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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged .
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why do n't the electrons in the atoms like that of calcium , sodium and others , emit some photons of energy and jump into the first shell ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged .
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any shell , including the first shell , is large enough , in terms of space , to accommodate the small volumes of a large number of electrons , is n't it ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells .
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so why do the shells have a maximum of 2n^2 electrons ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value .
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the lowest energy of electron in the ground state of an hydrogen atom is -13.6ev , what is ev here ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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\ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms .
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how did bohr explain the stability of an electron ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level .
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it says that an electron having energy will be more stable than an electron having no energy ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged .
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when an electron drops from a higher shell to a lower shell , is exactly 1 photon emitted ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms .
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what happens to the hydrogen atom once its electron has been ionized ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano .
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what is the significance of photoelectric effect ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value .
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why none of the spectral lines are created from moving an electron from n > 1 to n=1 ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure .
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is this same as how electromagnetic wave emitter works by oscillating the electron ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level .
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if an electron has infinite energy , why ca n't it stay in any orbit and even if it loses energy can still have infite energy right ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level .
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what if the an electron in the first shell lose energy ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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\ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ .
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what is the effect of hydrogen isotops on its spectrum ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition .
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is the transmission of energy same when an electron move to a higher level and back to the same level ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu .
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what is the difference between the energy absorbed and the energy emitted in these two actions ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus .
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what is heisenberg uncertainty principle , what does it state ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ?
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why dont electrons fall into the nucleus when shifting energy levels ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ?
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was the hydrogen atom used to determine how many energy levels were present in any given atom ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus .
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what does principle quatum number mean ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ?
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in 'the beginning ' which came first electrons or photons ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ?
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under the subtitle `` bohr 's model of the hydrogen atom : quantization of electronic structure '' in the 2nd paragraph , i still do not understand why the energy is always going to be a negative number -i do n't have facebook , can you answer this question ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition .
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is n for energy level same as the nth orbit ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen .
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if the new state is less stable and wo n't stay for long , why does it even make the transition in the first place ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra .
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can those equations be explained in a simpler way if possible ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ .
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what is the value of rydberg constant ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius .
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how many colours does the atom emits ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels .
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how is the emission spectrum of the sun found ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level .
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if we take a sample of sodium and heat on bunsen burner then will its electrons absorb energy in values of photons ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ .
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what is the difference between orbital/ subshell and ground state/ excited state ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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\ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ .
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how does bohr theory explain there are only 4 visible emission lines for hydrogen ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen .
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would dropping from the farther orbitals emit less energy than dropping nearer to the nucleus ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra .
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why ca n't you explain the exact location of an electron in an atom ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ?
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what is bhor 's model of atom ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ?
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in my equation for lab , i have 1.912s = ( 3.288 x 10^-15 ) ( 1/4 - 1/n2^2 ) ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano .
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how did bohr explain atomic structure with respect to planck 's quantum theory and einstein 's photoelectric effect ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ?
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how does an electron not follow classical physics but follow quantum physics ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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\ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ .
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when did bohr found the theory ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value .
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what are the 10 lowest energy states of hydrogen ( n=10 to n=1 ) ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu .
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when solving for the frequency of the photon emitted from the hydrogen , why is n't it nhv = change in energy instead of hv = change of energy ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ .
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how does being stable provide a lesser ( more negative ) magnitude of energy ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ?
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why is the wavelength released larger for the drop from 3 to 2 compared with a drop from something like 5 to 2 or 4 to 2 ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements .
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what is a quantum mechanic ?
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron . the planetary model of the atom at the beginning of the 20th century , a new field of study known as quantum mechanics emerged . one of the founders of this field was danish physicist niels bohr , who was interested in explaining the discrete line spectrum observed when light was emitted by different elements . bohr was also interested in the structure of the atom , which was a topic of much debate at the time . numerous models of the atom had been postulated based on experimental results including the discovery of the electron by j. j. thomson and the discovery of the nucleus by ernest rutherford . bohr supported the planetary model , in which electrons revolved around a positively charged nucleus like the rings around saturn—or alternatively , the planets around the sun . however , scientists still had many unanswered questions : $ $ where are the electrons , and what are they doing ? if the electrons are orbiting the nucleus , why don ’ t they fall into the nucleus as predicted by classical physics ? how is the internal structure of the atom related to the discrete emission lines produced by excited elements ? bohr addressed these questions using a seemingly simple assumption : what if some aspects of atomic structure , such as electron orbits and energies , could only take on certain values ? quantization and photons by the early 1900s , scientists were aware that some phenomena occurred in a discrete , as opposed to continuous , manner . physicists max planck and albert einstein had recently theorized that electromagnetic radiation not only behaves like a wave , but also sometimes like particles called photons . planck studied the electromagnetic radiation emitted by heated objects , and he proposed that the emitted electromagnetic radiation was `` quantized '' since the energy of light could only have values given by the following equation : $ e_ { \text { photon } } =nh\nu $ , where $ n $ is a positive integer , $ h $ is planck ’ s constant— $ 6.626 \times10^ { -34 } \ , \text { j } \cdot \text s $ —and $ \nu $ is the frequency of the light , which has units of $ \dfrac { 1 } { \text s } $ . as a consequence , the emitted electromagnetic radiation must have energies that are multiples of $ h\nu $ . einstein used planck 's results to explain why a minimum frequency of light was required to eject electrons from a metal surface in the photoelectric effect . when something is quantized , it means that only specific values are allowed , such as when playing a piano . since each key of a piano is tuned to a specific note , only a certain set of notes—which correspond to frequencies of sound waves—can be produced . as long as your piano is properly tuned , you can play an f or f sharp , but you ca n't play the note that is halfway between an f and f sharp . atomic line spectra atomic line spectra are another example of quantization . when an element or ion is heated by a flame or excited by electric current , the excited atoms emit light of a characteristic color . the emitted light can be refracted by a prism , producing spectra with a distinctive striped appearance due to the emission of certain wavelengths of light . for the relatively simple case of the hydrogen atom , the wavelengths of some emission lines could even be fitted to mathematical equations . the equations did not explain why the hydrogen atom emitted those particular wavelengths of light , however . prior to bohr 's model of the hydrogen atom , scientists were unclear of the reason behind the quantization of atomic emission spectra . bohr 's model of the hydrogen atom : quantization of electronic structure bohr ’ s model of the hydrogen atom started from the planetary model , but he added one assumption regarding the electrons . what if the electronic structure of the atom was quantized ? bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius . only shells with a radius given by the equation below would be allowed , and the electron could not exist in between these shells . mathematically , we could write the allowed values of the atomic radius as $ r ( n ) =n^2\cdot r ( 1 ) $ , where $ n $ is a positive integer , and $ r ( 1 ) $ is the bohr radius , the smallest allowed radius for hydrogen . he found that $ r ( 1 ) $ has the value $ \text { bohr radius } =r ( 1 ) =0.529 \times 10^ { -10 } \ , \text { m } $ by keeping the electrons in circular , quantized orbits around the positively-charged nucleus , bohr was able to calculate the energy of an electron in the $ n $ th energy level of hydrogen : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ , where the lowest possible energy or ground state energy of a hydrogen electron— $ e ( 1 ) $ —is $ -13.6\ , \text { ev } $ . note that the energy is always going to be a negative number , and the ground state , $ n=1 $ , has the most negative value . this is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus , $ n=\infty $ , which is defined to have an energy of $ 0\ , \text { ev } $ . since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus , the energy of an electron in orbit is always negative . absorption and emission bohr could now precisely describe the processes of absorption and emission in terms of electronic structure . according to bohr 's model , an electron would absorb energy in the form of photons to get excited to a higher energy level as long as the photon 's energy was equal to the energy difference between the initial and final energy levels . after jumping to the higher energy level—also called the excited state—the excited electron would be in a less stable position , so it would quickly emit a photon to relax back to a lower , more stable energy level . the energy levels and transitions between them can be illustrated using an energy level diagram , such as the example above showing electrons relaxing back to the $ n=2 $ level of hydrogen . the energy of the emitted photon is equal to the difference in energy between the two energy levels for a particular transition . the energy difference between energy levels $ n_ { high } $ and $ n_ { low } $ can be calculated using the equation for $ e ( n ) $ from the previous section : $ \begin { align } \delta e & amp ; = e ( n_ { high } ) -e ( n_ { low } ) \ \ & amp ; =\left ( -\dfrac { 1 } { { n_ { high } } ^2 } \cdot 13.6\ , \text { ev } \right ) -\left ( -\dfrac { 1 } { { n_ { low } } ^2 } \cdot 13.6\ , \text { ev } \right ) \ \ & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } \end { align } $ since we also know the relationship between the energy of a photon and its frequency from planck 's equation , we can solve for the frequency of the emitted photon : $ \begin { align } h\nu & amp ; =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } ~~~~~~~~~~~~\text { set photon energy equal to energy difference } \ \ \nu & amp ; = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~~~~~~~~~\text { solve for frequency } \end { align } $ we can also find the equation for the wavelenth of the emitted electromagnetic radiation using the relationship between the speed of light $ \text c $ , frequency $ \nu $ , and wavelength $ \lambda $ : $ \begin { align } \text c & amp ; =\lambda \nu ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { rearrange to solve for } \nu . \ \dfrac { \text c } { \lambda } & amp ; =\nu=\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h } ~~~~~~~~~~~~~~\text { divide both sides by c to solve for } \dfrac { 1 } { \lambda } .\ \ \dfrac { 1 } { \lambda } & amp ; =\left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot \dfrac { 13.6\ , \text { ev } } { h\text c } \end { align } $ thus , we can see that the frequency—and wavelength—of the emitted photon depends on the energies of the initial and final shells of an electron in hydrogen . what have we learned since bohr proposed his model of hydrogen ? the bohr model worked beautifully for explaining the hydrogen atom and other single electron systems such as $ \text { he } ^+ $ . unfortunately , it did not do as well when applied to the spectra of more complex atoms . furthermore , the bohr model had no way of explaining why some lines are more intense than others or why some spectral lines split into multiple lines in the presence of a magnetic field—the zeeman effect . in the following decades , work by scientists such as erwin schrödinger showed that electrons can be thought of as behaving like waves and behaving as particles . this means that it is not possible to know both a given electron ’ s position in space and its velocity at the same time , a concept that is more precisely stated in heisenberg 's uncertainty principle . the uncertainty principle contradicts bohr ’ s idea of electrons existing in specific orbits with a known velocity and radius . instead , we can only calculate probabilities of finding electrons in a particular region of space around the nucleus . the modern quantum mechanical model may sound like a huge leap from the bohr model , but the key idea is the same : classical physics is not sufficient to explain all phenomena on an atomic level . bohr was the first to recognize this by incorporating the idea of quantization into the electronic structure of the hydrogen atom , and he was able to thereby explain the emission spectra of hydrogen as well as other one-electron systems .
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key points bohr 's model of hydrogen is based on the nonclassical assumption that electrons travel in specific shells , or orbits , around the nucleus . bohr 's model calculated the following energies for an electron in the shell , $ n $ : $ e ( n ) =-\dfrac { 1 } { n^2 } \cdot 13.6\ , \text { ev } $ bohr explained the hydrogen spectrum in terms of electrons absorbing and emitting photons to change energy levels , where the photon energy is $ h\nu =\delta e = \left ( \dfrac { 1 } { { n_ { low } } ^2 } -\dfrac { 1 } { { n_ { high } } ^2 } \right ) \cdot 13.6\ , \text { ev } $ bohr 's model does not work for systems with more than one electron .
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why `` non classical '' assumption ?
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a luncheon with fur the story behind the creation of object , an ordinary cup , spoon , and saucer wrapped evocatively in gazelle fur , has been told so many times its importance in modernist history transcends the fact it might be apocryphal ( of dubious authenticity ) . the twenty-two year old basel-born artist , meret oppenheim , had been in paris for four years when , one day , she was at a café with pablo picasso and dora maar . oppenheim was wearing a brass bracelet covered in fur when picasso and maar , who were admiring it , proclaimed , “ almost anything can be covered in fur ! ” as oppenheim ’ s tea grew cold , she jokingly asked the waiter for “ more fur. ” inspiration struck—oppenheim is said to have gone straight from the café to a store where she purchased the cup , saucer , and spoon used in this piece . this amusing story belies the importance of object and the critical acclaim and public fascination that has elevated it to point where it has become the definitive surrealist object ... ultimately to oppenheim ’ s dismay . what is a surrealist object ? oppenheim ’ s object was created at a moment when sculpted objects and assemblages had become prominent features of surrealist art practice . in 1937 , british art critic herbert read emphasized that all surrealist objects were representative of an idea and salvador dalí described some of them as “ objects with symbolic function. ” in other words , how might an otherwise typical , functional object be modified so it represents something deeply personal and poetic ? how might it , in freudian terms , resonate as a sublimation of internal desire and aspiration ? such physical manifestations of our internal psyches were indicative of a surreality , or the point in which external and internal realities united , as described by andré breton ( one of surrealism ’ s founders and theorists ) in his first manifesto of surrealism . visceral responses what , then , do we make of this set of be-furred tableware ? interpretations vary wildly . the art historian whitney chadwick has described it as linked to the surrealist ’ s love of alchemical transformation by turning cool , smooth ceramic and metal into something warm and bristley , while many scholars have noted the fetishistic qualities of the fur-lined set—as the fur imbues these functional , hand-held objects with sexual connotations . in a 1936 issue of the new yorker magazine , it was reported that a woman fainted “ right in front of the fur-bearing cup and saucer [ while it was on exhibit at moma ] . “ she left no name with the attendants who revived her - only a vague feeling of apprehension. ” * such visceral reactions to oppenheim ’ s sculpture come closest , perhaps , to what were likely the artist ’ s aspirations . in an interview later in life , oppenheim described her creations as “ not an illustration of an idea , but the thing itself. ” unlike read and dalí , oppenheim stresses the physicality of object , reinforcing the way we can readily imagine the feeling of the fur while drinking from the cup , and using the saucer and spoon . the frisson we experience when china is unexpectedly wrapped in fur is based on our familiarity with both , and the fur requires us to extend our sensory experiences to fully appreciate the work . object insists we imagine what sipping warm tea from this cup feels like , how the bristles would feel upon our lips . with oppenheim ’ s elegant creation , how we understand those visceral memories , how we create metaphors and symbols out of this act of tactile extension , is entirely open to interpretation by each individual , which is , in many ways , the whole point of surrealism itself . presentation problems in spite of our individual response , the interpretation of object has been complicated by the ways it was assigned meaning by others . when object was finished , oppenheim submitted it to breton for an exhibition of surrealist objects at the charles ratton gallery in paris in 1936 . however , while oppenheim preferred a non-descriptive title , breton took the liberty of titling the piece le déjeneur en fourrure , or luncheon in fur . this title is a play on two nineteenth-century works : édouard manet ’ s infamous modernist painting luncheon on the grass ( le déjeneur sur l ’ herbe ) and leopold von sacher-masoch ’ s erotic novel venus in furs . with these two references , breton forces an explicit sexualized meaning onto object . recall that the original inspiration for this work was implicitly practical : when oppenheim asked the waiter for more fur for her cooling teacup , it was suggested as a way to keep her tea warm , and not necessarily as overtly sexual . the meaning of others certainly we can not assume that the spark of the idea for this piece and the piece itself are necessarily related , but the way meanings have been ascribed to oppenheim ’ s pieces by others has plagued many of her works . art historian edward powers has noted that when oppenheim sent her surrealist object das paar to a photographer before submitting it for exhibition , the photographer took the liberty of tying up the laces before photographing it . when breton saw the photo with tied laces , he dubbed this object à délacer which in french means to untie , typically either shoes or a corset . the title and laced shoes together suggest the potential act of undressing and a fascination with exposing the female body . however , when oppenheim later described das paar ( with the laces untied ) , she stated it was an “ odd unisexual pair : two shoes , unobserved at night , doing ‘ forbidden ’ things. ” she expressly assigned no gender , and suggests the “ forbidden ” acts already taking place between anthropomorphized shoes . she takes a more literal approach , the shoes as expressive things in themselves , rather than symbolically resonant of something else . this is not to suggest that all her interactions with breton were negative . when she happened across a wonderfully disturbing photograph of a bicycle seat covered in bees , she mailed it to breton , who republished the found photograph as an artistic contribution by oppenheim in the third issue of the new surrealist publication medium . dangerous success yet , the early acclaim for the fur-covered object had a negative effect on oppenheim ’ s early career . when it was purchased by the museum of modern art and featured in their influential 1936-37 exhibition `` fantastic art , dada , and surrealism '' visitors declared it the “ quintessential ” surrealist object . and that is how it has been seen ever since . but for oppenheim , the prestige and focus on this one object proved too much , and she spent more than a decade out of the artistic limelight , destroying much of the work she produced during that period . it was only later when she re-emerged , and began publicly showing new paintings and objects with renewed vigor and confidence , that she began reclaiming some of the intent of her work . when she was given an award for her work by the city of basel , she touched upon this in her acceptance speech : “ i think it is the duty of a woman to lead a life that expresses her disbelief in the validity of the taboos that have been imposed upon her kind for thousands of years . nobody will give you freedom ; you have to take it. ” *nelson landsdale and st. clair mckelway , talk of the town , “ critical note , ” the new yorker , december 26 , 1936 , p. 7 . essay by josh rose
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this amusing story belies the importance of object and the critical acclaim and public fascination that has elevated it to point where it has become the definitive surrealist object ... ultimately to oppenheim ’ s dismay . what is a surrealist object ? oppenheim ’ s object was created at a moment when sculpted objects and assemblages had become prominent features of surrealist art practice .
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how would this 'object ' have been made ?
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a luncheon with fur the story behind the creation of object , an ordinary cup , spoon , and saucer wrapped evocatively in gazelle fur , has been told so many times its importance in modernist history transcends the fact it might be apocryphal ( of dubious authenticity ) . the twenty-two year old basel-born artist , meret oppenheim , had been in paris for four years when , one day , she was at a café with pablo picasso and dora maar . oppenheim was wearing a brass bracelet covered in fur when picasso and maar , who were admiring it , proclaimed , “ almost anything can be covered in fur ! ” as oppenheim ’ s tea grew cold , she jokingly asked the waiter for “ more fur. ” inspiration struck—oppenheim is said to have gone straight from the café to a store where she purchased the cup , saucer , and spoon used in this piece . this amusing story belies the importance of object and the critical acclaim and public fascination that has elevated it to point where it has become the definitive surrealist object ... ultimately to oppenheim ’ s dismay . what is a surrealist object ? oppenheim ’ s object was created at a moment when sculpted objects and assemblages had become prominent features of surrealist art practice . in 1937 , british art critic herbert read emphasized that all surrealist objects were representative of an idea and salvador dalí described some of them as “ objects with symbolic function. ” in other words , how might an otherwise typical , functional object be modified so it represents something deeply personal and poetic ? how might it , in freudian terms , resonate as a sublimation of internal desire and aspiration ? such physical manifestations of our internal psyches were indicative of a surreality , or the point in which external and internal realities united , as described by andré breton ( one of surrealism ’ s founders and theorists ) in his first manifesto of surrealism . visceral responses what , then , do we make of this set of be-furred tableware ? interpretations vary wildly . the art historian whitney chadwick has described it as linked to the surrealist ’ s love of alchemical transformation by turning cool , smooth ceramic and metal into something warm and bristley , while many scholars have noted the fetishistic qualities of the fur-lined set—as the fur imbues these functional , hand-held objects with sexual connotations . in a 1936 issue of the new yorker magazine , it was reported that a woman fainted “ right in front of the fur-bearing cup and saucer [ while it was on exhibit at moma ] . “ she left no name with the attendants who revived her - only a vague feeling of apprehension. ” * such visceral reactions to oppenheim ’ s sculpture come closest , perhaps , to what were likely the artist ’ s aspirations . in an interview later in life , oppenheim described her creations as “ not an illustration of an idea , but the thing itself. ” unlike read and dalí , oppenheim stresses the physicality of object , reinforcing the way we can readily imagine the feeling of the fur while drinking from the cup , and using the saucer and spoon . the frisson we experience when china is unexpectedly wrapped in fur is based on our familiarity with both , and the fur requires us to extend our sensory experiences to fully appreciate the work . object insists we imagine what sipping warm tea from this cup feels like , how the bristles would feel upon our lips . with oppenheim ’ s elegant creation , how we understand those visceral memories , how we create metaphors and symbols out of this act of tactile extension , is entirely open to interpretation by each individual , which is , in many ways , the whole point of surrealism itself . presentation problems in spite of our individual response , the interpretation of object has been complicated by the ways it was assigned meaning by others . when object was finished , oppenheim submitted it to breton for an exhibition of surrealist objects at the charles ratton gallery in paris in 1936 . however , while oppenheim preferred a non-descriptive title , breton took the liberty of titling the piece le déjeneur en fourrure , or luncheon in fur . this title is a play on two nineteenth-century works : édouard manet ’ s infamous modernist painting luncheon on the grass ( le déjeneur sur l ’ herbe ) and leopold von sacher-masoch ’ s erotic novel venus in furs . with these two references , breton forces an explicit sexualized meaning onto object . recall that the original inspiration for this work was implicitly practical : when oppenheim asked the waiter for more fur for her cooling teacup , it was suggested as a way to keep her tea warm , and not necessarily as overtly sexual . the meaning of others certainly we can not assume that the spark of the idea for this piece and the piece itself are necessarily related , but the way meanings have been ascribed to oppenheim ’ s pieces by others has plagued many of her works . art historian edward powers has noted that when oppenheim sent her surrealist object das paar to a photographer before submitting it for exhibition , the photographer took the liberty of tying up the laces before photographing it . when breton saw the photo with tied laces , he dubbed this object à délacer which in french means to untie , typically either shoes or a corset . the title and laced shoes together suggest the potential act of undressing and a fascination with exposing the female body . however , when oppenheim later described das paar ( with the laces untied ) , she stated it was an “ odd unisexual pair : two shoes , unobserved at night , doing ‘ forbidden ’ things. ” she expressly assigned no gender , and suggests the “ forbidden ” acts already taking place between anthropomorphized shoes . she takes a more literal approach , the shoes as expressive things in themselves , rather than symbolically resonant of something else . this is not to suggest that all her interactions with breton were negative . when she happened across a wonderfully disturbing photograph of a bicycle seat covered in bees , she mailed it to breton , who republished the found photograph as an artistic contribution by oppenheim in the third issue of the new surrealist publication medium . dangerous success yet , the early acclaim for the fur-covered object had a negative effect on oppenheim ’ s early career . when it was purchased by the museum of modern art and featured in their influential 1936-37 exhibition `` fantastic art , dada , and surrealism '' visitors declared it the “ quintessential ” surrealist object . and that is how it has been seen ever since . but for oppenheim , the prestige and focus on this one object proved too much , and she spent more than a decade out of the artistic limelight , destroying much of the work she produced during that period . it was only later when she re-emerged , and began publicly showing new paintings and objects with renewed vigor and confidence , that she began reclaiming some of the intent of her work . when she was given an award for her work by the city of basel , she touched upon this in her acceptance speech : “ i think it is the duty of a woman to lead a life that expresses her disbelief in the validity of the taboos that have been imposed upon her kind for thousands of years . nobody will give you freedom ; you have to take it. ” *nelson landsdale and st. clair mckelway , talk of the town , “ critical note , ” the new yorker , december 26 , 1936 , p. 7 . essay by josh rose
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a luncheon with fur the story behind the creation of object , an ordinary cup , spoon , and saucer wrapped evocatively in gazelle fur , has been told so many times its importance in modernist history transcends the fact it might be apocryphal ( of dubious authenticity ) . the twenty-two year old basel-born artist , meret oppenheim , had been in paris for four years when , one day , she was at a café with pablo picasso and dora maar .
