglycerides , can be broken down into two components that enter the cellular respiration pathways at different stages . a triglyceride is made up of a three-carbon molecule called glycerol , and of three fatty acid tails attached to the glycerol . glycerol can be converted to glyceraldehyde-3-phosphate , an intermediate of glycolysis , and continue through the remainder of the cellular respiration breakdown pathway . fatty acids , on the other hand , must be broken down in a process called beta-oxidation , which takes place in the matrix of the mitochondria . in beta-oxidation , the fatty acid tails are broken down into a series of two-carbon units that combine with coenzyme a , forming acetyl coa . this acetyl coa feeds smoothly into the citric acid cycle . cellular respiration : it 's a two-way street we 've thought a lot about how molecules can enter cellular respiration , but it 's also important to consider how they can exit . molecules in the cellular respiration pathway can be pulled out at many stages and used to build other molecules , including amino acids , nucleotides , lipids , and carbohydrates . to give just one example , acetyl coa ( mentioned above ) that 's produced in cellular respiration can be diverted from the citric acid cycle and used to build the lipid cholesterol . cholesterol forms the backbone of the steroid hormones in our bodies , such as testosterone and estrogens . whether it 's better to `` burn '' molecules for fuel via cellular respiration or use them to build other molecules depends on the needs of the cell—and so does which specific molecules they 're used to build !
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because it enters so close to the top of the pathway , fructose yields the same number of atp as glucose during cellular respiration . how proteins enter the pathway when you eat proteins in food , your body has to break them down into amino acids before they can be used by your cells . most of the time , amino acids are recycled and used to make new proteins , not oxidized for fuel .
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how do lipids and proteins enter the pathway in plant cells ?
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introduction so far , we ’ ve spent a lot of time describing the pathways used to break down glucose . when you sit down for lunch , you might have a turkey sandwich , a veggie burger , or a salad , but you ’ re probably not going to dig in to a bowl of pure glucose . how , then , are the other components of food – such as proteins , lipids , and non-glucose carbohydrates – broken down to generate atp ? as it turns out , the cellular respiration pathways we ’ ve already seen are central to the extraction of energy from all these different molecules . amino acids , lipids , and other carbohydrates can be converted to various intermediates of glycolysis and the citric acid cycle , allowing them to slip into the cellular respiration pathway through a multitude of side doors . once these molecules enter the pathway , it makes no difference where they came from : they ’ ll simply go through the remaining steps , yielding nadh , fadh $ _2 $ , and atp . in addition , not every molecule that enters cellular respiration will complete the entire pathway . just as various types of molecules can feed into cellular respiration through different intermediates , so intermediates of glycolysis and the citric acid cycle may be removed at various stages and used to make other molecules . for instance , many intermediates of glycolysis and the citric acid cycle are used in the pathways that build amino acids $ ^1 $ . in the sections below , we ’ ll look at a few examples of how different non-glucose molecules can enter cellular respiration . how carbohydrates enter the pathway most carbohydrates enter cellular respiration during glycolysis . in some cases , entering the pathway simply involves breaking a glucose polymer down into individual glucose molecules . for instance , the glucose polymer glycogen is made and stored in both liver and muscle cells in our bodies . if blood sugar levels drop , the glycogen will be broken down into phosphate-bearing glucose molecules , which can easily enter glycolysis . non-glucose monosaccharides can also enter glycolysis . for instance , sucrose ( table sugar ) is made up of glucose and fructose . when this sugar is broken down , the fructose can easily enter glycolysis : addition of a phosphate group turns it into fructose-6-phosphate , the third molecule in the glycolysis pathway $ ^2 $ . because it enters so close to the top of the pathway , fructose yields the same number of atp as glucose during cellular respiration . how proteins enter the pathway when you eat proteins in food , your body has to break them down into amino acids before they can be used by your cells . most of the time , amino acids are recycled and used to make new proteins , not oxidized for fuel . however , if there are more amino acids than the body needs , or if cells are starving , some amino acids will broken down for energy via cellular respiration . in order to enter cellular respiration , amino acids must first have their amino group removed . this step makes ammonia $ ( \text { nh } _3 ) $ as a waste product , and in humans and other mammals , the ammonia is converted to urea and removed from the body in urine . once they ’ ve been deaminated , different amino acids enter the cellular respiration pathways at different stages . the chemical properties of each amino acid determine what intermediate it can be most easily converted into . for example , the amino acid glutamate , which has a carboxylic acid side chain , gets converted into the citric acid cycle intermediate α-ketoglutarate . this point of entry for glutamate makes sense because both molecules have a similar structure with two carboxyl groups , as shown below $ ^3 $ . how lipids enter the pathway fats , known more formally as triglycerides , can be broken down into two components that enter the cellular respiration pathways at different stages . a triglyceride is made up of a three-carbon molecule called glycerol , and of three fatty acid tails attached to the glycerol . glycerol can be converted to glyceraldehyde-3-phosphate , an intermediate of glycolysis , and continue through the remainder of the cellular respiration breakdown pathway . fatty acids , on the other hand , must be broken down in a process called beta-oxidation , which takes place in the matrix of the mitochondria . in beta-oxidation , the fatty acid tails are broken down into a series of two-carbon units that combine with coenzyme a , forming acetyl coa . this acetyl coa feeds smoothly into the citric acid cycle . cellular respiration : it 's a two-way street we 've thought a lot about how molecules can enter cellular respiration , but it 's also important to consider how they can exit . molecules in the cellular respiration pathway can be pulled out at many stages and used to build other molecules , including amino acids , nucleotides , lipids , and carbohydrates . to give just one example , acetyl coa ( mentioned above ) that 's produced in cellular respiration can be diverted from the citric acid cycle and used to build the lipid cholesterol . cholesterol forms the backbone of the steroid hormones in our bodies , such as testosterone and estrogens . whether it 's better to `` burn '' molecules for fuel via cellular respiration or use them to build other molecules depends on the needs of the cell—and so does which specific molecules they 're used to build !
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because it enters so close to the top of the pathway , fructose yields the same number of atp as glucose during cellular respiration . how proteins enter the pathway when you eat proteins in food , your body has to break them down into amino acids before they can be used by your cells . most of the time , amino acids are recycled and used to make new proteins , not oxidized for fuel .
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is there a difference in pathway between normal cells and cancerous cells ?
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