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would the fur have been simply glued to the surface of the spoon and the ceramics ?
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a luncheon with fur the story behind the creation of object , an ordinary cup , spoon , and saucer wrapped evocatively in gazelle fur , has been told so many times its importance in modernist history transcends the fact it might be apocryphal ( of dubious authenticity ) . the twenty-two year old basel-born artist , meret oppenheim , had been in paris for four years when , one day , she was at a café with pablo picasso and dora maar . oppenheim was wearing a brass bracelet covered in fur when picasso and maar , who were admiring it , proclaimed , “ almost anything can be covered in fur ! ” as oppenheim ’ s tea grew cold , she jokingly asked the waiter for “ more fur. ” inspiration struck—oppenheim is said to have gone straight from the café to a store where she purchased the cup , saucer , and spoon used in this piece . this amusing story belies the importance of object and the critical acclaim and public fascination that has elevated it to point where it has become the definitive surrealist object ... ultimately to oppenheim ’ s dismay . what is a surrealist object ? oppenheim ’ s object was created at a moment when sculpted objects and assemblages had become prominent features of surrealist art practice . in 1937 , british art critic herbert read emphasized that all surrealist objects were representative of an idea and salvador dalí described some of them as “ objects with symbolic function. ” in other words , how might an otherwise typical , functional object be modified so it represents something deeply personal and poetic ? how might it , in freudian terms , resonate as a sublimation of internal desire and aspiration ? such physical manifestations of our internal psyches were indicative of a surreality , or the point in which external and internal realities united , as described by andré breton ( one of surrealism ’ s founders and theorists ) in his first manifesto of surrealism . visceral responses what , then , do we make of this set of be-furred tableware ? interpretations vary wildly . the art historian whitney chadwick has described it as linked to the surrealist ’ s love of alchemical transformation by turning cool , smooth ceramic and metal into something warm and bristley , while many scholars have noted the fetishistic qualities of the fur-lined set—as the fur imbues these functional , hand-held objects with sexual connotations . in a 1936 issue of the new yorker magazine , it was reported that a woman fainted “ right in front of the fur-bearing cup and saucer [ while it was on exhibit at moma ] . “ she left no name with the attendants who revived her - only a vague feeling of apprehension. ” * such visceral reactions to oppenheim ’ s sculpture come closest , perhaps , to what were likely the artist ’ s aspirations . in an interview later in life , oppenheim described her creations as “ not an illustration of an idea , but the thing itself. ” unlike read and dalí , oppenheim stresses the physicality of object , reinforcing the way we can readily imagine the feeling of the fur while drinking from the cup , and using the saucer and spoon . the frisson we experience when china is unexpectedly wrapped in fur is based on our familiarity with both , and the fur requires us to extend our sensory experiences to fully appreciate the work . object insists we imagine what sipping warm tea from this cup feels like , how the bristles would feel upon our lips . with oppenheim ’ s elegant creation , how we understand those visceral memories , how we create metaphors and symbols out of this act of tactile extension , is entirely open to interpretation by each individual , which is , in many ways , the whole point of surrealism itself . presentation problems in spite of our individual response , the interpretation of object has been complicated by the ways it was assigned meaning by others . when object was finished , oppenheim submitted it to breton for an exhibition of surrealist objects at the charles ratton gallery in paris in 1936 . however , while oppenheim preferred a non-descriptive title , breton took the liberty of titling the piece le déjeneur en fourrure , or luncheon in fur . this title is a play on two nineteenth-century works : édouard manet ’ s infamous modernist painting luncheon on the grass ( le déjeneur sur l ’ herbe ) and leopold von sacher-masoch ’ s erotic novel venus in furs . with these two references , breton forces an explicit sexualized meaning onto object . recall that the original inspiration for this work was implicitly practical : when oppenheim asked the waiter for more fur for her cooling teacup , it was suggested as a way to keep her tea warm , and not necessarily as overtly sexual . the meaning of others certainly we can not assume that the spark of the idea for this piece and the piece itself are necessarily related , but the way meanings have been ascribed to oppenheim ’ s pieces by others has plagued many of her works . art historian edward powers has noted that when oppenheim sent her surrealist object das paar to a photographer before submitting it for exhibition , the photographer took the liberty of tying up the laces before photographing it . when breton saw the photo with tied laces , he dubbed this object à délacer which in french means to untie , typically either shoes or a corset . the title and laced shoes together suggest the potential act of undressing and a fascination with exposing the female body . however , when oppenheim later described das paar ( with the laces untied ) , she stated it was an “ odd unisexual pair : two shoes , unobserved at night , doing ‘ forbidden ’ things. ” she expressly assigned no gender , and suggests the “ forbidden ” acts already taking place between anthropomorphized shoes . she takes a more literal approach , the shoes as expressive things in themselves , rather than symbolically resonant of something else . this is not to suggest that all her interactions with breton were negative . when she happened across a wonderfully disturbing photograph of a bicycle seat covered in bees , she mailed it to breton , who republished the found photograph as an artistic contribution by oppenheim in the third issue of the new surrealist publication medium . dangerous success yet , the early acclaim for the fur-covered object had a negative effect on oppenheim ’ s early career . when it was purchased by the museum of modern art and featured in their influential 1936-37 exhibition `` fantastic art , dada , and surrealism '' visitors declared it the “ quintessential ” surrealist object . and that is how it has been seen ever since . but for oppenheim , the prestige and focus on this one object proved too much , and she spent more than a decade out of the artistic limelight , destroying much of the work she produced during that period . it was only later when she re-emerged , and began publicly showing new paintings and objects with renewed vigor and confidence , that she began reclaiming some of the intent of her work . when she was given an award for her work by the city of basel , she touched upon this in her acceptance speech : “ i think it is the duty of a woman to lead a life that expresses her disbelief in the validity of the taboos that have been imposed upon her kind for thousands of years . nobody will give you freedom ; you have to take it. ” *nelson landsdale and st. clair mckelway , talk of the town , “ critical note , ” the new yorker , december 26 , 1936 , p. 7 . essay by josh rose
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the frisson we experience when china is unexpectedly wrapped in fur is based on our familiarity with both , and the fur requires us to extend our sensory experiences to fully appreciate the work . object insists we imagine what sipping warm tea from this cup feels like , how the bristles would feel upon our lips . with oppenheim ’ s elegant creation , how we understand those visceral memories , how we create metaphors and symbols out of this act of tactile extension , is entirely open to interpretation by each individual , which is , in many ways , the whole point of surrealism itself .
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why would your kitchen utensils need fursuits ?
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a luncheon with fur the story behind the creation of object , an ordinary cup , spoon , and saucer wrapped evocatively in gazelle fur , has been told so many times its importance in modernist history transcends the fact it might be apocryphal ( of dubious authenticity ) . the twenty-two year old basel-born artist , meret oppenheim , had been in paris for four years when , one day , she was at a café with pablo picasso and dora maar . oppenheim was wearing a brass bracelet covered in fur when picasso and maar , who were admiring it , proclaimed , “ almost anything can be covered in fur ! ” as oppenheim ’ s tea grew cold , she jokingly asked the waiter for “ more fur. ” inspiration struck—oppenheim is said to have gone straight from the café to a store where she purchased the cup , saucer , and spoon used in this piece . this amusing story belies the importance of object and the critical acclaim and public fascination that has elevated it to point where it has become the definitive surrealist object ... ultimately to oppenheim ’ s dismay . what is a surrealist object ? oppenheim ’ s object was created at a moment when sculpted objects and assemblages had become prominent features of surrealist art practice . in 1937 , british art critic herbert read emphasized that all surrealist objects were representative of an idea and salvador dalí described some of them as “ objects with symbolic function. ” in other words , how might an otherwise typical , functional object be modified so it represents something deeply personal and poetic ? how might it , in freudian terms , resonate as a sublimation of internal desire and aspiration ? such physical manifestations of our internal psyches were indicative of a surreality , or the point in which external and internal realities united , as described by andré breton ( one of surrealism ’ s founders and theorists ) in his first manifesto of surrealism . visceral responses what , then , do we make of this set of be-furred tableware ? interpretations vary wildly . the art historian whitney chadwick has described it as linked to the surrealist ’ s love of alchemical transformation by turning cool , smooth ceramic and metal into something warm and bristley , while many scholars have noted the fetishistic qualities of the fur-lined set—as the fur imbues these functional , hand-held objects with sexual connotations . in a 1936 issue of the new yorker magazine , it was reported that a woman fainted “ right in front of the fur-bearing cup and saucer [ while it was on exhibit at moma ] . “ she left no name with the attendants who revived her - only a vague feeling of apprehension. ” * such visceral reactions to oppenheim ’ s sculpture come closest , perhaps , to what were likely the artist ’ s aspirations . in an interview later in life , oppenheim described her creations as “ not an illustration of an idea , but the thing itself. ” unlike read and dalí , oppenheim stresses the physicality of object , reinforcing the way we can readily imagine the feeling of the fur while drinking from the cup , and using the saucer and spoon . the frisson we experience when china is unexpectedly wrapped in fur is based on our familiarity with both , and the fur requires us to extend our sensory experiences to fully appreciate the work . object insists we imagine what sipping warm tea from this cup feels like , how the bristles would feel upon our lips . with oppenheim ’ s elegant creation , how we understand those visceral memories , how we create metaphors and symbols out of this act of tactile extension , is entirely open to interpretation by each individual , which is , in many ways , the whole point of surrealism itself . presentation problems in spite of our individual response , the interpretation of object has been complicated by the ways it was assigned meaning by others . when object was finished , oppenheim submitted it to breton for an exhibition of surrealist objects at the charles ratton gallery in paris in 1936 . however , while oppenheim preferred a non-descriptive title , breton took the liberty of titling the piece le déjeneur en fourrure , or luncheon in fur . this title is a play on two nineteenth-century works : édouard manet ’ s infamous modernist painting luncheon on the grass ( le déjeneur sur l ’ herbe ) and leopold von sacher-masoch ’ s erotic novel venus in furs . with these two references , breton forces an explicit sexualized meaning onto object . recall that the original inspiration for this work was implicitly practical : when oppenheim asked the waiter for more fur for her cooling teacup , it was suggested as a way to keep her tea warm , and not necessarily as overtly sexual . the meaning of others certainly we can not assume that the spark of the idea for this piece and the piece itself are necessarily related , but the way meanings have been ascribed to oppenheim ’ s pieces by others has plagued many of her works . art historian edward powers has noted that when oppenheim sent her surrealist object das paar to a photographer before submitting it for exhibition , the photographer took the liberty of tying up the laces before photographing it . when breton saw the photo with tied laces , he dubbed this object à délacer which in french means to untie , typically either shoes or a corset . the title and laced shoes together suggest the potential act of undressing and a fascination with exposing the female body . however , when oppenheim later described das paar ( with the laces untied ) , she stated it was an “ odd unisexual pair : two shoes , unobserved at night , doing ‘ forbidden ’ things. ” she expressly assigned no gender , and suggests the “ forbidden ” acts already taking place between anthropomorphized shoes . she takes a more literal approach , the shoes as expressive things in themselves , rather than symbolically resonant of something else . this is not to suggest that all her interactions with breton were negative . when she happened across a wonderfully disturbing photograph of a bicycle seat covered in bees , she mailed it to breton , who republished the found photograph as an artistic contribution by oppenheim in the third issue of the new surrealist publication medium . dangerous success yet , the early acclaim for the fur-covered object had a negative effect on oppenheim ’ s early career . when it was purchased by the museum of modern art and featured in their influential 1936-37 exhibition `` fantastic art , dada , and surrealism '' visitors declared it the “ quintessential ” surrealist object . and that is how it has been seen ever since . but for oppenheim , the prestige and focus on this one object proved too much , and she spent more than a decade out of the artistic limelight , destroying much of the work she produced during that period . it was only later when she re-emerged , and began publicly showing new paintings and objects with renewed vigor and confidence , that she began reclaiming some of the intent of her work . when she was given an award for her work by the city of basel , she touched upon this in her acceptance speech : “ i think it is the duty of a woman to lead a life that expresses her disbelief in the validity of the taboos that have been imposed upon her kind for thousands of years . nobody will give you freedom ; you have to take it. ” *nelson landsdale and st. clair mckelway , talk of the town , “ critical note , ” the new yorker , december 26 , 1936 , p. 7 . essay by josh rose
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however , while oppenheim preferred a non-descriptive title , breton took the liberty of titling the piece le déjeneur en fourrure , or luncheon in fur . this title is a play on two nineteenth-century works : édouard manet ’ s infamous modernist painting luncheon on the grass ( le déjeneur sur l ’ herbe ) and leopold von sacher-masoch ’ s erotic novel venus in furs . with these two references , breton forces an explicit sexualized meaning onto object .
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why is is that people assume the artwork has erotic suggestions ?
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean . jacques has a brand new submarine that he ’ s been itching to try out , and he wants you to come with him to check out some hydrothermal vents at the bottom of the marianas trench that he ’ s been talking about for weeks . you don your itchiest wetsuit and climb aboard his submarine , which has suspiciously thick iron walls given how tiny and cramped it is inside . jacques reminds you that the super-thick walls are necessary in order to survive the descent to the bottom of the trench , since the external pressure down there is nearly 1000 times what you ’ re used to at sea level . the stiff walls hold the pressure inside constant even while the pressure outside increases . the walls themselves actually get compressed due to the gradually-increasing difference in pressure across them . the reason that they don ’ t collapse onto you and jacques is that they compress ( like springs ) , which counter balances the force arising from the pressure difference . so as the submarine dives deeper , the internal pressure ( thankfully ) stays the same… but the walls actually get thinner ! recall that , at sea-level , you experience a pressure of about 101 kpa due to the weight of the earth ’ s entire atmosphere sitting on top of you . because air is not very dense this pressure only barely varies with elevation . for example , at the top of the empire state building the pressure is roughly 95 kpa . it ’ s only at colossal distances that the change in pressure becomes noticeable . at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation . because water is very dense , pressure rapidly increases with depth in the ocean . for every ten meters deeper you dive , the pressure of the surrounding water increases by an amount that ’ s equal to the total ambient pressure that you feel when you ’ re at the surface ( 101 kpa ) . so if you dive down to 10 m , the total pressure your body feels is now 202 kpa . if you dive even deeper to 20 m , you ’ ll feel 303 kpa ! it ’ s important to remember that this pressure arises purely due to the combined weight of all the water that ’ s sitting above you . if you were diving on a planet with less gravity than earth , the pressure you feel at 10 meters would be less than 202 kpa . jacque ’ s submarine is filled with air , which is much less dense than water . as you ’ d expect , the sub would float on the water ’ s surface for the same reason that boats and bubbles float . the force that allows the submarine to stay afloat is known as the buoyant force . in order to successfully descend , the submarine has to use a propeller that pushes against the buoyant force and drives the sub deeper into the ocean . a strange property of the buoyant force is that it stays the same regardless of how deep you go ; it is independent of the surrounding pressure . this means that , if you were watching jacques ’ submarine dive at a constant speed , it would appear that the propeller always spins at the same speed and that the engines consistently draw the same amount of fuel . because water is incompressible , its density , stickiness , and other properties stay pretty much the same as you go deeper… and so the buoyant force stays the same as well . what determines the size of the buoyant force ? back on land , you decide to write down some equations to describe jacque ’ s submarine . you start by making a free-body diagram describing the forces that push and pull on the submarine as it sinks . the first one is obviously gravity , which exerts a force f $ \text { } { g } $ proportional to the mass of the sub ( m $ \text { } { sub } $ ) $ f_g = m_ { sub } \cdot g $ where g is the acceleration due to gravity , 9.8 m/s/s . but you know that gravity isn ’ t the only force that acts on the submarine . there must be a buoyant force that acts to counteract it . the submarine is filled with air ( like a balloon ) , so you expect it would float on top of the water were it not for the action of its propeller : even though the steel walls of the submarine make it heavy , this added weight is offset by a huge amount of trapped air . this effect is similar to a balloon , which doesn ’ t float until it ’ s filled with air . the submarine thus requires a propeller that acts together with gravity to make the submarine sink , despite the buoyant force acting on it . another way of thinking about this is to realize that the submarine floats because it is less dense than the surrounding water . even though the steel walls are definitely denser than the surrounding water , the enclosed air is much less dense , and so the overall density of the submarine is less than water and so it floats . so unlike a rock ( denser than water ) that immediately sinks when it ’ s dropped into the ocean , the submarine has to actively use energy ( in the form of a spinning propeller ) to push itself against the buoyant force and in the direction of gravity . the equation that gives you the size of the buoyant force is called archimede ’ s principle , and it states : $ f_b = d_ { water } v_ { sub } \cdot g $ this says that the buoyant force f $ \text { } { b } $ acting on the sub is determined by the density of water ( d $ \text { } { water } $ , which is roughly 1 g/cm $ ^\text { 3 } $ ) , the volume of the submarine ( v $ \text { } { sub } $ ) , and gravity ( g ) . you might be surprised to see that “ g ” appears in the equation for buoyant force , which always points in the opposite direction to the weight of an object due to gravity . but there ’ s a good reason for this : the buoyant force on an object equals the total weight of water that it pushes out of the way . for bigger subs ( larger v $ \text { } { sub } $ ) , more water needs to get pushed out of the way , and so the buoyant force is larger . we can combine this equation with the weight of the sub to get the net force acting on the submarine . $ f_ { total } = d_ { water } v_ { sub } \cdot g - f_ { propeller } - m_ { sub } \cdot g $ f $ \text { } { propeller } $ is the force that the propeller exerts during the dive . if f $ \text { } { total } $ is positive , the submarine floats upwards , and if f $ \text { } { total } $ is negative , the submarine sinks . jacques can determine which one of these occurs by altering f $ \text { } { propeller } $ . the free-body diagram corresponding to this equation looks something like : in the equation for f $ \text { } _ { total } $ there is no term that is proportional to depth , which shows that the buoyant force does not get smaller as you sink . this is because water is incompressible . for this reason , a stiff object like a steel submersible ( which has a roughly constant volume as it dives , since the compression of the walls is a tiny effect ) displaces the same amount of water regardless of whether it ’ s just below the surface or right next to a sperm whale at the bottom of the marianas trench . because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels .
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but would n't the amount of gas dissolved in the blood increase as the diver went deeper and the pressure increased ?
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean . jacques has a brand new submarine that he ’ s been itching to try out , and he wants you to come with him to check out some hydrothermal vents at the bottom of the marianas trench that he ’ s been talking about for weeks . you don your itchiest wetsuit and climb aboard his submarine , which has suspiciously thick iron walls given how tiny and cramped it is inside . jacques reminds you that the super-thick walls are necessary in order to survive the descent to the bottom of the trench , since the external pressure down there is nearly 1000 times what you ’ re used to at sea level . the stiff walls hold the pressure inside constant even while the pressure outside increases . the walls themselves actually get compressed due to the gradually-increasing difference in pressure across them . the reason that they don ’ t collapse onto you and jacques is that they compress ( like springs ) , which counter balances the force arising from the pressure difference . so as the submarine dives deeper , the internal pressure ( thankfully ) stays the same… but the walls actually get thinner ! recall that , at sea-level , you experience a pressure of about 101 kpa due to the weight of the earth ’ s entire atmosphere sitting on top of you . because air is not very dense this pressure only barely varies with elevation . for example , at the top of the empire state building the pressure is roughly 95 kpa . it ’ s only at colossal distances that the change in pressure becomes noticeable . at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation . because water is very dense , pressure rapidly increases with depth in the ocean . for every ten meters deeper you dive , the pressure of the surrounding water increases by an amount that ’ s equal to the total ambient pressure that you feel when you ’ re at the surface ( 101 kpa ) . so if you dive down to 10 m , the total pressure your body feels is now 202 kpa . if you dive even deeper to 20 m , you ’ ll feel 303 kpa ! it ’ s important to remember that this pressure arises purely due to the combined weight of all the water that ’ s sitting above you . if you were diving on a planet with less gravity than earth , the pressure you feel at 10 meters would be less than 202 kpa . jacque ’ s submarine is filled with air , which is much less dense than water . as you ’ d expect , the sub would float on the water ’ s surface for the same reason that boats and bubbles float . the force that allows the submarine to stay afloat is known as the buoyant force . in order to successfully descend , the submarine has to use a propeller that pushes against the buoyant force and drives the sub deeper into the ocean . a strange property of the buoyant force is that it stays the same regardless of how deep you go ; it is independent of the surrounding pressure . this means that , if you were watching jacques ’ submarine dive at a constant speed , it would appear that the propeller always spins at the same speed and that the engines consistently draw the same amount of fuel . because water is incompressible , its density , stickiness , and other properties stay pretty much the same as you go deeper… and so the buoyant force stays the same as well . what determines the size of the buoyant force ? back on land , you decide to write down some equations to describe jacque ’ s submarine . you start by making a free-body diagram describing the forces that push and pull on the submarine as it sinks . the first one is obviously gravity , which exerts a force f $ \text { } { g } $ proportional to the mass of the sub ( m $ \text { } { sub } $ ) $ f_g = m_ { sub } \cdot g $ where g is the acceleration due to gravity , 9.8 m/s/s . but you know that gravity isn ’ t the only force that acts on the submarine . there must be a buoyant force that acts to counteract it . the submarine is filled with air ( like a balloon ) , so you expect it would float on top of the water were it not for the action of its propeller : even though the steel walls of the submarine make it heavy , this added weight is offset by a huge amount of trapped air . this effect is similar to a balloon , which doesn ’ t float until it ’ s filled with air . the submarine thus requires a propeller that acts together with gravity to make the submarine sink , despite the buoyant force acting on it . another way of thinking about this is to realize that the submarine floats because it is less dense than the surrounding water . even though the steel walls are definitely denser than the surrounding water , the enclosed air is much less dense , and so the overall density of the submarine is less than water and so it floats . so unlike a rock ( denser than water ) that immediately sinks when it ’ s dropped into the ocean , the submarine has to actively use energy ( in the form of a spinning propeller ) to push itself against the buoyant force and in the direction of gravity . the equation that gives you the size of the buoyant force is called archimede ’ s principle , and it states : $ f_b = d_ { water } v_ { sub } \cdot g $ this says that the buoyant force f $ \text { } { b } $ acting on the sub is determined by the density of water ( d $ \text { } { water } $ , which is roughly 1 g/cm $ ^\text { 3 } $ ) , the volume of the submarine ( v $ \text { } { sub } $ ) , and gravity ( g ) . you might be surprised to see that “ g ” appears in the equation for buoyant force , which always points in the opposite direction to the weight of an object due to gravity . but there ’ s a good reason for this : the buoyant force on an object equals the total weight of water that it pushes out of the way . for bigger subs ( larger v $ \text { } { sub } $ ) , more water needs to get pushed out of the way , and so the buoyant force is larger . we can combine this equation with the weight of the sub to get the net force acting on the submarine . $ f_ { total } = d_ { water } v_ { sub } \cdot g - f_ { propeller } - m_ { sub } \cdot g $ f $ \text { } { propeller } $ is the force that the propeller exerts during the dive . if f $ \text { } { total } $ is positive , the submarine floats upwards , and if f $ \text { } { total } $ is negative , the submarine sinks . jacques can determine which one of these occurs by altering f $ \text { } { propeller } $ . the free-body diagram corresponding to this equation looks something like : in the equation for f $ \text { } _ { total } $ there is no term that is proportional to depth , which shows that the buoyant force does not get smaller as you sink . this is because water is incompressible . for this reason , a stiff object like a steel submersible ( which has a roughly constant volume as it dives , since the compression of the walls is a tiny effect ) displaces the same amount of water regardless of whether it ’ s just below the surface or right next to a sperm whale at the bottom of the marianas trench . because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean .
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`` the buoyant force does not get smaller as you sink '' does that mean if i was originally more dense then water , that i would fall at constant velocity ( even with drag ) until i hit sea floor ?
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean . jacques has a brand new submarine that he ’ s been itching to try out , and he wants you to come with him to check out some hydrothermal vents at the bottom of the marianas trench that he ’ s been talking about for weeks . you don your itchiest wetsuit and climb aboard his submarine , which has suspiciously thick iron walls given how tiny and cramped it is inside . jacques reminds you that the super-thick walls are necessary in order to survive the descent to the bottom of the trench , since the external pressure down there is nearly 1000 times what you ’ re used to at sea level . the stiff walls hold the pressure inside constant even while the pressure outside increases . the walls themselves actually get compressed due to the gradually-increasing difference in pressure across them . the reason that they don ’ t collapse onto you and jacques is that they compress ( like springs ) , which counter balances the force arising from the pressure difference . so as the submarine dives deeper , the internal pressure ( thankfully ) stays the same… but the walls actually get thinner ! recall that , at sea-level , you experience a pressure of about 101 kpa due to the weight of the earth ’ s entire atmosphere sitting on top of you . because air is not very dense this pressure only barely varies with elevation . for example , at the top of the empire state building the pressure is roughly 95 kpa . it ’ s only at colossal distances that the change in pressure becomes noticeable . at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation . because water is very dense , pressure rapidly increases with depth in the ocean . for every ten meters deeper you dive , the pressure of the surrounding water increases by an amount that ’ s equal to the total ambient pressure that you feel when you ’ re at the surface ( 101 kpa ) . so if you dive down to 10 m , the total pressure your body feels is now 202 kpa . if you dive even deeper to 20 m , you ’ ll feel 303 kpa ! it ’ s important to remember that this pressure arises purely due to the combined weight of all the water that ’ s sitting above you . if you were diving on a planet with less gravity than earth , the pressure you feel at 10 meters would be less than 202 kpa . jacque ’ s submarine is filled with air , which is much less dense than water . as you ’ d expect , the sub would float on the water ’ s surface for the same reason that boats and bubbles float . the force that allows the submarine to stay afloat is known as the buoyant force . in order to successfully descend , the submarine has to use a propeller that pushes against the buoyant force and drives the sub deeper into the ocean . a strange property of the buoyant force is that it stays the same regardless of how deep you go ; it is independent of the surrounding pressure . this means that , if you were watching jacques ’ submarine dive at a constant speed , it would appear that the propeller always spins at the same speed and that the engines consistently draw the same amount of fuel . because water is incompressible , its density , stickiness , and other properties stay pretty much the same as you go deeper… and so the buoyant force stays the same as well . what determines the size of the buoyant force ? back on land , you decide to write down some equations to describe jacque ’ s submarine . you start by making a free-body diagram describing the forces that push and pull on the submarine as it sinks . the first one is obviously gravity , which exerts a force f $ \text { } { g } $ proportional to the mass of the sub ( m $ \text { } { sub } $ ) $ f_g = m_ { sub } \cdot g $ where g is the acceleration due to gravity , 9.8 m/s/s . but you know that gravity isn ’ t the only force that acts on the submarine . there must be a buoyant force that acts to counteract it . the submarine is filled with air ( like a balloon ) , so you expect it would float on top of the water were it not for the action of its propeller : even though the steel walls of the submarine make it heavy , this added weight is offset by a huge amount of trapped air . this effect is similar to a balloon , which doesn ’ t float until it ’ s filled with air . the submarine thus requires a propeller that acts together with gravity to make the submarine sink , despite the buoyant force acting on it . another way of thinking about this is to realize that the submarine floats because it is less dense than the surrounding water . even though the steel walls are definitely denser than the surrounding water , the enclosed air is much less dense , and so the overall density of the submarine is less than water and so it floats . so unlike a rock ( denser than water ) that immediately sinks when it ’ s dropped into the ocean , the submarine has to actively use energy ( in the form of a spinning propeller ) to push itself against the buoyant force and in the direction of gravity . the equation that gives you the size of the buoyant force is called archimede ’ s principle , and it states : $ f_b = d_ { water } v_ { sub } \cdot g $ this says that the buoyant force f $ \text { } { b } $ acting on the sub is determined by the density of water ( d $ \text { } { water } $ , which is roughly 1 g/cm $ ^\text { 3 } $ ) , the volume of the submarine ( v $ \text { } { sub } $ ) , and gravity ( g ) . you might be surprised to see that “ g ” appears in the equation for buoyant force , which always points in the opposite direction to the weight of an object due to gravity . but there ’ s a good reason for this : the buoyant force on an object equals the total weight of water that it pushes out of the way . for bigger subs ( larger v $ \text { } { sub } $ ) , more water needs to get pushed out of the way , and so the buoyant force is larger . we can combine this equation with the weight of the sub to get the net force acting on the submarine . $ f_ { total } = d_ { water } v_ { sub } \cdot g - f_ { propeller } - m_ { sub } \cdot g $ f $ \text { } { propeller } $ is the force that the propeller exerts during the dive . if f $ \text { } { total } $ is positive , the submarine floats upwards , and if f $ \text { } { total } $ is negative , the submarine sinks . jacques can determine which one of these occurs by altering f $ \text { } { propeller } $ . the free-body diagram corresponding to this equation looks something like : in the equation for f $ \text { } _ { total } $ there is no term that is proportional to depth , which shows that the buoyant force does not get smaller as you sink . this is because water is incompressible . for this reason , a stiff object like a steel submersible ( which has a roughly constant volume as it dives , since the compression of the walls is a tiny effect ) displaces the same amount of water regardless of whether it ’ s just below the surface or right next to a sperm whale at the bottom of the marianas trench . because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation .
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do manufacturers of compressed air tanks for scuba diving intentionally decrease the partial pressure of nitrogen in their tanks to reduce the risk of getting the bends ?
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean . jacques has a brand new submarine that he ’ s been itching to try out , and he wants you to come with him to check out some hydrothermal vents at the bottom of the marianas trench that he ’ s been talking about for weeks . you don your itchiest wetsuit and climb aboard his submarine , which has suspiciously thick iron walls given how tiny and cramped it is inside . jacques reminds you that the super-thick walls are necessary in order to survive the descent to the bottom of the trench , since the external pressure down there is nearly 1000 times what you ’ re used to at sea level . the stiff walls hold the pressure inside constant even while the pressure outside increases . the walls themselves actually get compressed due to the gradually-increasing difference in pressure across them . the reason that they don ’ t collapse onto you and jacques is that they compress ( like springs ) , which counter balances the force arising from the pressure difference . so as the submarine dives deeper , the internal pressure ( thankfully ) stays the same… but the walls actually get thinner ! recall that , at sea-level , you experience a pressure of about 101 kpa due to the weight of the earth ’ s entire atmosphere sitting on top of you . because air is not very dense this pressure only barely varies with elevation . for example , at the top of the empire state building the pressure is roughly 95 kpa . it ’ s only at colossal distances that the change in pressure becomes noticeable . at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation . because water is very dense , pressure rapidly increases with depth in the ocean . for every ten meters deeper you dive , the pressure of the surrounding water increases by an amount that ’ s equal to the total ambient pressure that you feel when you ’ re at the surface ( 101 kpa ) . so if you dive down to 10 m , the total pressure your body feels is now 202 kpa . if you dive even deeper to 20 m , you ’ ll feel 303 kpa ! it ’ s important to remember that this pressure arises purely due to the combined weight of all the water that ’ s sitting above you . if you were diving on a planet with less gravity than earth , the pressure you feel at 10 meters would be less than 202 kpa . jacque ’ s submarine is filled with air , which is much less dense than water . as you ’ d expect , the sub would float on the water ’ s surface for the same reason that boats and bubbles float . the force that allows the submarine to stay afloat is known as the buoyant force . in order to successfully descend , the submarine has to use a propeller that pushes against the buoyant force and drives the sub deeper into the ocean . a strange property of the buoyant force is that it stays the same regardless of how deep you go ; it is independent of the surrounding pressure . this means that , if you were watching jacques ’ submarine dive at a constant speed , it would appear that the propeller always spins at the same speed and that the engines consistently draw the same amount of fuel . because water is incompressible , its density , stickiness , and other properties stay pretty much the same as you go deeper… and so the buoyant force stays the same as well . what determines the size of the buoyant force ? back on land , you decide to write down some equations to describe jacque ’ s submarine . you start by making a free-body diagram describing the forces that push and pull on the submarine as it sinks . the first one is obviously gravity , which exerts a force f $ \text { } { g } $ proportional to the mass of the sub ( m $ \text { } { sub } $ ) $ f_g = m_ { sub } \cdot g $ where g is the acceleration due to gravity , 9.8 m/s/s . but you know that gravity isn ’ t the only force that acts on the submarine . there must be a buoyant force that acts to counteract it . the submarine is filled with air ( like a balloon ) , so you expect it would float on top of the water were it not for the action of its propeller : even though the steel walls of the submarine make it heavy , this added weight is offset by a huge amount of trapped air . this effect is similar to a balloon , which doesn ’ t float until it ’ s filled with air . the submarine thus requires a propeller that acts together with gravity to make the submarine sink , despite the buoyant force acting on it . another way of thinking about this is to realize that the submarine floats because it is less dense than the surrounding water . even though the steel walls are definitely denser than the surrounding water , the enclosed air is much less dense , and so the overall density of the submarine is less than water and so it floats . so unlike a rock ( denser than water ) that immediately sinks when it ’ s dropped into the ocean , the submarine has to actively use energy ( in the form of a spinning propeller ) to push itself against the buoyant force and in the direction of gravity . the equation that gives you the size of the buoyant force is called archimede ’ s principle , and it states : $ f_b = d_ { water } v_ { sub } \cdot g $ this says that the buoyant force f $ \text { } { b } $ acting on the sub is determined by the density of water ( d $ \text { } { water } $ , which is roughly 1 g/cm $ ^\text { 3 } $ ) , the volume of the submarine ( v $ \text { } { sub } $ ) , and gravity ( g ) . you might be surprised to see that “ g ” appears in the equation for buoyant force , which always points in the opposite direction to the weight of an object due to gravity . but there ’ s a good reason for this : the buoyant force on an object equals the total weight of water that it pushes out of the way . for bigger subs ( larger v $ \text { } { sub } $ ) , more water needs to get pushed out of the way , and so the buoyant force is larger . we can combine this equation with the weight of the sub to get the net force acting on the submarine . $ f_ { total } = d_ { water } v_ { sub } \cdot g - f_ { propeller } - m_ { sub } \cdot g $ f $ \text { } { propeller } $ is the force that the propeller exerts during the dive . if f $ \text { } { total } $ is positive , the submarine floats upwards , and if f $ \text { } { total } $ is negative , the submarine sinks . jacques can determine which one of these occurs by altering f $ \text { } { propeller } $ . the free-body diagram corresponding to this equation looks something like : in the equation for f $ \text { } _ { total } $ there is no term that is proportional to depth , which shows that the buoyant force does not get smaller as you sink . this is because water is incompressible . for this reason , a stiff object like a steel submersible ( which has a roughly constant volume as it dives , since the compression of the walls is a tiny effect ) displaces the same amount of water regardless of whether it ’ s just below the surface or right next to a sperm whale at the bottom of the marianas trench . because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean .
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does the buoyant force remain the same ?
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean . jacques has a brand new submarine that he ’ s been itching to try out , and he wants you to come with him to check out some hydrothermal vents at the bottom of the marianas trench that he ’ s been talking about for weeks . you don your itchiest wetsuit and climb aboard his submarine , which has suspiciously thick iron walls given how tiny and cramped it is inside . jacques reminds you that the super-thick walls are necessary in order to survive the descent to the bottom of the trench , since the external pressure down there is nearly 1000 times what you ’ re used to at sea level . the stiff walls hold the pressure inside constant even while the pressure outside increases . the walls themselves actually get compressed due to the gradually-increasing difference in pressure across them . the reason that they don ’ t collapse onto you and jacques is that they compress ( like springs ) , which counter balances the force arising from the pressure difference . so as the submarine dives deeper , the internal pressure ( thankfully ) stays the same… but the walls actually get thinner ! recall that , at sea-level , you experience a pressure of about 101 kpa due to the weight of the earth ’ s entire atmosphere sitting on top of you . because air is not very dense this pressure only barely varies with elevation . for example , at the top of the empire state building the pressure is roughly 95 kpa . it ’ s only at colossal distances that the change in pressure becomes noticeable . at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation . because water is very dense , pressure rapidly increases with depth in the ocean . for every ten meters deeper you dive , the pressure of the surrounding water increases by an amount that ’ s equal to the total ambient pressure that you feel when you ’ re at the surface ( 101 kpa ) . so if you dive down to 10 m , the total pressure your body feels is now 202 kpa . if you dive even deeper to 20 m , you ’ ll feel 303 kpa ! it ’ s important to remember that this pressure arises purely due to the combined weight of all the water that ’ s sitting above you . if you were diving on a planet with less gravity than earth , the pressure you feel at 10 meters would be less than 202 kpa . jacque ’ s submarine is filled with air , which is much less dense than water . as you ’ d expect , the sub would float on the water ’ s surface for the same reason that boats and bubbles float . the force that allows the submarine to stay afloat is known as the buoyant force . in order to successfully descend , the submarine has to use a propeller that pushes against the buoyant force and drives the sub deeper into the ocean . a strange property of the buoyant force is that it stays the same regardless of how deep you go ; it is independent of the surrounding pressure . this means that , if you were watching jacques ’ submarine dive at a constant speed , it would appear that the propeller always spins at the same speed and that the engines consistently draw the same amount of fuel . because water is incompressible , its density , stickiness , and other properties stay pretty much the same as you go deeper… and so the buoyant force stays the same as well . what determines the size of the buoyant force ? back on land , you decide to write down some equations to describe jacque ’ s submarine . you start by making a free-body diagram describing the forces that push and pull on the submarine as it sinks . the first one is obviously gravity , which exerts a force f $ \text { } { g } $ proportional to the mass of the sub ( m $ \text { } { sub } $ ) $ f_g = m_ { sub } \cdot g $ where g is the acceleration due to gravity , 9.8 m/s/s . but you know that gravity isn ’ t the only force that acts on the submarine . there must be a buoyant force that acts to counteract it . the submarine is filled with air ( like a balloon ) , so you expect it would float on top of the water were it not for the action of its propeller : even though the steel walls of the submarine make it heavy , this added weight is offset by a huge amount of trapped air . this effect is similar to a balloon , which doesn ’ t float until it ’ s filled with air . the submarine thus requires a propeller that acts together with gravity to make the submarine sink , despite the buoyant force acting on it . another way of thinking about this is to realize that the submarine floats because it is less dense than the surrounding water . even though the steel walls are definitely denser than the surrounding water , the enclosed air is much less dense , and so the overall density of the submarine is less than water and so it floats . so unlike a rock ( denser than water ) that immediately sinks when it ’ s dropped into the ocean , the submarine has to actively use energy ( in the form of a spinning propeller ) to push itself against the buoyant force and in the direction of gravity . the equation that gives you the size of the buoyant force is called archimede ’ s principle , and it states : $ f_b = d_ { water } v_ { sub } \cdot g $ this says that the buoyant force f $ \text { } { b } $ acting on the sub is determined by the density of water ( d $ \text { } { water } $ , which is roughly 1 g/cm $ ^\text { 3 } $ ) , the volume of the submarine ( v $ \text { } { sub } $ ) , and gravity ( g ) . you might be surprised to see that “ g ” appears in the equation for buoyant force , which always points in the opposite direction to the weight of an object due to gravity . but there ’ s a good reason for this : the buoyant force on an object equals the total weight of water that it pushes out of the way . for bigger subs ( larger v $ \text { } { sub } $ ) , more water needs to get pushed out of the way , and so the buoyant force is larger . we can combine this equation with the weight of the sub to get the net force acting on the submarine . $ f_ { total } = d_ { water } v_ { sub } \cdot g - f_ { propeller } - m_ { sub } \cdot g $ f $ \text { } { propeller } $ is the force that the propeller exerts during the dive . if f $ \text { } { total } $ is positive , the submarine floats upwards , and if f $ \text { } { total } $ is negative , the submarine sinks . jacques can determine which one of these occurs by altering f $ \text { } { propeller } $ . the free-body diagram corresponding to this equation looks something like : in the equation for f $ \text { } _ { total } $ there is no term that is proportional to depth , which shows that the buoyant force does not get smaller as you sink . this is because water is incompressible . for this reason , a stiff object like a steel submersible ( which has a roughly constant volume as it dives , since the compression of the walls is a tiny effect ) displaces the same amount of water regardless of whether it ’ s just below the surface or right next to a sperm whale at the bottom of the marianas trench . because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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for example , do free divers have to slowly rise back up when they come from let 's say , a 50-100 m dive ?
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean . jacques has a brand new submarine that he ’ s been itching to try out , and he wants you to come with him to check out some hydrothermal vents at the bottom of the marianas trench that he ’ s been talking about for weeks . you don your itchiest wetsuit and climb aboard his submarine , which has suspiciously thick iron walls given how tiny and cramped it is inside . jacques reminds you that the super-thick walls are necessary in order to survive the descent to the bottom of the trench , since the external pressure down there is nearly 1000 times what you ’ re used to at sea level . the stiff walls hold the pressure inside constant even while the pressure outside increases . the walls themselves actually get compressed due to the gradually-increasing difference in pressure across them . the reason that they don ’ t collapse onto you and jacques is that they compress ( like springs ) , which counter balances the force arising from the pressure difference . so as the submarine dives deeper , the internal pressure ( thankfully ) stays the same… but the walls actually get thinner ! recall that , at sea-level , you experience a pressure of about 101 kpa due to the weight of the earth ’ s entire atmosphere sitting on top of you . because air is not very dense this pressure only barely varies with elevation . for example , at the top of the empire state building the pressure is roughly 95 kpa . it ’ s only at colossal distances that the change in pressure becomes noticeable . at the top of mount everest the pressure is closer to 33 kpa . the decrease in pressure occurs simply because as you go higher there is less air above you pushing down on you . under water is a different situation . because water is very dense , pressure rapidly increases with depth in the ocean . for every ten meters deeper you dive , the pressure of the surrounding water increases by an amount that ’ s equal to the total ambient pressure that you feel when you ’ re at the surface ( 101 kpa ) . so if you dive down to 10 m , the total pressure your body feels is now 202 kpa . if you dive even deeper to 20 m , you ’ ll feel 303 kpa ! it ’ s important to remember that this pressure arises purely due to the combined weight of all the water that ’ s sitting above you . if you were diving on a planet with less gravity than earth , the pressure you feel at 10 meters would be less than 202 kpa . jacque ’ s submarine is filled with air , which is much less dense than water . as you ’ d expect , the sub would float on the water ’ s surface for the same reason that boats and bubbles float . the force that allows the submarine to stay afloat is known as the buoyant force . in order to successfully descend , the submarine has to use a propeller that pushes against the buoyant force and drives the sub deeper into the ocean . a strange property of the buoyant force is that it stays the same regardless of how deep you go ; it is independent of the surrounding pressure . this means that , if you were watching jacques ’ submarine dive at a constant speed , it would appear that the propeller always spins at the same speed and that the engines consistently draw the same amount of fuel . because water is incompressible , its density , stickiness , and other properties stay pretty much the same as you go deeper… and so the buoyant force stays the same as well . what determines the size of the buoyant force ? back on land , you decide to write down some equations to describe jacque ’ s submarine . you start by making a free-body diagram describing the forces that push and pull on the submarine as it sinks . the first one is obviously gravity , which exerts a force f $ \text { } { g } $ proportional to the mass of the sub ( m $ \text { } { sub } $ ) $ f_g = m_ { sub } \cdot g $ where g is the acceleration due to gravity , 9.8 m/s/s . but you know that gravity isn ’ t the only force that acts on the submarine . there must be a buoyant force that acts to counteract it . the submarine is filled with air ( like a balloon ) , so you expect it would float on top of the water were it not for the action of its propeller : even though the steel walls of the submarine make it heavy , this added weight is offset by a huge amount of trapped air . this effect is similar to a balloon , which doesn ’ t float until it ’ s filled with air . the submarine thus requires a propeller that acts together with gravity to make the submarine sink , despite the buoyant force acting on it . another way of thinking about this is to realize that the submarine floats because it is less dense than the surrounding water . even though the steel walls are definitely denser than the surrounding water , the enclosed air is much less dense , and so the overall density of the submarine is less than water and so it floats . so unlike a rock ( denser than water ) that immediately sinks when it ’ s dropped into the ocean , the submarine has to actively use energy ( in the form of a spinning propeller ) to push itself against the buoyant force and in the direction of gravity . the equation that gives you the size of the buoyant force is called archimede ’ s principle , and it states : $ f_b = d_ { water } v_ { sub } \cdot g $ this says that the buoyant force f $ \text { } { b } $ acting on the sub is determined by the density of water ( d $ \text { } { water } $ , which is roughly 1 g/cm $ ^\text { 3 } $ ) , the volume of the submarine ( v $ \text { } { sub } $ ) , and gravity ( g ) . you might be surprised to see that “ g ” appears in the equation for buoyant force , which always points in the opposite direction to the weight of an object due to gravity . but there ’ s a good reason for this : the buoyant force on an object equals the total weight of water that it pushes out of the way . for bigger subs ( larger v $ \text { } { sub } $ ) , more water needs to get pushed out of the way , and so the buoyant force is larger . we can combine this equation with the weight of the sub to get the net force acting on the submarine . $ f_ { total } = d_ { water } v_ { sub } \cdot g - f_ { propeller } - m_ { sub } \cdot g $ f $ \text { } { propeller } $ is the force that the propeller exerts during the dive . if f $ \text { } { total } $ is positive , the submarine floats upwards , and if f $ \text { } { total } $ is negative , the submarine sinks . jacques can determine which one of these occurs by altering f $ \text { } { propeller } $ . the free-body diagram corresponding to this equation looks something like : in the equation for f $ \text { } _ { total } $ there is no term that is proportional to depth , which shows that the buoyant force does not get smaller as you sink . this is because water is incompressible . for this reason , a stiff object like a steel submersible ( which has a roughly constant volume as it dives , since the compression of the walls is a tiny effect ) displaces the same amount of water regardless of whether it ’ s just below the surface or right next to a sperm whale at the bottom of the marianas trench . because the volume is the same at any depth , and the density of water is the same at any depth , the total mass of displaced water ( mass = volume x density ) is the same at any depth—making the buoyant force constant . consider the following… the bends the amount of dissolved gases in your bloodstream is related to the pressure that you ’ re sitting at . that means that when you scuba dive with a pressurized air tank , the amount of dissolved nitrogen in your bloodstream actually increases as you get deeper . if , at the end of a dive , you attempt to re-surface very quickly , this dissolved nitrogen will suddenly exit your bloodstream in the form of tiny bubbles that can disrupt or damage your blood vessels . this condition is known as decompression sickness or the bends , and it constitutes a life-threatening risk in deep-sea divers . the primary means by which divers can avoid developing the bends is by carefully controlling their rates of re-ascent during a very long dive . the reason that this condition is less of a risk for submarine-divers is because submarines have thick walls that hold out the external pressure , keeping the internal pressure pretty much constant .
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what is the buoyant force ? imagine you ’ re hanging out with your friends on a friday night , when your good friend jacques texts you and asks you to join him on a trip to the bottom of the ocean .
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assuming there was a strong enough gravity to pull you to the left , would the buoyant force push you to the right ?
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key points the budget constraint is the boundary of the opportunity set—all possible combinations of consumption that someone can afford given the prices of goods and the individual ’ s income . opportunity cost measures cost in terms of what must be given up in exchange . marginal analysis is the process of comparing the benefits and costs of choosing a little more or a little less of a certain good . the law of diminishing marginal utility indicates that as a person receives more of a good , the additional—or marginal—utility from each additional unit of the good declines . sunk costs are costs that occurred in the past and can not be recovered ; they should be disregarded in making current decisions . utility is the satisfaction , usefulness , or value one obtains from consuming goods and services . introduction most consumers have a limited amount of income to spend on the things they need and want . alphonso , for example , has \ $ 10 in spending money each week that he can use to buy bus tickets for getting to work and the burgers that he eats for lunch . burgers cost \ $ 2 each , and bus tickets are 50 cents each . there are a lot of combinations of burgers and bus tickets that alphonso could buy . so many , in fact , that it might be easier for us to describe the situation using a graph ! the figure above shows alphonso ’ s budget constraint—the outer boundary of his opportunity set . the opportunity set identifies all the opportunities for spending within his budget—in this case , bus tickets and burgers . the budget constraint indicates all the combinations of burgers and bus tickets alphonso can afford before he exhausts his budget , given the prices of the two goods . the vertical axis in the figure shows burger purchases , and the horizontal axis shows bus ticket purchases . if alphonso spends all his money on burgers , he can afford five per week—\ $ 10 per week divided by \ $ 2 per burger equals five burgers per week . but if alphonso uses all his money on burgers , he will not be able to afford any bus tickets . this choice—zero bus tickets and five burgers—is shown by point a in the figure . alternatively , if alphonso spends all his money on bus tickets , he can afford 20 per week—\ $ 10 per week divided by \ $ 0.50 per bus ticket equals 20 bus tickets per week . if he does this , however , he will not be able to afford any burgers . this choice—20 bus tickets and zero burgers—is shown by point f. if alphonso is like most people , he will choose some combination that includes both bus tickets and burgers . that is , he will choose some combination on the budget constraint that connects points a and f. every point on or inside the constraint shows a combination of burgers and bus tickets that alphonso can afford . any point outside the constraint is not affordable because it would cost more money than alphonso has in his budget . the budget constraint shows the tradeoff alphonso faces in choosing between burgers and bus tickets . suppose he is currently at point d , where he chooses to buy 12 bus tickets and two burgers . what would it cost alphonso for one more burger ? it would be natural to answer \ $ 2 , but that ’ s not the way economists think . economists think about the true cost of a burger—the number of bus tickets alphonso will have to sacrifice . what is opportunity cost ? economists use the term opportunity cost to indicate what must be given up to obtain something that is desired . the idea behind opportunity cost is that the cost of one item is the lost opportunity to do or consume something else ; in short , opportunity cost is the value of the next best alternative . for alphonso , the opportunity cost of a burger is the four bus tickets he would have to give up in order to afford another burger . he must decide whether or not to choose the burger depending on whether the value of the burger exceeds the value of the forgone alternative—in this case , bus tickets . since few if any people have unlimited financial resources , consumers inevitably face tradeoffs in which they have to give up things they desire to get other things they desire more . a fundamental principle of economics is that every choice has an opportunity cost . if you sleep through your economics class—not recommended , by the way—the opportunity cost is the learning you miss from not attending class . if you spend your income on video games , you can not spend it on movies . if you choose to marry one person , you give up the opportunity to marry anyone else . in short , opportunity cost is all around us and is part of human existence . understanding budget constraints one way for us to better understand budget constraints is to build an equation . let 's make $ p $ and $ q $ the price and quantity of items purchased and $ \text { budget } $ the amount of income one has to spend . $ \text { budget } =\text { p } { 1 } \mathrm { ~ \times ~ q } { 1 } \mathrm { ~ +~ p } { 2\ , } \mathrm { \times ~ q } { 2 } $ we can apply the budget constraint equation to alphonso 's scenario : $ \begin { array } { ccc } \text { budget } & amp ; = & amp ; \text { p } { 1 } \mathrm { \times q } { 1 } \mathrm { + p } { 2\ , } \mathrm { \times q } { 2 } \ \mathrm { \ $ 10 } & amp ; = & amp ; \mathrm { \ $ 2~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ \ $ 0.50~ \times ~ q } { \mathrm { bus~ tickets } } \end { array } $ using a little algebra , let 's turn this into the equation of a line : $ \begin { array } { ccc } \text { y } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { b~ +~ mx } \end { array } $ if we plug in the variables from alphonso 's scenario , we get the following : $ \begin { array } { ccc } \mathrm { \ $ 10 } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { \ $ 2~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ } \mathrm { \ $ 0.50 } \mathrm { ~ \times ~ } \text { q } { \mathrm { bus~ tickets } } \end { array } $ next , we simplify the equation by multiplying both sides of the equation by two : $ \begin { array } { ccc } \mathrm { 2~ \times ~ 10 } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { 2~ \times ~ 2~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ 2~ \times ~ 0.5~ \times ~ q } { \mathrm { bus~ tickets } } ~ \ \text { 20 } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { 4~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ 1~ \times ~ q } { \mathrm { bus~ tickets } } \end { array } $ then we subtract one bus ticket from both sides : $ \begin { array } { ccc } \mathrm { 20 - q } { \text { bus tickets } } & amp ; \mathrm { = } & amp ; \mathrm { 4 \times q } { \text { burgers } } \end { array } $ next , we divide each side by four to yield the answer : $ \begin { array } { ccc } \mathrm { 5 - 0.25 \times q } { \text { bus tickets } } & amp ; \mathrm { = } & amp ; \text { q } { \text { burgers } } \ & amp ; \text { or } & amp ; \ \text { q } { \text { burgers } } & amp ; \mathrm { = } & amp ; \mathrm { 5 - 0.25 \times q } { \text { bus tickets } } \end { array } $ notice that this equation fits alphonso 's budget constraint figure above . the vertical intercept is five and the slope is –0.25 , just as the equation says . if you plug 20 bus tickets into the equation , you get 0 burgers . if you plug other numbers of bus tickets into the equation , you get the results shown in the table below , which are also the points on alphonso ’ s budget constraint . point | quantity of burgers at \ $ 2 | quantity of bus tickets at 50 cents - | - | - a | 5 | 0 b | 4 | 4 c | 3 | 8 d | 2 | 12 e | 1 | 16 f | 0 | 20 notice that the slope of a budget constraint always shows the opportunity cost of the good which is on the horizontal axis . for alphonso , the slope is −0.25 , indicating that for every four bus tickets he buys , alphonso must give up one burger . there are two important observations here . first , the algebraic sign of the slope is negative , which means that the only way to get more of one good is to give up some of the other . second , the slope is defined as the price of whatever is on the horizontal axis in the graph—in this case , bus tickets—divided by the price of whatever is on the vertical axis—in this case , burgers . so , in our scenario , the slope is $ \ $ 0.50/\ $ 2 = 0.25 $ . if you want to determine the opportunity cost quickly , just divide the two prices . identifying opportunity cost in many cases , it is reasonable to refer to the opportunity cost as the price . if your cousin buys a new bicycle for \ $ 300 , then \ $ 300 measures the amount of other spending opportunities , or other consumption , that he has given up . for practical purposes , there may be no special need to identify the specific alternative product or products that could have been bought with that \ $ 300 , but sometimes the price as measured in dollars may not accurately capture the true opportunity cost . this problem can loom especially large when costs of time are involved . for example , consider a boss who decides that all employees will attend a two-day retreat to build team spirit . the out-of-pocket monetary cost of the event may involve hiring an outside consulting firm to run the retreat as well as room and board for all participants . but an opportunity cost exists as well : during the two days of the retreat , none of the employees are doing any other work . attending college is another case where the opportunity cost exceeds the monetary cost . the out-of-pocket costs of attending college include tuition , books , room and board , and other expenses . but in addition , during the hours that a student is attending class and studying , it is impossible for them to work at a paying job . thus , college imposes both an out-of-pocket cost and an opportunity cost of lost earnings . in some cases , recognizing opportunity cost can alter behavior . imagine , for example , that you spend \ $ 8 on lunch every day at work . you may know perfectly well that bringing a lunch from home would cost only \ $ 3 a day . so , the opportunity cost of buying lunch at the restaurant is \ $ 5 each day—the \ $ 8 buying lunch costs minus the \ $ 3 your lunch from home would cost . five dollars each day does not seem to be that much ; but , if you add up the cost over a year—250 days a year times \ $ 5 per day equals \ $ 1,250—it 's actually equivalent to a decent vacation . if the opportunity cost were described as “ a nice vacation ” instead of “ \ $ 5 a day ” , you might make different choices . marginal decision-making and diminishing marginal utility the budget constraint framework helps to emphasize that most choices in the real world are not about getting all of one thing or all of another—choosing a point at one end of the budget constraint or all the way at the other end . instead , most choices involve marginal analysis , comparing the benefits and costs of choosing a little more or a little less of a certain good . people desire goods and services for the satisfaction or utility those goods and services provide . utility is subjective , but that does n't make it any less real . economists typically assume that the more of some good one consumes—for example , slices of pizza—the more utility one obtains . at the same time , the utility a person receives from consuming the first unit of a good is typically more than the utility received from consuming the fifth or the 10th unit of that same good . when alphonso chooses between burgers and bus tickets , for example , the first few bus rides that he chooses might provide him with a great deal of utility—perhaps they help him get to a job interview or a doctor ’ s appointment . but later bus rides might provide much less utility—they may only serve to kill time on a rainy day . similarly , the first burger that alphonso chooses to buy may be on a day when he missed breakfast and is ravenously hungry . however , if alphonso has a burger every single day , the last few burgers may taste pretty boring . it is a common pattern for consumption of the first few units of any good to bring a higher level of utility to a person than consumption of later units . economists refer to this pattern—described succinctly , `` as a person receives more of a good , the additional , or marginal , utility from each additional unit of the good declines '' —as the law of diminishing marginal utility . you could describe this law in more simple terms as `` the first slice of pizza brings more satisfaction than the sixth . '' the law of diminishing marginal utility explains why people and societies rarely make all-or-nothing choices . you would probably not say , “ my favorite food is ice cream , so i will eat nothing but ice cream from now on. ” even though your favorite food has a high level of utility , if you chose to eat it exclusively , the additional or marginal utility from those last few servings would not be very high . similarly , most workers would not say : “ i enjoy leisure , so i ’ ll never work. ” instead , workers recognize that even though some leisure is very nice , a combination of all leisure and no income is not so attractive . the budget constraint framework suggests that when people make choices in a world of scarcity , they will use marginal analysis and think about whether they would prefer a little more or a little less . sunk costs in the budget constraint framework , all decisions involve what will happen next—what quantities of goods will you consume , how many hours will you work , or how much will you save . these decisions do not look back to past choices . thus , the budget constraint framework assumes that sunk costs—costs that were incurred in the past and can not be recovered—should not affect the current decision . consider the case of selena , who pays \ $ 8 to see a movie ; after watching the film for 30 minutes , she knows that it is truly terrible . should she stay and watch the rest of the movie because she paid for the ticket , or should she leave ? the money she spent is a sunk cost , and unless the theater manager is feeling kindly , selena will not get a refund . but , staying in the movie still means paying an opportunity cost in time . her choice is whether to spend the next 90 minutes suffering through a cinematic disaster or to do something—anything—else . the lesson of sunk costs is to forget about the money and time that is irretrievably gone and instead to focus on the marginal costs and benefits of current and future options . for people and firms alike , dealing with sunk costs can be frustrating . it often means admitting an earlier error in judgment . many firms , for example , find it hard to give up on a new product that is doing poorly because they spent so much money in creating and launching the product . but the lesson of sunk costs is to ignore them and make decisions based on what will happen in the future . from a model with two goods to one of many goods the budget constraint diagram we used to examine alphonso 's situation containing just two goods is not realistic . after all , in a modern economy people choose from thousands of goods . we can , however , think about a model with many goods by extending the ideas we 've discussed here . instead of drawing just one budget constraint showing the tradeoff between two goods , you can draw multiple budget constraints showing the possible tradeoffs between many different pairs of goods . or , in more advanced classes in economics , you would use mathematical equations that include many possible goods and services that can be purchased together with their quantities and prices to show how the total spending on all goods and services is limited to the overall budget available . it 's important to remember , though , that the graph above with two goods clearly illustrates that every choice has an opportunity cost , which is an idea that carries over to the real world . key concepts and summary economists see the real world as one of scarcity—a world in which people ’ s desires exceed what is possible . economic behavior involves tradeoffs in which individuals , firms , and society must give up something that they desire to obtain things that they desire more . individuals must choose which quantities and combinations of goods and services to consume . the budget constraint , which is the outer boundary of the opportunity set , illustrates the range of choices available . the slope of the budget constraint is determined by the relative price of the choices . choices beyond the budget constraint are not affordable . opportunity cost measures cost by what is given up in exchange . sometimes opportunity cost can be measured in money , but it is often useful to consider time costs as well or to measure opportunity cost in terms of the actual resources that must be given up . most economic decisions and tradeoffs are not all or nothing . instead , they involve marginal analysis , which means they are about decisions on the margin—involving a little more or a little less . the law of diminishing marginal utility points out that as a person receives more of something , whether it is a specific good or another resource , the additional marginal gains tend to become smaller . because sunk costs occurred in the past and can not be recovered , they should be disregarded in making current decisions . self-check question suppose alphonso ’ s town raised the price of bus tickets to \ $ 1 per trip , the price of burgers stayed at \ $ 2 , and alphonso 's budget remained \ $ 10 per week . draw alphonso ’ s new budget constraint . what happens to the opportunity cost of bus tickets ? review questions explain why scarcity leads to tradeoffs . explain why individuals make choices that are directly on the budget constraint rather than inside the budget constraint or outside it . critical thinking questions suppose alphonso ’ s town raises the price of bus tickets from \ $ 0.50 to \ $ 1 and the price of burgers rises from \ $ 2 to \ $ 4 . why is the opportunity cost of bus tickets unchanged ? suppose in addition to the above changes , alphonso ’ s weekly spending money increases from \ $ 10 to \ $ 20 . how is his budget constraint affected by all three changes ? explain . problems marie has a weekly budget of \ $ 24 , which she likes to spend on magazines and pies . if the price of one magazine is \ $ 4 , what is the maximum number of magazines she can buy in a week ? if the price of a pie is \ $ 12 , what is the maximum number of pies she can buy in a week ? draw marie ’ s budget constraint with pies on the horizontal axis and magazines on the vertical axis . what is the slope of the budget constraint ? what is marie ’ s opportunity cost of purchasing a pie ?
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self-check question suppose alphonso ’ s town raised the price of bus tickets to \ $ 1 per trip , the price of burgers stayed at \ $ 2 , and alphonso 's budget remained \ $ 10 per week . draw alphonso ’ s new budget constraint . what happens to the opportunity cost of bus tickets ?
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is n't the slope of the new budget constraint steeper than the original one ?
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key points the budget constraint is the boundary of the opportunity set—all possible combinations of consumption that someone can afford given the prices of goods and the individual ’ s income . opportunity cost measures cost in terms of what must be given up in exchange . marginal analysis is the process of comparing the benefits and costs of choosing a little more or a little less of a certain good . the law of diminishing marginal utility indicates that as a person receives more of a good , the additional—or marginal—utility from each additional unit of the good declines . sunk costs are costs that occurred in the past and can not be recovered ; they should be disregarded in making current decisions . utility is the satisfaction , usefulness , or value one obtains from consuming goods and services . introduction most consumers have a limited amount of income to spend on the things they need and want . alphonso , for example , has \ $ 10 in spending money each week that he can use to buy bus tickets for getting to work and the burgers that he eats for lunch . burgers cost \ $ 2 each , and bus tickets are 50 cents each . there are a lot of combinations of burgers and bus tickets that alphonso could buy . so many , in fact , that it might be easier for us to describe the situation using a graph ! the figure above shows alphonso ’ s budget constraint—the outer boundary of his opportunity set . the opportunity set identifies all the opportunities for spending within his budget—in this case , bus tickets and burgers . the budget constraint indicates all the combinations of burgers and bus tickets alphonso can afford before he exhausts his budget , given the prices of the two goods . the vertical axis in the figure shows burger purchases , and the horizontal axis shows bus ticket purchases . if alphonso spends all his money on burgers , he can afford five per week—\ $ 10 per week divided by \ $ 2 per burger equals five burgers per week . but if alphonso uses all his money on burgers , he will not be able to afford any bus tickets . this choice—zero bus tickets and five burgers—is shown by point a in the figure . alternatively , if alphonso spends all his money on bus tickets , he can afford 20 per week—\ $ 10 per week divided by \ $ 0.50 per bus ticket equals 20 bus tickets per week . if he does this , however , he will not be able to afford any burgers . this choice—20 bus tickets and zero burgers—is shown by point f. if alphonso is like most people , he will choose some combination that includes both bus tickets and burgers . that is , he will choose some combination on the budget constraint that connects points a and f. every point on or inside the constraint shows a combination of burgers and bus tickets that alphonso can afford . any point outside the constraint is not affordable because it would cost more money than alphonso has in his budget . the budget constraint shows the tradeoff alphonso faces in choosing between burgers and bus tickets . suppose he is currently at point d , where he chooses to buy 12 bus tickets and two burgers . what would it cost alphonso for one more burger ? it would be natural to answer \ $ 2 , but that ’ s not the way economists think . economists think about the true cost of a burger—the number of bus tickets alphonso will have to sacrifice . what is opportunity cost ? economists use the term opportunity cost to indicate what must be given up to obtain something that is desired . the idea behind opportunity cost is that the cost of one item is the lost opportunity to do or consume something else ; in short , opportunity cost is the value of the next best alternative . for alphonso , the opportunity cost of a burger is the four bus tickets he would have to give up in order to afford another burger . he must decide whether or not to choose the burger depending on whether the value of the burger exceeds the value of the forgone alternative—in this case , bus tickets . since few if any people have unlimited financial resources , consumers inevitably face tradeoffs in which they have to give up things they desire to get other things they desire more . a fundamental principle of economics is that every choice has an opportunity cost . if you sleep through your economics class—not recommended , by the way—the opportunity cost is the learning you miss from not attending class . if you spend your income on video games , you can not spend it on movies . if you choose to marry one person , you give up the opportunity to marry anyone else . in short , opportunity cost is all around us and is part of human existence . understanding budget constraints one way for us to better understand budget constraints is to build an equation . let 's make $ p $ and $ q $ the price and quantity of items purchased and $ \text { budget } $ the amount of income one has to spend . $ \text { budget } =\text { p } { 1 } \mathrm { ~ \times ~ q } { 1 } \mathrm { ~ +~ p } { 2\ , } \mathrm { \times ~ q } { 2 } $ we can apply the budget constraint equation to alphonso 's scenario : $ \begin { array } { ccc } \text { budget } & amp ; = & amp ; \text { p } { 1 } \mathrm { \times q } { 1 } \mathrm { + p } { 2\ , } \mathrm { \times q } { 2 } \ \mathrm { \ $ 10 } & amp ; = & amp ; \mathrm { \ $ 2~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ \ $ 0.50~ \times ~ q } { \mathrm { bus~ tickets } } \end { array } $ using a little algebra , let 's turn this into the equation of a line : $ \begin { array } { ccc } \text { y } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { b~ +~ mx } \end { array } $ if we plug in the variables from alphonso 's scenario , we get the following : $ \begin { array } { ccc } \mathrm { \ $ 10 } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { \ $ 2~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ } \mathrm { \ $ 0.50 } \mathrm { ~ \times ~ } \text { q } { \mathrm { bus~ tickets } } \end { array } $ next , we simplify the equation by multiplying both sides of the equation by two : $ \begin { array } { ccc } \mathrm { 2~ \times ~ 10 } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { 2~ \times ~ 2~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ 2~ \times ~ 0.5~ \times ~ q } { \mathrm { bus~ tickets } } ~ \ \text { 20 } & amp ; \mathrm { ~ =~ } & amp ; \mathrm { 4~ \times ~ q } { \text { burgers } } \mathrm { ~ +~ 1~ \times ~ q } { \mathrm { bus~ tickets } } \end { array } $ then we subtract one bus ticket from both sides : $ \begin { array } { ccc } \mathrm { 20 - q } { \text { bus tickets } } & amp ; \mathrm { = } & amp ; \mathrm { 4 \times q } { \text { burgers } } \end { array } $ next , we divide each side by four to yield the answer : $ \begin { array } { ccc } \mathrm { 5 - 0.25 \times q } { \text { bus tickets } } & amp ; \mathrm { = } & amp ; \text { q } { \text { burgers } } \ & amp ; \text { or } & amp ; \ \text { q } { \text { burgers } } & amp ; \mathrm { = } & amp ; \mathrm { 5 - 0.25 \times q } { \text { bus tickets } } \end { array } $ notice that this equation fits alphonso 's budget constraint figure above . the vertical intercept is five and the slope is –0.25 , just as the equation says . if you plug 20 bus tickets into the equation , you get 0 burgers . if you plug other numbers of bus tickets into the equation , you get the results shown in the table below , which are also the points on alphonso ’ s budget constraint . point | quantity of burgers at \ $ 2 | quantity of bus tickets at 50 cents - | - | - a | 5 | 0 b | 4 | 4 c | 3 | 8 d | 2 | 12 e | 1 | 16 f | 0 | 20 notice that the slope of a budget constraint always shows the opportunity cost of the good which is on the horizontal axis . for alphonso , the slope is −0.25 , indicating that for every four bus tickets he buys , alphonso must give up one burger . there are two important observations here . first , the algebraic sign of the slope is negative , which means that the only way to get more of one good is to give up some of the other . second , the slope is defined as the price of whatever is on the horizontal axis in the graph—in this case , bus tickets—divided by the price of whatever is on the vertical axis—in this case , burgers . so , in our scenario , the slope is $ \ $ 0.50/\ $ 2 = 0.25 $ . if you want to determine the opportunity cost quickly , just divide the two prices . identifying opportunity cost in many cases , it is reasonable to refer to the opportunity cost as the price . if your cousin buys a new bicycle for \ $ 300 , then \ $ 300 measures the amount of other spending opportunities , or other consumption , that he has given up . for practical purposes , there may be no special need to identify the specific alternative product or products that could have been bought with that \ $ 300 , but sometimes the price as measured in dollars may not accurately capture the true opportunity cost . this problem can loom especially large when costs of time are involved . for example , consider a boss who decides that all employees will attend a two-day retreat to build team spirit . the out-of-pocket monetary cost of the event may involve hiring an outside consulting firm to run the retreat as well as room and board for all participants . but an opportunity cost exists as well : during the two days of the retreat , none of the employees are doing any other work . attending college is another case where the opportunity cost exceeds the monetary cost . the out-of-pocket costs of attending college include tuition , books , room and board , and other expenses . but in addition , during the hours that a student is attending class and studying , it is impossible for them to work at a paying job . thus , college imposes both an out-of-pocket cost and an opportunity cost of lost earnings . in some cases , recognizing opportunity cost can alter behavior . imagine , for example , that you spend \ $ 8 on lunch every day at work . you may know perfectly well that bringing a lunch from home would cost only \ $ 3 a day . so , the opportunity cost of buying lunch at the restaurant is \ $ 5 each day—the \ $ 8 buying lunch costs minus the \ $ 3 your lunch from home would cost . five dollars each day does not seem to be that much ; but , if you add up the cost over a year—250 days a year times \ $ 5 per day equals \ $ 1,250—it 's actually equivalent to a decent vacation . if the opportunity cost were described as “ a nice vacation ” instead of “ \ $ 5 a day ” , you might make different choices . marginal decision-making and diminishing marginal utility the budget constraint framework helps to emphasize that most choices in the real world are not about getting all of one thing or all of another—choosing a point at one end of the budget constraint or all the way at the other end . instead , most choices involve marginal analysis , comparing the benefits and costs of choosing a little more or a little less of a certain good . people desire goods and services for the satisfaction or utility those goods and services provide . utility is subjective , but that does n't make it any less real . economists typically assume that the more of some good one consumes—for example , slices of pizza—the more utility one obtains . at the same time , the utility a person receives from consuming the first unit of a good is typically more than the utility received from consuming the fifth or the 10th unit of that same good . when alphonso chooses between burgers and bus tickets , for example , the first few bus rides that he chooses might provide him with a great deal of utility—perhaps they help him get to a job interview or a doctor ’ s appointment . but later bus rides might provide much less utility—they may only serve to kill time on a rainy day . similarly , the first burger that alphonso chooses to buy may be on a day when he missed breakfast and is ravenously hungry . however , if alphonso has a burger every single day , the last few burgers may taste pretty boring . it is a common pattern for consumption of the first few units of any good to bring a higher level of utility to a person than consumption of later units . economists refer to this pattern—described succinctly , `` as a person receives more of a good , the additional , or marginal , utility from each additional unit of the good declines '' —as the law of diminishing marginal utility . you could describe this law in more simple terms as `` the first slice of pizza brings more satisfaction than the sixth . '' the law of diminishing marginal utility explains why people and societies rarely make all-or-nothing choices . you would probably not say , “ my favorite food is ice cream , so i will eat nothing but ice cream from now on. ” even though your favorite food has a high level of utility , if you chose to eat it exclusively , the additional or marginal utility from those last few servings would not be very high . similarly , most workers would not say : “ i enjoy leisure , so i ’ ll never work. ” instead , workers recognize that even though some leisure is very nice , a combination of all leisure and no income is not so attractive . the budget constraint framework suggests that when people make choices in a world of scarcity , they will use marginal analysis and think about whether they would prefer a little more or a little less . sunk costs in the budget constraint framework , all decisions involve what will happen next—what quantities of goods will you consume , how many hours will you work , or how much will you save . these decisions do not look back to past choices . thus , the budget constraint framework assumes that sunk costs—costs that were incurred in the past and can not be recovered—should not affect the current decision . consider the case of selena , who pays \ $ 8 to see a movie ; after watching the film for 30 minutes , she knows that it is truly terrible . should she stay and watch the rest of the movie because she paid for the ticket , or should she leave ? the money she spent is a sunk cost , and unless the theater manager is feeling kindly , selena will not get a refund . but , staying in the movie still means paying an opportunity cost in time . her choice is whether to spend the next 90 minutes suffering through a cinematic disaster or to do something—anything—else . the lesson of sunk costs is to forget about the money and time that is irretrievably gone and instead to focus on the marginal costs and benefits of current and future options . for people and firms alike , dealing with sunk costs can be frustrating . it often means admitting an earlier error in judgment . many firms , for example , find it hard to give up on a new product that is doing poorly because they spent so much money in creating and launching the product . but the lesson of sunk costs is to ignore them and make decisions based on what will happen in the future . from a model with two goods to one of many goods the budget constraint diagram we used to examine alphonso 's situation containing just two goods is not realistic . after all , in a modern economy people choose from thousands of goods . we can , however , think about a model with many goods by extending the ideas we 've discussed here . instead of drawing just one budget constraint showing the tradeoff between two goods , you can draw multiple budget constraints showing the possible tradeoffs between many different pairs of goods . or , in more advanced classes in economics , you would use mathematical equations that include many possible goods and services that can be purchased together with their quantities and prices to show how the total spending on all goods and services is limited to the overall budget available . it 's important to remember , though , that the graph above with two goods clearly illustrates that every choice has an opportunity cost , which is an idea that carries over to the real world . key concepts and summary economists see the real world as one of scarcity—a world in which people ’ s desires exceed what is possible . economic behavior involves tradeoffs in which individuals , firms , and society must give up something that they desire to obtain things that they desire more . individuals must choose which quantities and combinations of goods and services to consume . the budget constraint , which is the outer boundary of the opportunity set , illustrates the range of choices available . the slope of the budget constraint is determined by the relative price of the choices . choices beyond the budget constraint are not affordable . opportunity cost measures cost by what is given up in exchange . sometimes opportunity cost can be measured in money , but it is often useful to consider time costs as well or to measure opportunity cost in terms of the actual resources that must be given up . most economic decisions and tradeoffs are not all or nothing . instead , they involve marginal analysis , which means they are about decisions on the margin—involving a little more or a little less . the law of diminishing marginal utility points out that as a person receives more of something , whether it is a specific good or another resource , the additional marginal gains tend to become smaller . because sunk costs occurred in the past and can not be recovered , they should be disregarded in making current decisions . self-check question suppose alphonso ’ s town raised the price of bus tickets to \ $ 1 per trip , the price of burgers stayed at \ $ 2 , and alphonso 's budget remained \ $ 10 per week . draw alphonso ’ s new budget constraint . what happens to the opportunity cost of bus tickets ? review questions explain why scarcity leads to tradeoffs . explain why individuals make choices that are directly on the budget constraint rather than inside the budget constraint or outside it . critical thinking questions suppose alphonso ’ s town raises the price of bus tickets from \ $ 0.50 to \ $ 1 and the price of burgers rises from \ $ 2 to \ $ 4 . why is the opportunity cost of bus tickets unchanged ? suppose in addition to the above changes , alphonso ’ s weekly spending money increases from \ $ 10 to \ $ 20 . how is his budget constraint affected by all three changes ? explain . problems marie has a weekly budget of \ $ 24 , which she likes to spend on magazines and pies . if the price of one magazine is \ $ 4 , what is the maximum number of magazines she can buy in a week ? if the price of a pie is \ $ 12 , what is the maximum number of pies she can buy in a week ? draw marie ’ s budget constraint with pies on the horizontal axis and magazines on the vertical axis . what is the slope of the budget constraint ? what is marie ’ s opportunity cost of purchasing a pie ?
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that is , he will choose some combination on the budget constraint that connects points a and f. every point on or inside the constraint shows a combination of burgers and bus tickets that alphonso can afford . any point outside the constraint is not affordable because it would cost more money than alphonso has in his budget . the budget constraint shows the tradeoff alphonso faces in choosing between burgers and bus tickets .
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or would investments be part of the budget line ?
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in rebellious silence , the central figure ’ s portrait is bisected along a vertical seam created by the long barrel of a rifle . presumably the rifle is clasped in her hands near her lap , but the image is cropped so that the gun rises perpendicular to the lower edge of the photo and grazes her face at the lips , nose , and forehead . the woman 's eyes stare intensely towards the viewer from both sides of this divide . shirin neshat ’ s photographic series `` women of allah '' examines the complexities of women ’ s identities in the midst of a changing cultural landscape in the middle east—both through the lens of western representations of muslim women , and through the more intimate subject of personal and religious conviction . while the composition—defined by the hard edge of her black chador against the bright white background—appears sparse , measured and symmetrical , the split created by the weapon implies a more violent rupture or psychic fragmentation . a single subject , it suggests , might be host to internal contradictions alongside binaries such as tradition and modernity , east and west , beauty and violence . in the artist ’ s own words , “ every image , every woman ’ s submissive gaze , suggests a far more complex and paradoxical reality behind the surface. ” [ 1 ] shirin neshat , rebellious silence , women of allah series , 1994 , b & amp ; w rc print & amp ; ink , photo by cynthia preston ©shirin neshat ( courtesy barbara gladstone gallery , new york and brussel ) the women of allah series confronts this “ paradoxical reality ” through a haunting suite of black-and-white images . each contains a set of four symbols that are associated with western representations of the muslim world : the veil , the gun , the text and the gaze . while these symbols have taken on a particular charge since 9/11 , the series was created earlier and reflects changes that have taken place in the region since 1979 , the year of the islamic revolution in iran . islamic revolution iran had been ruled by the shah ( mohammad reza pahlavi ) , who took power in 1941 during the second world war and reigned as king until 1979 , when the persian monarchy was overthrown by revolutionaries . his dictatorship was known for the violent repression of political and religious freedom , but also for its modernization of the country along western cultural models . post-war iran was an ally of britain and the united states , and was markedly progressive with regards to women ’ s rights . the shah ’ s regime , however , steadily grew more restrictive , and revolutionaries eventually rose to abolish the monarchy in favor of a conservative religious government headed by ayatollah khomeini . shirin neshat was born in 1957 in the town of qazvin . in line with the shah ’ s expansion of women ’ s rights , her father prioritized his daughters ’ access to education , and the young artist attended a catholic school where she learned about both western and iranian intellectual and cultural history . she left , however , in the mid-1970s , pursuing her studies in california as the environment in iran grew increasingly hostile . it would be seventeen years before she returned to her homeland . when she did , she confronted a society that was completely opposed to the one that she had grown up in . looking back one of the most visible signs of cultural change in iran has been the requirement for all women to wear the veil in public . while many muslim women find this practice empowering and affirmative of their religious identities , the veil has been coded in western eyes as a sign of islam ’ s oppression of women . this opposition is made more clear , perhaps , when one considers the simultaneity of the islamic revolution with women ’ s liberation movements in the u.s. and europe , both developing throughout the 1970s . neshat decided to explore this fraught symbol in her art as a way to reconcile her own conflicting feelings . in women of allah , initiated shortly after her return to iran in 1991 , the veil functions as both a symbol of freedom and of repression . the veil and the gaze the veil is intended to protect women ’ s bodies from becoming the sexualized object of the male gaze , but it also protects women from being seen at all . the “ gaze ” in this context becomes a charged signifier of sexuality , sin , shame , and power . neshat is cognizant of feminist theories that explain how the “ male gaze ” is normalized in visual and popular culture : women ’ s bodies are commonly paraded as objects of desire in advertising and film , available to be looked at without consequence . many feminist artists have used the action of “ gazing back ” as a means to free the female body from this objectification . the gaze , here , might also reflect exotic fantasies of the east . in orientalist painting of the eighteenth and nineteenth centuries , for instance , eastern women are often depicted nude , surrounded by richly colored and patterned textiles and decorations ; women are envisaged amongst other beautiful objects that can be possessed . in neshat ’ s images , women return the gaze , breaking free from centuries of subservience to male or european desire . most of the subjects in the series are photographed holding a gun , sometimes passively , as in rebellious silence , and sometimes threateningly , with the muzzle pointed directly towards the camera lens . with the complex ideas of the “ gaze ” in mind , we might reflect on the double meaning of the word “ shoot , ” and consider that the camera—especially during the colonial era—was used to violate women ’ s bodies . the gun , aside from its obvious references to control , also represents religious martyrdom , a subject about which the artist feels ambivalently , as an outsider to iranian revolutionary culture . poetry the contradictions between piety and violence , empowerment and suppression , are most prevalent in the use of calligraphic text that is applied to each photograph . western viewers who do not read farsi may understand the calligraphy as an aesthetic signifier , a reference to the importance of text in the long history of islamic art . yet , most of the texts are transcriptions of poetry and other writings by women , which express multiple viewpoints and date both before and after the revolution . some of the texts that neshat has chosen are feminist in nature . however , in rebellious silence , the script that runs across the artist 's face is from tahereh saffarzadeh ’ s poem “ allegiance with wakefulness ” which honors the conviction and bravery of martyrdom . reflecting the paradoxical nature of each of these themes , histories and discourses , the photograph is both melancholic and powerful—invoking the quiet and intense beauty for which neshat ’ s work has become known . as an outspoken , feminist and progressive artist , neshat is aware that it would be dangerous to show her work in conservative modern-day iran , and she has been living in exile in the united states since the 1990s . for audiences in the west , the `` women of allah '' series has allowed a more nuanced contemplation of common stereotypes and assumptions about muslim women , and serves to challenge the suppression of female voices in any community . essay by allison young [ 1 ] shirin neshat , “ artist statement , ” signs journal , http : //signsjournal.org/shirin-neshat/ ( accessed july 2015 ) additional resources : neshat at gladstone gallery neshat on npr ( audio ) neshat from lacma interview with neshat from pbs
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in women of allah , initiated shortly after her return to iran in 1991 , the veil functions as both a symbol of freedom and of repression . the veil and the gaze the veil is intended to protect women ’ s bodies from becoming the sexualized object of the male gaze , but it also protects women from being seen at all . the “ gaze ” in this context becomes a charged signifier of sexuality , sin , shame , and power .
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how were ( or are ) women 's bodies violated with cameras ?
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in rebellious silence , the central figure ’ s portrait is bisected along a vertical seam created by the long barrel of a rifle . presumably the rifle is clasped in her hands near her lap , but the image is cropped so that the gun rises perpendicular to the lower edge of the photo and grazes her face at the lips , nose , and forehead . the woman 's eyes stare intensely towards the viewer from both sides of this divide . shirin neshat ’ s photographic series `` women of allah '' examines the complexities of women ’ s identities in the midst of a changing cultural landscape in the middle east—both through the lens of western representations of muslim women , and through the more intimate subject of personal and religious conviction . while the composition—defined by the hard edge of her black chador against the bright white background—appears sparse , measured and symmetrical , the split created by the weapon implies a more violent rupture or psychic fragmentation . a single subject , it suggests , might be host to internal contradictions alongside binaries such as tradition and modernity , east and west , beauty and violence . in the artist ’ s own words , “ every image , every woman ’ s submissive gaze , suggests a far more complex and paradoxical reality behind the surface. ” [ 1 ] shirin neshat , rebellious silence , women of allah series , 1994 , b & amp ; w rc print & amp ; ink , photo by cynthia preston ©shirin neshat ( courtesy barbara gladstone gallery , new york and brussel ) the women of allah series confronts this “ paradoxical reality ” through a haunting suite of black-and-white images . each contains a set of four symbols that are associated with western representations of the muslim world : the veil , the gun , the text and the gaze . while these symbols have taken on a particular charge since 9/11 , the series was created earlier and reflects changes that have taken place in the region since 1979 , the year of the islamic revolution in iran . islamic revolution iran had been ruled by the shah ( mohammad reza pahlavi ) , who took power in 1941 during the second world war and reigned as king until 1979 , when the persian monarchy was overthrown by revolutionaries . his dictatorship was known for the violent repression of political and religious freedom , but also for its modernization of the country along western cultural models . post-war iran was an ally of britain and the united states , and was markedly progressive with regards to women ’ s rights . the shah ’ s regime , however , steadily grew more restrictive , and revolutionaries eventually rose to abolish the monarchy in favor of a conservative religious government headed by ayatollah khomeini . shirin neshat was born in 1957 in the town of qazvin . in line with the shah ’ s expansion of women ’ s rights , her father prioritized his daughters ’ access to education , and the young artist attended a catholic school where she learned about both western and iranian intellectual and cultural history . she left , however , in the mid-1970s , pursuing her studies in california as the environment in iran grew increasingly hostile . it would be seventeen years before she returned to her homeland . when she did , she confronted a society that was completely opposed to the one that she had grown up in . looking back one of the most visible signs of cultural change in iran has been the requirement for all women to wear the veil in public . while many muslim women find this practice empowering and affirmative of their religious identities , the veil has been coded in western eyes as a sign of islam ’ s oppression of women . this opposition is made more clear , perhaps , when one considers the simultaneity of the islamic revolution with women ’ s liberation movements in the u.s. and europe , both developing throughout the 1970s . neshat decided to explore this fraught symbol in her art as a way to reconcile her own conflicting feelings . in women of allah , initiated shortly after her return to iran in 1991 , the veil functions as both a symbol of freedom and of repression . the veil and the gaze the veil is intended to protect women ’ s bodies from becoming the sexualized object of the male gaze , but it also protects women from being seen at all . the “ gaze ” in this context becomes a charged signifier of sexuality , sin , shame , and power . neshat is cognizant of feminist theories that explain how the “ male gaze ” is normalized in visual and popular culture : women ’ s bodies are commonly paraded as objects of desire in advertising and film , available to be looked at without consequence . many feminist artists have used the action of “ gazing back ” as a means to free the female body from this objectification . the gaze , here , might also reflect exotic fantasies of the east . in orientalist painting of the eighteenth and nineteenth centuries , for instance , eastern women are often depicted nude , surrounded by richly colored and patterned textiles and decorations ; women are envisaged amongst other beautiful objects that can be possessed . in neshat ’ s images , women return the gaze , breaking free from centuries of subservience to male or european desire . most of the subjects in the series are photographed holding a gun , sometimes passively , as in rebellious silence , and sometimes threateningly , with the muzzle pointed directly towards the camera lens . with the complex ideas of the “ gaze ” in mind , we might reflect on the double meaning of the word “ shoot , ” and consider that the camera—especially during the colonial era—was used to violate women ’ s bodies . the gun , aside from its obvious references to control , also represents religious martyrdom , a subject about which the artist feels ambivalently , as an outsider to iranian revolutionary culture . poetry the contradictions between piety and violence , empowerment and suppression , are most prevalent in the use of calligraphic text that is applied to each photograph . western viewers who do not read farsi may understand the calligraphy as an aesthetic signifier , a reference to the importance of text in the long history of islamic art . yet , most of the texts are transcriptions of poetry and other writings by women , which express multiple viewpoints and date both before and after the revolution . some of the texts that neshat has chosen are feminist in nature . however , in rebellious silence , the script that runs across the artist 's face is from tahereh saffarzadeh ’ s poem “ allegiance with wakefulness ” which honors the conviction and bravery of martyrdom . reflecting the paradoxical nature of each of these themes , histories and discourses , the photograph is both melancholic and powerful—invoking the quiet and intense beauty for which neshat ’ s work has become known . as an outspoken , feminist and progressive artist , neshat is aware that it would be dangerous to show her work in conservative modern-day iran , and she has been living in exile in the united states since the 1990s . for audiences in the west , the `` women of allah '' series has allowed a more nuanced contemplation of common stereotypes and assumptions about muslim women , and serves to challenge the suppression of female voices in any community . essay by allison young [ 1 ] shirin neshat , “ artist statement , ” signs journal , http : //signsjournal.org/shirin-neshat/ ( accessed july 2015 ) additional resources : neshat at gladstone gallery neshat on npr ( audio ) neshat from lacma interview with neshat from pbs
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the gaze , here , might also reflect exotic fantasies of the east . in orientalist painting of the eighteenth and nineteenth centuries , for instance , eastern women are often depicted nude , surrounded by richly colored and patterned textiles and decorations ; women are envisaged amongst other beautiful objects that can be possessed . in neshat ’ s images , women return the gaze , breaking free from centuries of subservience to male or european desire .
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did early users of cameras and/or imperialist colonizers , such as the british , u.s. , french , or even dutch or other westerners , or even imperial japan , force women in their colonies to be photographed nude ?
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in rebellious silence , the central figure ’ s portrait is bisected along a vertical seam created by the long barrel of a rifle . presumably the rifle is clasped in her hands near her lap , but the image is cropped so that the gun rises perpendicular to the lower edge of the photo and grazes her face at the lips , nose , and forehead . the woman 's eyes stare intensely towards the viewer from both sides of this divide . shirin neshat ’ s photographic series `` women of allah '' examines the complexities of women ’ s identities in the midst of a changing cultural landscape in the middle east—both through the lens of western representations of muslim women , and through the more intimate subject of personal and religious conviction . while the composition—defined by the hard edge of her black chador against the bright white background—appears sparse , measured and symmetrical , the split created by the weapon implies a more violent rupture or psychic fragmentation . a single subject , it suggests , might be host to internal contradictions alongside binaries such as tradition and modernity , east and west , beauty and violence . in the artist ’ s own words , “ every image , every woman ’ s submissive gaze , suggests a far more complex and paradoxical reality behind the surface. ” [ 1 ] shirin neshat , rebellious silence , women of allah series , 1994 , b & amp ; w rc print & amp ; ink , photo by cynthia preston ©shirin neshat ( courtesy barbara gladstone gallery , new york and brussel ) the women of allah series confronts this “ paradoxical reality ” through a haunting suite of black-and-white images . each contains a set of four symbols that are associated with western representations of the muslim world : the veil , the gun , the text and the gaze . while these symbols have taken on a particular charge since 9/11 , the series was created earlier and reflects changes that have taken place in the region since 1979 , the year of the islamic revolution in iran . islamic revolution iran had been ruled by the shah ( mohammad reza pahlavi ) , who took power in 1941 during the second world war and reigned as king until 1979 , when the persian monarchy was overthrown by revolutionaries . his dictatorship was known for the violent repression of political and religious freedom , but also for its modernization of the country along western cultural models . post-war iran was an ally of britain and the united states , and was markedly progressive with regards to women ’ s rights . the shah ’ s regime , however , steadily grew more restrictive , and revolutionaries eventually rose to abolish the monarchy in favor of a conservative religious government headed by ayatollah khomeini . shirin neshat was born in 1957 in the town of qazvin . in line with the shah ’ s expansion of women ’ s rights , her father prioritized his daughters ’ access to education , and the young artist attended a catholic school where she learned about both western and iranian intellectual and cultural history . she left , however , in the mid-1970s , pursuing her studies in california as the environment in iran grew increasingly hostile . it would be seventeen years before she returned to her homeland . when she did , she confronted a society that was completely opposed to the one that she had grown up in . looking back one of the most visible signs of cultural change in iran has been the requirement for all women to wear the veil in public . while many muslim women find this practice empowering and affirmative of their religious identities , the veil has been coded in western eyes as a sign of islam ’ s oppression of women . this opposition is made more clear , perhaps , when one considers the simultaneity of the islamic revolution with women ’ s liberation movements in the u.s. and europe , both developing throughout the 1970s . neshat decided to explore this fraught symbol in her art as a way to reconcile her own conflicting feelings . in women of allah , initiated shortly after her return to iran in 1991 , the veil functions as both a symbol of freedom and of repression . the veil and the gaze the veil is intended to protect women ’ s bodies from becoming the sexualized object of the male gaze , but it also protects women from being seen at all . the “ gaze ” in this context becomes a charged signifier of sexuality , sin , shame , and power . neshat is cognizant of feminist theories that explain how the “ male gaze ” is normalized in visual and popular culture : women ’ s bodies are commonly paraded as objects of desire in advertising and film , available to be looked at without consequence . many feminist artists have used the action of “ gazing back ” as a means to free the female body from this objectification . the gaze , here , might also reflect exotic fantasies of the east . in orientalist painting of the eighteenth and nineteenth centuries , for instance , eastern women are often depicted nude , surrounded by richly colored and patterned textiles and decorations ; women are envisaged amongst other beautiful objects that can be possessed . in neshat ’ s images , women return the gaze , breaking free from centuries of subservience to male or european desire . most of the subjects in the series are photographed holding a gun , sometimes passively , as in rebellious silence , and sometimes threateningly , with the muzzle pointed directly towards the camera lens . with the complex ideas of the “ gaze ” in mind , we might reflect on the double meaning of the word “ shoot , ” and consider that the camera—especially during the colonial era—was used to violate women ’ s bodies . the gun , aside from its obvious references to control , also represents religious martyrdom , a subject about which the artist feels ambivalently , as an outsider to iranian revolutionary culture . poetry the contradictions between piety and violence , empowerment and suppression , are most prevalent in the use of calligraphic text that is applied to each photograph . western viewers who do not read farsi may understand the calligraphy as an aesthetic signifier , a reference to the importance of text in the long history of islamic art . yet , most of the texts are transcriptions of poetry and other writings by women , which express multiple viewpoints and date both before and after the revolution . some of the texts that neshat has chosen are feminist in nature . however , in rebellious silence , the script that runs across the artist 's face is from tahereh saffarzadeh ’ s poem “ allegiance with wakefulness ” which honors the conviction and bravery of martyrdom . reflecting the paradoxical nature of each of these themes , histories and discourses , the photograph is both melancholic and powerful—invoking the quiet and intense beauty for which neshat ’ s work has become known . as an outspoken , feminist and progressive artist , neshat is aware that it would be dangerous to show her work in conservative modern-day iran , and she has been living in exile in the united states since the 1990s . for audiences in the west , the `` women of allah '' series has allowed a more nuanced contemplation of common stereotypes and assumptions about muslim women , and serves to challenge the suppression of female voices in any community . essay by allison young [ 1 ] shirin neshat , “ artist statement , ” signs journal , http : //signsjournal.org/shirin-neshat/ ( accessed july 2015 ) additional resources : neshat at gladstone gallery neshat on npr ( audio ) neshat from lacma interview with neshat from pbs
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in rebellious silence , the central figure ’ s portrait is bisected along a vertical seam created by the long barrel of a rifle . presumably the rifle is clasped in her hands near her lap , but the image is cropped so that the gun rises perpendicular to the lower edge of the photo and grazes her face at the lips , nose , and forehead .
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what is the meaning behind the rifle in the rebellious silence ?
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intimate and lively tlatilco figurines are wonderful small ceramic figures , often of women , found in central mexico . this is the region of the later and much better-known aztec empire , but the people of tlatilco flourished 2,000-3,000 years before the aztec came to power in this valley . although tlatilco was already settled by the early preclassic period ( c. 1800-1200 b.c.e . ) , most scholars believe that the many figurines date from the middle preclassic period , or about 1200-400 b.c.e . their intimate , lively poses and elaborate hairstyles are indicative of the already sophisticated artistic tradition . this is remarkable given the early dates . ceramic figures of any sort were widespread for only a few centuries before the appearance of tlatilco figurines . appearance the tlatilco figurine at the princeton university art museum has several traits that directly relate to many other tlatilco female figures : the emphasis on the wide hips , the spherical upper thighs , and the pinched waist . many tlatilco figurines also show no interest in the hands or feet , as we see here . artists treated hairstyles with great care and detail , however , suggesting that it was hair and its styling was important for the people of tlatilco , as it was for many peoples of this region . this figurine not only shows an elaborate hairstyle , but shows it for two connected heads ( on the single body ) . we have other two-headed femaile figures from tlatilco , but they are rare when compared with the figures that show a single head . it is very difficult to know exactly why the artist depicted a bicephalic ( two-headed ) figure ( as opposed to the normal single head ) , as we have no documents or other aids that would help us define the meaning . it may be that the people of tlatilco were interested in expressing an idea of duality , as many scholars have argued . the makers of tlatilco figurines lived in a large farming village near the great inland lake in the center of the basin of mexico . modern mexico city sits on top of the remains of the village , making archaeological work difficult . we don ’ t know what the village would have looked beyond the basic shape of the common house—a mud and reed hut that was the favored house design of many early peoples of mexico . we do know that most of the inhabitants made their living by growing maize ( corn ) and taking advantage of the rich lake resources nearby . some of the motifs found on other tlatilco ceramics , such as ducks and fish , would have come directly from their lakeside surroundings . male figures are rare tlatilco artists rarely depicted males , but when they did the males were often wearing costumes and even masks . masks were very rare on female figures ; most female figures stress hairstyle and/or body paint . thus the male figures seem to be valued more for their ritual roles as priests or other religious specialists , while the religious role of the females is less clear but was very likely present . how they were found in the first half of the 20th century , a great number of graves were found by brick-makers mining clay in the area . these brick-makers would often sell the objects—many of them figurines—that came out of these graves to interested collectors . later archaeologists were able to dig a number of complete burials , and they too found a wealth of objects buried with the dead . the objects that were found in largest quantities—and that enchanted many collectors and scholars of ancient mexico—were the ceramic figurines . craftsmanship unlike some later mexican figurines , those of tlatilco were made exclusively by hand , without relying on molds . it is important to think , then , about the consistent mastery shown by the artists of many of these figurines . the main forms were created through pinching the clay and then shaping it by hand , while some of the details were created by a sharp instrument cutting linear motifs onto the wet clay . the forms of the body were depicted in a specific proportion that , while non-naturalistic , was striking and effective . the artist was given a very small space ( most figures are less than 15 cm high ) in which to create elaborate hairstyles . even for today ’ s viewer , the details in this area are endlessly fascinating . the pieces have a nice finish , and the paint that must indicate body decoration was firmly applied ( when it is preserved , as in the two-headed figure above ) . many scholars doubt that there were already full-time artists in such farming villages , but it is certain that the skills necessary to function as an artist in the tradition were passed down and mastered over generations . essay by dr. rex koontz additional resources : ceramics from tlatilco ( including the two headed figurine at the princeton art museum ) national museum of anthropology , mexico city
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the makers of tlatilco figurines lived in a large farming village near the great inland lake in the center of the basin of mexico . modern mexico city sits on top of the remains of the village , making archaeological work difficult . we don ’ t know what the village would have looked beyond the basic shape of the common house—a mud and reed hut that was the favored house design of many early peoples of mexico .
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i wonder if the figurine at the top could be of a pair of actual olmec conjoined diprosopus twins ?
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intimate and lively tlatilco figurines are wonderful small ceramic figures , often of women , found in central mexico . this is the region of the later and much better-known aztec empire , but the people of tlatilco flourished 2,000-3,000 years before the aztec came to power in this valley . although tlatilco was already settled by the early preclassic period ( c. 1800-1200 b.c.e . ) , most scholars believe that the many figurines date from the middle preclassic period , or about 1200-400 b.c.e . their intimate , lively poses and elaborate hairstyles are indicative of the already sophisticated artistic tradition . this is remarkable given the early dates . ceramic figures of any sort were widespread for only a few centuries before the appearance of tlatilco figurines . appearance the tlatilco figurine at the princeton university art museum has several traits that directly relate to many other tlatilco female figures : the emphasis on the wide hips , the spherical upper thighs , and the pinched waist . many tlatilco figurines also show no interest in the hands or feet , as we see here . artists treated hairstyles with great care and detail , however , suggesting that it was hair and its styling was important for the people of tlatilco , as it was for many peoples of this region . this figurine not only shows an elaborate hairstyle , but shows it for two connected heads ( on the single body ) . we have other two-headed femaile figures from tlatilco , but they are rare when compared with the figures that show a single head . it is very difficult to know exactly why the artist depicted a bicephalic ( two-headed ) figure ( as opposed to the normal single head ) , as we have no documents or other aids that would help us define the meaning . it may be that the people of tlatilco were interested in expressing an idea of duality , as many scholars have argued . the makers of tlatilco figurines lived in a large farming village near the great inland lake in the center of the basin of mexico . modern mexico city sits on top of the remains of the village , making archaeological work difficult . we don ’ t know what the village would have looked beyond the basic shape of the common house—a mud and reed hut that was the favored house design of many early peoples of mexico . we do know that most of the inhabitants made their living by growing maize ( corn ) and taking advantage of the rich lake resources nearby . some of the motifs found on other tlatilco ceramics , such as ducks and fish , would have come directly from their lakeside surroundings . male figures are rare tlatilco artists rarely depicted males , but when they did the males were often wearing costumes and even masks . masks were very rare on female figures ; most female figures stress hairstyle and/or body paint . thus the male figures seem to be valued more for their ritual roles as priests or other religious specialists , while the religious role of the females is less clear but was very likely present . how they were found in the first half of the 20th century , a great number of graves were found by brick-makers mining clay in the area . these brick-makers would often sell the objects—many of them figurines—that came out of these graves to interested collectors . later archaeologists were able to dig a number of complete burials , and they too found a wealth of objects buried with the dead . the objects that were found in largest quantities—and that enchanted many collectors and scholars of ancient mexico—were the ceramic figurines . craftsmanship unlike some later mexican figurines , those of tlatilco were made exclusively by hand , without relying on molds . it is important to think , then , about the consistent mastery shown by the artists of many of these figurines . the main forms were created through pinching the clay and then shaping it by hand , while some of the details were created by a sharp instrument cutting linear motifs onto the wet clay . the forms of the body were depicted in a specific proportion that , while non-naturalistic , was striking and effective . the artist was given a very small space ( most figures are less than 15 cm high ) in which to create elaborate hairstyles . even for today ’ s viewer , the details in this area are endlessly fascinating . the pieces have a nice finish , and the paint that must indicate body decoration was firmly applied ( when it is preserved , as in the two-headed figure above ) . many scholars doubt that there were already full-time artists in such farming villages , but it is certain that the skills necessary to function as an artist in the tradition were passed down and mastered over generations . essay by dr. rex koontz additional resources : ceramics from tlatilco ( including the two headed figurine at the princeton art museum ) national museum of anthropology , mexico city
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intimate and lively tlatilco figurines are wonderful small ceramic figures , often of women , found in central mexico . this is the region of the later and much better-known aztec empire , but the people of tlatilco flourished 2,000-3,000 years before the aztec came to power in this valley .
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in your opinion , why would be important for this community to replicate daily day actions in ceramic ?
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overview proponents of the new south envisioned a post-reconstruction southern economy modeled on the north ’ s embrace of the industrial revolution . henry w. grady , a newspaper editor in atlanta , georgia , coined the phrase the `` new south ” in 1874 . he urged the south to abandon its longstanding agrarian economy for a modern economy grounded in factories , mines , and mills . but grady ’ s vision was not to be . by 1900 , per-capita income in the south was forty percent less than the national average , and rural poverty persisted across much of the south well into the twentieth century . rural agrarian poverty after the civil war , sharecropping and tenant farming took the place of slavery and the plantation system in the south . sharecropping and tenant farming were systems in which white landlords ( often former plantation slaveowners ) entered into contracts with impoverished farm laborers to work their lands . those who worked the fields shared a portion of the crop yield with the landlord as payment for renting the land . under the sharecropping system , the landlord typically supplied the capital to buy the seed and equipment needed to sow , cultivate , and harvest a crop , while the sharecropper supplied the labor . in other tenancy farming arrangements the laborer , not the landowner , took responsibility for purchase of seed and equipment . yet , because prices on cotton and other crops remained low , sharecroppers and tenant farmers often fell into a cycle of indebtedness called debt peonage : farmers found that the money they made selling their crops at the end of the growing season was not enough to pay back the loans they had taken out for seed , tools , farm equipment , and living expenses , leaving them owing more after a year of labor than they had when they started . this system left both black and white tenant farmers living in dire poverty . in addition , since no one had any money to spend , the southern economy stagnated. $ ^1 $ an economic vision for a new south enter henry w. grady , editor of the atlanta constitution , a newspaper in georgia ’ s capital city . in a series of impassioned public speeches and articles , grady envisioned a southern economy enriched with broadly expanded manufacturing facilities and commerce . grady and like-minded southerners referred to this regional economic remake as the “ new south. ” following the civil war , the north experienced a period of rapid industrialization and technological advancement known as the second industrial revolution . but the dynamic and expansive economic growth that came to the north in consequence of the second industrial revolution largely bypassed the south . proponents of the new south wanted the nation ’ s southern states to remake themselves along similar lines. $ ^2 $ successes and failures of the new south there were some new south successes . birmingham , alabama prospered from iron and steel manufacturing , and mining and furniture production benefited other parts of the south . likewise , james duke made use of newly-invented cigarette rolling machines to feed the growing market for tobacco and founded the american tobacco company in north carolina in 1890 . the most notable new south initiative was the introduction of textile mills in the south . beginning in the early 1880s , northern capitalists invested in building textile mills in the southern appalachian foothills of north carolina , south carolina , and georgia , drawn to the region by the fact that they could pay southern mill workers at half the rate of workers in northern mills . in consequence of the low wages the mills gave only a modest boost to the southern economies in which they were built. $ ^3 $ although new industries did emerge in this era , the benefits of the new south did not accrue to african americans or poor whites . although grady dreamed of a new south of increasing economic prosperity , his vision did not extend to civil rights for african americans . `` i declare , ” said grady in an 1888 address , “ that . . . the white race must dominate forever in the south. ” in the new south , landlords and factory owners prospered , but sharecropping and low-wage factory work kept many across the region from escaping dire poverty. $ ^4 $ what do you think ? what kept the southern economy from prospering in the post-civil war era ? what do you think your life would have been like if you had been a sharecropper or a textile mill worker in the late nineteenth and early twentieth century south ? why do you think henry w. grady ’ s vision of the new south did not include equality for african americans ?
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beginning in the early 1880s , northern capitalists invested in building textile mills in the southern appalachian foothills of north carolina , south carolina , and georgia , drawn to the region by the fact that they could pay southern mill workers at half the rate of workers in northern mills . in consequence of the low wages the mills gave only a modest boost to the southern economies in which they were built. $ ^3 $ although new industries did emerge in this era , the benefits of the new south did not accrue to african americans or poor whites . although grady dreamed of a new south of increasing economic prosperity , his vision did not extend to civil rights for african americans .
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were n't many of these new industries built upon labor supplied by convict lease ?
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overview proponents of the new south envisioned a post-reconstruction southern economy modeled on the north ’ s embrace of the industrial revolution . henry w. grady , a newspaper editor in atlanta , georgia , coined the phrase the `` new south ” in 1874 . he urged the south to abandon its longstanding agrarian economy for a modern economy grounded in factories , mines , and mills . but grady ’ s vision was not to be . by 1900 , per-capita income in the south was forty percent less than the national average , and rural poverty persisted across much of the south well into the twentieth century . rural agrarian poverty after the civil war , sharecropping and tenant farming took the place of slavery and the plantation system in the south . sharecropping and tenant farming were systems in which white landlords ( often former plantation slaveowners ) entered into contracts with impoverished farm laborers to work their lands . those who worked the fields shared a portion of the crop yield with the landlord as payment for renting the land . under the sharecropping system , the landlord typically supplied the capital to buy the seed and equipment needed to sow , cultivate , and harvest a crop , while the sharecropper supplied the labor . in other tenancy farming arrangements the laborer , not the landowner , took responsibility for purchase of seed and equipment . yet , because prices on cotton and other crops remained low , sharecroppers and tenant farmers often fell into a cycle of indebtedness called debt peonage : farmers found that the money they made selling their crops at the end of the growing season was not enough to pay back the loans they had taken out for seed , tools , farm equipment , and living expenses , leaving them owing more after a year of labor than they had when they started . this system left both black and white tenant farmers living in dire poverty . in addition , since no one had any money to spend , the southern economy stagnated. $ ^1 $ an economic vision for a new south enter henry w. grady , editor of the atlanta constitution , a newspaper in georgia ’ s capital city . in a series of impassioned public speeches and articles , grady envisioned a southern economy enriched with broadly expanded manufacturing facilities and commerce . grady and like-minded southerners referred to this regional economic remake as the “ new south. ” following the civil war , the north experienced a period of rapid industrialization and technological advancement known as the second industrial revolution . but the dynamic and expansive economic growth that came to the north in consequence of the second industrial revolution largely bypassed the south . proponents of the new south wanted the nation ’ s southern states to remake themselves along similar lines. $ ^2 $ successes and failures of the new south there were some new south successes . birmingham , alabama prospered from iron and steel manufacturing , and mining and furniture production benefited other parts of the south . likewise , james duke made use of newly-invented cigarette rolling machines to feed the growing market for tobacco and founded the american tobacco company in north carolina in 1890 . the most notable new south initiative was the introduction of textile mills in the south . beginning in the early 1880s , northern capitalists invested in building textile mills in the southern appalachian foothills of north carolina , south carolina , and georgia , drawn to the region by the fact that they could pay southern mill workers at half the rate of workers in northern mills . in consequence of the low wages the mills gave only a modest boost to the southern economies in which they were built. $ ^3 $ although new industries did emerge in this era , the benefits of the new south did not accrue to african americans or poor whites . although grady dreamed of a new south of increasing economic prosperity , his vision did not extend to civil rights for african americans . `` i declare , ” said grady in an 1888 address , “ that . . . the white race must dominate forever in the south. ” in the new south , landlords and factory owners prospered , but sharecropping and low-wage factory work kept many across the region from escaping dire poverty. $ ^4 $ what do you think ? what kept the southern economy from prospering in the post-civil war era ? what do you think your life would have been like if you had been a sharecropper or a textile mill worker in the late nineteenth and early twentieth century south ? why do you think henry w. grady ’ s vision of the new south did not include equality for african americans ?
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this system left both black and white tenant farmers living in dire poverty . in addition , since no one had any money to spend , the southern economy stagnated. $ ^1 $ an economic vision for a new south enter henry w. grady , editor of the atlanta constitution , a newspaper in georgia ’ s capital city . in a series of impassioned public speeches and articles , grady envisioned a southern economy enriched with broadly expanded manufacturing facilities and commerce .
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further depressing the real social-economic benefits of southern industrialization ?
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overview proponents of the new south envisioned a post-reconstruction southern economy modeled on the north ’ s embrace of the industrial revolution . henry w. grady , a newspaper editor in atlanta , georgia , coined the phrase the `` new south ” in 1874 . he urged the south to abandon its longstanding agrarian economy for a modern economy grounded in factories , mines , and mills . but grady ’ s vision was not to be . by 1900 , per-capita income in the south was forty percent less than the national average , and rural poverty persisted across much of the south well into the twentieth century . rural agrarian poverty after the civil war , sharecropping and tenant farming took the place of slavery and the plantation system in the south . sharecropping and tenant farming were systems in which white landlords ( often former plantation slaveowners ) entered into contracts with impoverished farm laborers to work their lands . those who worked the fields shared a portion of the crop yield with the landlord as payment for renting the land . under the sharecropping system , the landlord typically supplied the capital to buy the seed and equipment needed to sow , cultivate , and harvest a crop , while the sharecropper supplied the labor . in other tenancy farming arrangements the laborer , not the landowner , took responsibility for purchase of seed and equipment . yet , because prices on cotton and other crops remained low , sharecroppers and tenant farmers often fell into a cycle of indebtedness called debt peonage : farmers found that the money they made selling their crops at the end of the growing season was not enough to pay back the loans they had taken out for seed , tools , farm equipment , and living expenses , leaving them owing more after a year of labor than they had when they started . this system left both black and white tenant farmers living in dire poverty . in addition , since no one had any money to spend , the southern economy stagnated. $ ^1 $ an economic vision for a new south enter henry w. grady , editor of the atlanta constitution , a newspaper in georgia ’ s capital city . in a series of impassioned public speeches and articles , grady envisioned a southern economy enriched with broadly expanded manufacturing facilities and commerce . grady and like-minded southerners referred to this regional economic remake as the “ new south. ” following the civil war , the north experienced a period of rapid industrialization and technological advancement known as the second industrial revolution . but the dynamic and expansive economic growth that came to the north in consequence of the second industrial revolution largely bypassed the south . proponents of the new south wanted the nation ’ s southern states to remake themselves along similar lines. $ ^2 $ successes and failures of the new south there were some new south successes . birmingham , alabama prospered from iron and steel manufacturing , and mining and furniture production benefited other parts of the south . likewise , james duke made use of newly-invented cigarette rolling machines to feed the growing market for tobacco and founded the american tobacco company in north carolina in 1890 . the most notable new south initiative was the introduction of textile mills in the south . beginning in the early 1880s , northern capitalists invested in building textile mills in the southern appalachian foothills of north carolina , south carolina , and georgia , drawn to the region by the fact that they could pay southern mill workers at half the rate of workers in northern mills . in consequence of the low wages the mills gave only a modest boost to the southern economies in which they were built. $ ^3 $ although new industries did emerge in this era , the benefits of the new south did not accrue to african americans or poor whites . although grady dreamed of a new south of increasing economic prosperity , his vision did not extend to civil rights for african americans . `` i declare , ” said grady in an 1888 address , “ that . . . the white race must dominate forever in the south. ” in the new south , landlords and factory owners prospered , but sharecropping and low-wage factory work kept many across the region from escaping dire poverty. $ ^4 $ what do you think ? what kept the southern economy from prospering in the post-civil war era ? what do you think your life would have been like if you had been a sharecropper or a textile mill worker in the late nineteenth and early twentieth century south ? why do you think henry w. grady ’ s vision of the new south did not include equality for african americans ?
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those who worked the fields shared a portion of the crop yield with the landlord as payment for renting the land . under the sharecropping system , the landlord typically supplied the capital to buy the seed and equipment needed to sow , cultivate , and harvest a crop , while the sharecropper supplied the labor . in other tenancy farming arrangements the laborer , not the landowner , took responsibility for purchase of seed and equipment .
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why do the farmers ( sharecroppers ) have loans given that `` under the sharecropping system , the landlord typically supplied the capital to buy the seed and equipment needed to sow , cultivate , and harvest a crop '' ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion .
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what properties of such foods make it so ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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in the final paragraph what does atypical mean ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ?
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if it does develop over time does the pancreas just stop producing insulin ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood .
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are there any follow up articles about the benefits of eating a ketogenic way of eating , safely of course , to combat diabetes ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood .
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can people die from diabetes ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue .
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how can you help when you know that someone maybe in your family or a friend who has diabetes and they get those symptoms that you have shown in this article ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system .
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if a type 1 diabetic has ketoacids can it be treated with a high dose of insulin ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death .
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what is the difference between atherosclerosis caused by dm and high cholesterol concentration in the body ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system .
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in paragraph nine , talking about diabetes causing kidney damage , is the damage caused by large amounts of glucose going through the nephrons and stretching or harming them ?
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what is diabetes mellitus ? diabetes mellitus is a common disease where there is too much sugar ( glucose ) floating around in your blood . this occurs because either the pancreas can ’ t produce enough insulin or the cells in your body have become resistant to insulin . how does your body normally regulate glucose ? when you eat food , the amount of glucose in your blood skyrockets . that ’ s because the food you eat is converted into glucose ( usable energy for your cells ) and enters your blood to be transported to your cells around the body . special cells in your pancreas sense the increase of glucose and release insulin into your blood . insulin has a lot of different jobs , but one of its main tasks is to help decrease blood glucose levels . it does this by activating a system which transports glucose from your blood into your cells . it also decreases blood glucose by stimulating an enzyme called glycogen synthase in the liver . this molecule is responsible for making glycogen , a long string of glucose , which is then stored in the liver and used in the future when there is a period of low blood glucose . as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate . what happens in diabetes mellitus ? there are two types of diabetes mellitus , type 1 and type 2 . in both types , your body has trouble transporting sugar from your blood into your cells . this leads to high levels of glucose in your blood and a deficiency of glucose in your cells . the main difference between type 1 and type 2 diabetes mellitus is the underlying mechanisms that cause your blood sugar to stray from the normal range . type 1 dm : type 1 diabetics suffer from a complete lack of insulin in their bodies . although the exact cause has not been identified , it is clear that the cells which make insulin are destroyed by the body ’ s own immune system . this occurs due to autoimmunity , a process by which the immune system believes some of the body ’ s cells are foreign and targets them for destruction . eventually the body destroys all of these cells and the symptoms of diabetes manifest . type 2 dm : people with type 2 diabetes can still make insulin , but their cells have some degree of insulin resistance . type 2 diabetes is a continuum which begins with insulin resistance and can end in loss of insulin secretion . when cells initially become resistant to insulin , the body increases the amount of insulin made to counteract this effect and keep glucose levels in a normal range . in fact , early type 2 diabetics have higher levels of insulin in their body than non-diabetics . eventually the body can not compensate enough , and blood glucose levels begin to rise . the pancreatic cells begin working overtime to produce more and more insulin and eventually burn out . as type 2 diabetes continues to progress , patients have to start taking insulin to ensure they have enough of the molecule in their body . what are the symptoms of diabetes mellitus ? initial symptoms : type 1 : the classic initial presentation of type 1 diabetes is increased thirst , increased urination , weight loss , hunger due to starvation of cells , and fatigue . as blood glucose levels increase , the body tries to remove excess glucose in the urine and dilute the blood by increasing water intake . however , many patients are initially diagnosed when they come to the hospital very sick in a state called diabetic ketoacidosis . this occurs when cells use alternative energy producing mechanisms , leading to high levels of byproducts called ketoacids . ketoacids acidify the blood , leading to dangerous acid base disturbances . diabetic ketoacidosis causes abdominal pain , nausea/vomiting , and drowsiness and is a potentially life threatening condition . type 2 : the symptoms of type 2 dm are similar to type 1 , but generally occur later in life and have a more gradual onset . 40 % of patients have no symptoms . the other 60 % can present with increased thirst and urination , diabetic ketoacidosis , or a condition called hyperosmolar hyperglycemic state , a state of severe dehydration requiring hospitalization . long-term complications of diabetes mellitus : many of the major complications of diabetes , including coronary artery disease , cardiovascular disease , peripheral vascular disease , and cerebrovascular disease are caused by damage to large vessels in the body . high glucose levels lead to chronic inflammation in the body , including the walls of the arteries in the blood . this chronic inflammation leads to atherosclerosis , a buildup of a plaque with a fibrous cap on the walls of the arteries . this narrows the arteries and leads to decreased blood flow in the arteries . in addition , these plaques can rupture and lead to formation of a blood clot which blocks off blood flow . if this happens in the brain or the heart , it causes a stroke or a heart attack . high blood glucose levels may also damage the smallest vessels in the body , leading to multiple long-term microvascular complications . this damage both destroys the cells in the blood vessels and leads to decreased blood flow and tissue death . poorly controlled diabetes can cause retinopathy ( damage to the retina in the eyes , leading to blindness ) , nephropathy ( damage to the kidneys resulting in kidney failure ) , neuropathy ( damage to your nerves , which can cause numbness or tingling ) , and gastroparesis ( dysfunction of your digestive system causing chronic vomiting and abdominal pain ) . all of these symptoms are caused by glucose induced damage to blood vessels . diabetes has a large negative effect on the body ’ s immune system . high glucose levels ramp up activity of immune cells . these cells eventually become exhausted and desensitized , decreasing their effectiveness against invading pathogens . poorly controlled diabetics are more prone to severe skin infections and have longer hospital stays for infections like pneumonia or urinary tract infections . how likely are you to get it ? it ’ s unclear who gets type 1 diabetes or how to prevent it . given the main cause of type 1 diabetes is autoimmunity , environmental factors is likely the largest risk factor . type 2 diabetes , on the other hand , is directly related to obesity and diet . overweight individual become more and more resistant to insulin and are much more likely to get diabetes . physical fitness and a healthy diet are the most important aspects of type 2 diabetes prevention . both types of diabetes have genetic predispositions , with type 2 having a larger genetic component to disease . how do you treat it ? the only effective treatment in type 1 diabetes is administering insulin as these patients no longer produce it . there are many different types of insulin and different regimens but many patients will use a long-acting insulin at night supplemented by a short-acting insulin before meal times . newer treatment regimens include the use of an insulin pump where blood glucose levels are entered into a machine which then uses an algorithm to pump insulin into the body . type 2 diabetics have more options . initial therapy for type 2 diabetics with mild disease is lifestyle modification : a healthy diet with exercise to help lose weight . if this fails , the first medication used is typically metformin , a drug which stops the liver from making glucose in a process called gluconeogenesis . it also increases the number of insulin receptors present on cells , so they become more sensitive to insulin . between metformin and insulin therapy are a number of drugs which help increase the release of insulin from the pancreas . these include sulfonylureas , a-glucosidase inhibitors , and glinides . consider the following : sometimes , pregnant women can develop diabetes while they are pregnant , a process called gestational diabetes . this usually reverses once they give birth , but can persist after the pregnancy . gestational diabetes is similar to type 2 diabetes : the hallmark of this disease is insulin resistance . during the second trimester , pregnant women increase their resistance to insulin and have higher blood sugar levels , likely to increase delivery of glucose to the fetus . most women increase the amount of insulin produced from the pancreas , but women with gestational diabetes can not produce enough and functionally become type 2 diabetics throughout their pregnancy . diabetes can alter your body ’ s response to certain diseases . for example , diabetics who have heart attacks are more likely to present with atypical symptoms ( and oftentimes present without chest pain altogether ) . this is likely partly due to nerve damage . many diabetics have peripheral neuropathy , a nerve condition where they feel constant numbness and tingling in their toes and feet and have trouble recognizing pain in those limbs . these patients likely have nerve damage to other parts of their body , including their heart . the atypical symptoms lead to a delay in diagnosis of heart attacks .
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as insulin works on your body , the amount of glucose in the blood slowly returns to the same level it was before you ate.. this glucose level when you haven ’ t eaten recently ( called fasting glucose ) sits around 3.5-6 mmol/l ( 70-110 mg/dl ) . just after a meal , your blood glucose can jump as high as 7.8mmol/l ( 140 mg/dl ) depending on how much and what you ate .
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can glucose completely block up kidneys ?
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society . the study of human remains in poor cemeteries is often the only way of learning about the short lives of most ancient egyptians . many of the objects belonged to the wealthy and survived only because they were buried in tombs . they provide a glimpse of these people ’ s lavish lifestyles . glass bottle in the form of a fish glass vessels seem to have been primarily functional rather than ritual objects ; their main use was as containers for cosmetics or precious oils . however , in this case the fish design might hint at some further meaning , complementing its beauty as an elite personal item . the fish represented is a nile tilapia fish which hatches and shelters her young in her mouth . the emergence of the live offspring from the tilapia 's mouth led to the fish being used as a symbol of rebirth and regeneration , frequently worn as an amulet . this is the most complete and spectacular example of several surviving fish-shaped glass vessels made around this period . it was found under the floor in a house at tell el-amarna , where it may have been buried by its owner . glass vessels from the new kingdom ( 1550-1070 b.c.e . ) are highly colorful objects , and glass was often used as a more versatile and less expensive substitute for semiprecious stones . this fish was made by trailing molten glass over a core made of a clay mixture . next , colored rods of glass were wrapped around the body and dragged with a tool to create a fish-scale pattern . the body was then smoothed , the eyes and fins added and the core scraped out . wooden toy cat cats may have been kept as pets as early as the fourth millennium b.c.e . two wild species of cat lived in egypt , the jungle cat and the african wild cat . by the late first millennium b.c.e . cats were bred on an industrial scale for use in the cult of the cat goddess bastet . from the twelfth dynasty , cats are shown in tomb decoration , seated beneath the chair of the deceased or accompanying him on a hunt in the marshes . there is a fine example of the latter type of scene in the tomb of nebamun , showing a ginger cat catching birds in its mouth and with all four paws at the same time . such hunting scenes may also represent the struggle between civilized humans and the forces of chaos , shown as wild fowl . the cat had a similar role on the divine plane . in the funerary text called the litany of re , the sun god appears as a cat and battles the snake apep . this serpent , a manifestation of the forces of chaos , attacked the solar boat as it passed through the night sky . the god overcame apep by cutting him in two with a knife , allowing the sun to continue its journey to be reborn at dawn . additional resources : r.m . and j.j. janssen , growing up in ancient egypt ( london , the rubicon press , 1990 ) . m. stead , egyptian life ( london , the british museum press , 1986 ) . i. shaw and p. nicholson ( eds . ) , british museum dictionary of ancient egypt ( london , the british museum press , 1995 ) . a.p . kozloff and b.m . bryan , egypts dazzling sun : amenhotep iii and history world ( cleveland museum of art , 1992 ) e.r . russmann , eternal egypt : masterworks of ancient art from the british museum ( university of california press , 2001 ) . j.d . cooney , catalogue of egyptian antiqu-3 ( london , the british museum press , 1976 ) . s. quirke and a.j . spencer , the british museum book of ancient egypt ( london , the british museum press , 1992 ) . learn more about egyptian objects on the british museum website © trustees of the british museum
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the body was then smoothed , the eyes and fins added and the core scraped out . wooden toy cat cats may have been kept as pets as early as the fourth millennium b.c.e . two wild species of cat lived in egypt , the jungle cat and the african wild cat .
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did the ancient egyptians domesticate dogs to keep as pets as well or just cats ?
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society . the study of human remains in poor cemeteries is often the only way of learning about the short lives of most ancient egyptians . many of the objects belonged to the wealthy and survived only because they were buried in tombs . they provide a glimpse of these people ’ s lavish lifestyles . glass bottle in the form of a fish glass vessels seem to have been primarily functional rather than ritual objects ; their main use was as containers for cosmetics or precious oils . however , in this case the fish design might hint at some further meaning , complementing its beauty as an elite personal item . the fish represented is a nile tilapia fish which hatches and shelters her young in her mouth . the emergence of the live offspring from the tilapia 's mouth led to the fish being used as a symbol of rebirth and regeneration , frequently worn as an amulet . this is the most complete and spectacular example of several surviving fish-shaped glass vessels made around this period . it was found under the floor in a house at tell el-amarna , where it may have been buried by its owner . glass vessels from the new kingdom ( 1550-1070 b.c.e . ) are highly colorful objects , and glass was often used as a more versatile and less expensive substitute for semiprecious stones . this fish was made by trailing molten glass over a core made of a clay mixture . next , colored rods of glass were wrapped around the body and dragged with a tool to create a fish-scale pattern . the body was then smoothed , the eyes and fins added and the core scraped out . wooden toy cat cats may have been kept as pets as early as the fourth millennium b.c.e . two wild species of cat lived in egypt , the jungle cat and the african wild cat . by the late first millennium b.c.e . cats were bred on an industrial scale for use in the cult of the cat goddess bastet . from the twelfth dynasty , cats are shown in tomb decoration , seated beneath the chair of the deceased or accompanying him on a hunt in the marshes . there is a fine example of the latter type of scene in the tomb of nebamun , showing a ginger cat catching birds in its mouth and with all four paws at the same time . such hunting scenes may also represent the struggle between civilized humans and the forces of chaos , shown as wild fowl . the cat had a similar role on the divine plane . in the funerary text called the litany of re , the sun god appears as a cat and battles the snake apep . this serpent , a manifestation of the forces of chaos , attacked the solar boat as it passed through the night sky . the god overcame apep by cutting him in two with a knife , allowing the sun to continue its journey to be reborn at dawn . additional resources : r.m . and j.j. janssen , growing up in ancient egypt ( london , the rubicon press , 1990 ) . m. stead , egyptian life ( london , the british museum press , 1986 ) . i. shaw and p. nicholson ( eds . ) , british museum dictionary of ancient egypt ( london , the british museum press , 1995 ) . a.p . kozloff and b.m . bryan , egypts dazzling sun : amenhotep iii and history world ( cleveland museum of art , 1992 ) e.r . russmann , eternal egypt : masterworks of ancient art from the british museum ( university of california press , 2001 ) . j.d . cooney , catalogue of egyptian antiqu-3 ( london , the british museum press , 1976 ) . s. quirke and a.j . spencer , the british museum book of ancient egypt ( london , the british museum press , 1992 ) . learn more about egyptian objects on the british museum website © trustees of the british museum
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by the late first millennium b.c.e . cats were bred on an industrial scale for use in the cult of the cat goddess bastet . from the twelfth dynasty , cats are shown in tomb decoration , seated beneath the chair of the deceased or accompanying him on a hunt in the marshes .
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what on earth were they doing with those cats that they needed to be bred 'on an indurstrial scale ' ?
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society . the study of human remains in poor cemeteries is often the only way of learning about the short lives of most ancient egyptians . many of the objects belonged to the wealthy and survived only because they were buried in tombs . they provide a glimpse of these people ’ s lavish lifestyles . glass bottle in the form of a fish glass vessels seem to have been primarily functional rather than ritual objects ; their main use was as containers for cosmetics or precious oils . however , in this case the fish design might hint at some further meaning , complementing its beauty as an elite personal item . the fish represented is a nile tilapia fish which hatches and shelters her young in her mouth . the emergence of the live offspring from the tilapia 's mouth led to the fish being used as a symbol of rebirth and regeneration , frequently worn as an amulet . this is the most complete and spectacular example of several surviving fish-shaped glass vessels made around this period . it was found under the floor in a house at tell el-amarna , where it may have been buried by its owner . glass vessels from the new kingdom ( 1550-1070 b.c.e . ) are highly colorful objects , and glass was often used as a more versatile and less expensive substitute for semiprecious stones . this fish was made by trailing molten glass over a core made of a clay mixture . next , colored rods of glass were wrapped around the body and dragged with a tool to create a fish-scale pattern . the body was then smoothed , the eyes and fins added and the core scraped out . wooden toy cat cats may have been kept as pets as early as the fourth millennium b.c.e . two wild species of cat lived in egypt , the jungle cat and the african wild cat . by the late first millennium b.c.e . cats were bred on an industrial scale for use in the cult of the cat goddess bastet . from the twelfth dynasty , cats are shown in tomb decoration , seated beneath the chair of the deceased or accompanying him on a hunt in the marshes . there is a fine example of the latter type of scene in the tomb of nebamun , showing a ginger cat catching birds in its mouth and with all four paws at the same time . such hunting scenes may also represent the struggle between civilized humans and the forces of chaos , shown as wild fowl . the cat had a similar role on the divine plane . in the funerary text called the litany of re , the sun god appears as a cat and battles the snake apep . this serpent , a manifestation of the forces of chaos , attacked the solar boat as it passed through the night sky . the god overcame apep by cutting him in two with a knife , allowing the sun to continue its journey to be reborn at dawn . additional resources : r.m . and j.j. janssen , growing up in ancient egypt ( london , the rubicon press , 1990 ) . m. stead , egyptian life ( london , the british museum press , 1986 ) . i. shaw and p. nicholson ( eds . ) , british museum dictionary of ancient egypt ( london , the british museum press , 1995 ) . a.p . kozloff and b.m . bryan , egypts dazzling sun : amenhotep iii and history world ( cleveland museum of art , 1992 ) e.r . russmann , eternal egypt : masterworks of ancient art from the british museum ( university of california press , 2001 ) . j.d . cooney , catalogue of egyptian antiqu-3 ( london , the british museum press , 1976 ) . s. quirke and a.j . spencer , the british museum book of ancient egypt ( london , the british museum press , 1992 ) . learn more about egyptian objects on the british museum website © trustees of the british museum
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society .
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are re and ra the same deity ?
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society . the study of human remains in poor cemeteries is often the only way of learning about the short lives of most ancient egyptians . many of the objects belonged to the wealthy and survived only because they were buried in tombs . they provide a glimpse of these people ’ s lavish lifestyles . glass bottle in the form of a fish glass vessels seem to have been primarily functional rather than ritual objects ; their main use was as containers for cosmetics or precious oils . however , in this case the fish design might hint at some further meaning , complementing its beauty as an elite personal item . the fish represented is a nile tilapia fish which hatches and shelters her young in her mouth . the emergence of the live offspring from the tilapia 's mouth led to the fish being used as a symbol of rebirth and regeneration , frequently worn as an amulet . this is the most complete and spectacular example of several surviving fish-shaped glass vessels made around this period . it was found under the floor in a house at tell el-amarna , where it may have been buried by its owner . glass vessels from the new kingdom ( 1550-1070 b.c.e . ) are highly colorful objects , and glass was often used as a more versatile and less expensive substitute for semiprecious stones . this fish was made by trailing molten glass over a core made of a clay mixture . next , colored rods of glass were wrapped around the body and dragged with a tool to create a fish-scale pattern . the body was then smoothed , the eyes and fins added and the core scraped out . wooden toy cat cats may have been kept as pets as early as the fourth millennium b.c.e . two wild species of cat lived in egypt , the jungle cat and the african wild cat . by the late first millennium b.c.e . cats were bred on an industrial scale for use in the cult of the cat goddess bastet . from the twelfth dynasty , cats are shown in tomb decoration , seated beneath the chair of the deceased or accompanying him on a hunt in the marshes . there is a fine example of the latter type of scene in the tomb of nebamun , showing a ginger cat catching birds in its mouth and with all four paws at the same time . such hunting scenes may also represent the struggle between civilized humans and the forces of chaos , shown as wild fowl . the cat had a similar role on the divine plane . in the funerary text called the litany of re , the sun god appears as a cat and battles the snake apep . this serpent , a manifestation of the forces of chaos , attacked the solar boat as it passed through the night sky . the god overcame apep by cutting him in two with a knife , allowing the sun to continue its journey to be reborn at dawn . additional resources : r.m . and j.j. janssen , growing up in ancient egypt ( london , the rubicon press , 1990 ) . m. stead , egyptian life ( london , the british museum press , 1986 ) . i. shaw and p. nicholson ( eds . ) , british museum dictionary of ancient egypt ( london , the british museum press , 1995 ) . a.p . kozloff and b.m . bryan , egypts dazzling sun : amenhotep iii and history world ( cleveland museum of art , 1992 ) e.r . russmann , eternal egypt : masterworks of ancient art from the british museum ( university of california press , 2001 ) . j.d . cooney , catalogue of egyptian antiqu-3 ( london , the british museum press , 1976 ) . s. quirke and a.j . spencer , the british museum book of ancient egypt ( london , the british museum press , 1992 ) . learn more about egyptian objects on the british museum website © trustees of the british museum
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the cat had a similar role on the divine plane . in the funerary text called the litany of re , the sun god appears as a cat and battles the snake apep . this serpent , a manifestation of the forces of chaos , attacked the solar boat as it passed through the night sky .
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what is the `` snake apep `` ?
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society . the study of human remains in poor cemeteries is often the only way of learning about the short lives of most ancient egyptians . many of the objects belonged to the wealthy and survived only because they were buried in tombs . they provide a glimpse of these people ’ s lavish lifestyles . glass bottle in the form of a fish glass vessels seem to have been primarily functional rather than ritual objects ; their main use was as containers for cosmetics or precious oils . however , in this case the fish design might hint at some further meaning , complementing its beauty as an elite personal item . the fish represented is a nile tilapia fish which hatches and shelters her young in her mouth . the emergence of the live offspring from the tilapia 's mouth led to the fish being used as a symbol of rebirth and regeneration , frequently worn as an amulet . this is the most complete and spectacular example of several surviving fish-shaped glass vessels made around this period . it was found under the floor in a house at tell el-amarna , where it may have been buried by its owner . glass vessels from the new kingdom ( 1550-1070 b.c.e . ) are highly colorful objects , and glass was often used as a more versatile and less expensive substitute for semiprecious stones . this fish was made by trailing molten glass over a core made of a clay mixture . next , colored rods of glass were wrapped around the body and dragged with a tool to create a fish-scale pattern . the body was then smoothed , the eyes and fins added and the core scraped out . wooden toy cat cats may have been kept as pets as early as the fourth millennium b.c.e . two wild species of cat lived in egypt , the jungle cat and the african wild cat . by the late first millennium b.c.e . cats were bred on an industrial scale for use in the cult of the cat goddess bastet . from the twelfth dynasty , cats are shown in tomb decoration , seated beneath the chair of the deceased or accompanying him on a hunt in the marshes . there is a fine example of the latter type of scene in the tomb of nebamun , showing a ginger cat catching birds in its mouth and with all four paws at the same time . such hunting scenes may also represent the struggle between civilized humans and the forces of chaos , shown as wild fowl . the cat had a similar role on the divine plane . in the funerary text called the litany of re , the sun god appears as a cat and battles the snake apep . this serpent , a manifestation of the forces of chaos , attacked the solar boat as it passed through the night sky . the god overcame apep by cutting him in two with a knife , allowing the sun to continue its journey to be reborn at dawn . additional resources : r.m . and j.j. janssen , growing up in ancient egypt ( london , the rubicon press , 1990 ) . m. stead , egyptian life ( london , the british museum press , 1986 ) . i. shaw and p. nicholson ( eds . ) , british museum dictionary of ancient egypt ( london , the british museum press , 1995 ) . a.p . kozloff and b.m . bryan , egypts dazzling sun : amenhotep iii and history world ( cleveland museum of art , 1992 ) e.r . russmann , eternal egypt : masterworks of ancient art from the british museum ( university of california press , 2001 ) . j.d . cooney , catalogue of egyptian antiqu-3 ( london , the british museum press , 1976 ) . s. quirke and a.j . spencer , the british museum book of ancient egypt ( london , the british museum press , 1992 ) . learn more about egyptian objects on the british museum website © trustees of the british museum
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the wall paintings from nebamun 's tomb-chapel show an idealized vision of daily ancient egyptian life . much less is known about the lives of the majority of society .
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would only the wealthier families have been able to afford toys for their spawns or were they economical enough for lower class kids ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel .
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if judaism is religion , why are people now associating with a race/culture of people ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion .
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`` black jews '' why are they not just jews ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum .
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they traded with egypt , how is it that egyptian writing is not `` indigenous '' to africa ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum .
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have i missed some reorganization of the world where egypt has been relocated to a different continent ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires .
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do the african civilizations still tell tales about the older civilizations ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e .
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was part of eritrea in the kingdom of axum ( aksum ) ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia .
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the aksum ruler was described as the ''king of kings '' , wouldn't that mean that jesus was a kind of symbolic head of state ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended .
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did queen sheba really rule over aksum ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . ''
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were there any laws/rules that ran the kingdom , i cant find examples , and what was the impact that the government had in axum ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e .
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what was the relationship between the religions of askum and their government ?
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e . as a civilization it had a profound impact upon the people of egypt , southern arabia , europe and asia , all of whom were visitors to its shores , and in some cases were residents . aksum developed a civilization and empire whose influence , at its height in the 4th and 5th centuries c.e. , extended throughout the regions lying south of the roman empire , from the fringes of the sahara in the west , across the red sea to the inner arabian desert in the east . the aksumites developed africa ’ s only indigenous written script , ge ’ ez . they traded with egypt , the eastern mediterranean and arabia . despite its power and reputation—it was described by a persian writer as one of the four greatest powers in the world at the time—very little is known about aksum . written scripts existed , but no histories or descriptions have been found to make this african civilization come alive . a counterpoint to the greek and roman worlds aksum provides a counterpoint to the greek and roman worlds , and is an interesting example of a sub-saharan civilization flourishing towards the end of the period of the great mediterranean empires . it provides a link between the trading systems of the mediterranean and the asiatic world , and shows the extent of international commerce at that time . it holds the fascination of being a `` lost '' civilization , yet one that was african , christian , with its own script and coinage , and with an international reputation . it was arguably as advanced as the western european societies of the time . the society was hierarchical with a king at the top , then nobles , and the general population below . this can be discerned by the buildings that have been found , and the wealth of the goods found in them . although aksum had writing , very little has been found out about society from inscriptions . it can be assumed that priests were important , and probably traders , too , because of the money they would have made . most of the poor were probably craftsmen or farmers . in some descriptions , the ruler is described as `` king of kings '' which might suggest that there were other , junior kings in outlying parts of the empire which the aksumites gradually took over.there is evidence of at least 10–12 small towns in the kingdom , which suggests it was an urban society , but for descriptions of these there is only archaeological evidence . little or nothing is known about such things as the role of women and family life . christianity aksum embraced the orthodox tradition of christianity in the 4th century ( c. 340–356 c.e . ) under the rule of king ezana . the king had been converted by frumentius , a former syrian captive who was made bishop of aksum . on his return , frumentius had promptly baptized king ezana , who then declared aksum a christian state , followed by the king ’ s active converting of the aksumites . by the 6th century , king kaleb was recognized as a christian by the emperor justin i of byzantium ( ruled 518–527 ) when he sought kaleb ’ s support in avenging atrocities suffered by fellow christians in south arabia . this invasion saw the inclusion of the region into the aksumite kingdom for the next seven decades . judaism although christianity had a profound effect upon aksum , judaism also had a substantial impact on the kingdom . a group of people from the region called the beta israel have been described as `` black jews . '' although their scriptures and prayers are in ge ’ ez , rather than in hebrew , they adhere to religious beliefs and practices set out in the pentateuch ( torah ) , the religious texts of the jewish religion . although often regarded by scholars/academics as not technically ‘ `` jewish '' but instead a pre-christian , semitic people , their religion shares a common ancestry with modern judaism . between 1985 and 1991 almost the whole beta israel population of ethiopia was moved to israel . solomon and sheba the queen of sheba and king solomon are important figures in ethiopian heritage . traditional accounts describe their meeting when sheba , queen of aksum , went to jerusalem , and their son menelik i formed the solomonic dynasty from which the rulers of ethiopia ( up to the 1970s ) are said to be descended . it has also been claimed that aksum is the home of the biblical ark of the covenant , in which lies the `` tablets of law '' upon which the ten commandments are inscribed . menelik is believed to have taken it on a visit to jerusalem to see his father . it is supposed to reside still in the church of st mary in aksum , though no-one is allowed to set eyes on it . replicas of the ark , called tabots , are housed in all of ethiopia ’ s churches , and are carried in procession on special days . © trustees of the british museum
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one of the four greatest powers in the world aksum was the name of a city and a kingdom which is essentially modern-day northern ethiopia ( tigray province ) and eritrea . research shows that aksum was a major naval and trading power from the 1st to the 7th centuries c.e .
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what are some geography differences between the ancient kingdom of aksum and modern-day ethiopia ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . ''
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does anyone know what the doomsday clock stood at in 1962 during the cuban missile crisis ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr .
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how in the world is ducking and covering going to work when your out in the open when a atomic bomb goes off ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . ''
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where does the doomsday clock currently stand ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . ''
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what is the doomsday clock ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr .
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what is more powerful an h-bomb or a a-bomb ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb .
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cant special material protect you from the excess radiation ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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did the public not realise how dangerous radiation or an atomic blast was then ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
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when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr .
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is the hydrogen bomb the one that was not dropped ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
|
overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat .
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when was the last time a atomic bomb was used , and how many have been used since the first ?
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overview the us government 's decision to develop a hydrogen bomb , first tested in 1952 , committed the united states to an ever-escalating arms race with the soviet union . the arms race led many americans to fear that nuclear war could happen at any time , and the us government urged citizens to prepare to survive an atomic bomb . in 1950 , the us national security council released nsc-68 , a secret policy paper that called for quadrupling defense spending in order to meet the perceived soviet threat . nsc-68 would define us defense strategy throughout the cold war . president eisenhower attempted to cut defense spending by investing in a system of `` massive retaliation , '' hoping that the prospect of `` mutually-assured destruction '' from a large nuclear arsenal would deter potential aggressors . the doomsday clock and the h-bomb shortly after the us dropped the atomic bomb on japan , the scientists who had developed the bomb formed the bulletin of the atomic scientists , an organization dedicated to alerting the world to the dangers of nuclear weaponry . early contributors included j. robert oppenheimer , the director of the manhattan project , and albert einstein , who dedicated the final years of his life to promoting nuclear disarmament . in 1947 , they printed their first magazine , placing on its cover what would become an iconic symbol of the nuclear age : the doomsday clock . the clock purported to show how close humanity was to nuclear annihilation , or `` midnight . '' when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr . despite the specter of nuclear holocaust , both the united states and the soviet union vied to build ever more powerful nuclear weapons . nsc-68 the development of the h-bomb was just part of the us project to increase its military might in this period . in 1950 , the newly-created national security council issued a report on the current state of world affairs and the steps the united states should take to confront the perceived crisis . their report , `` united states objectives and programs for national security , '' or nsc-68 , cast the tension between the us and ussr as an apocalyptic battle between good and evil . `` the issues that face us are momentous , involving the fulfillment or destruction not only of this republic but of civilization itself , '' the report began . it went on to assert that the ultimate goal of the soviet union was `` the complete subversion or forcible destruction of the machinery of government and structure of society in the countries of the non-soviet world and their replacement by an apparatus and structure subservient to and controlled from the kremlin . '' the report concluded by recommending that united states vastly increase its investment in national security , quadrupling its annual defense spending to \ $ 50 billion per year . although at first this proposal seemed both expensive and impractical , the us entry into the korean war just two months later put nsc-68 's plans in motion. $ ^3 $ nsc-68 became the cornerstone of us national security policy during the cold war , but it was a flawed document in many ways . for one thing , it assumed two `` worst-case '' scenarios : that the soviet union had both the capacity and the desire to take over the world — neither of which was necessarily true. $ ^4 $ atomic fears with both the us and ussr stockpiling nuclear weapons , american society and culture in the 1950s was pervaded by fears of nuclear warfare . schools began issuing dog tags to students so that their families could identify their bodies in the event of an attack . the us government provided instructions for building and equipping bomb shelters in basements or backyards , and some cities constructed municipal shelters . nuclear bomb drills became a routine part of disaster preparedness. $ ^5 $ the civil defense film duck and cover , first screened in 1952 , sought to help schoolchildren protect themselves from injury during a nuclear attack by instructing them to find shelter and cover themselves to prevent burns . though `` ducking and covering '' hardly would have helped to prevent serious injury in a real atomic bombing , these rehearsals for disaster at least gave american citizens an illusion of control in the face of atomic warfare. $ ^6 $ duck and cover , directed by anthony rizzo ( archer productions , 1951 ) , was a civil defense film designed to help schoolchildren react to a nuclear bomb . massive retaliation one problem with the enormous military buildup prescribed by nsc-68 was its expense . although the economic prosperity of the 1950s seemed as if it would never end , president eisenhower hoped to cut government spending . secretary of state john foster dulles proposed a new plan for getting maximum defense capabilities at an affordable cost : massive retaliation . instead of focusing on conventional military forces , the us would rely on its enormous stockpile of nuclear weapons to deter its foes from aggression , on the principle that attacking the united states would result in `` mutually-assured destruction . `` $ ^7 $ unfortunately , massive retaliation was a sledgehammer , not a scalpel . because it dealt in worst-case scenarios , it presented no intermediate measures between all-out nuclear warfare and no response whatsoever . for example , when an uprising against soviet control broke out in hungary in 1956 , the united states feared to support it for fear of antagonizing the soviet union and triggering a nuclear war. $ ^8 $ moreover , to eisenhower 's chagrin , developing and maintaining the technology required to implement massive retaliation was in fact extremely expensive . in his farewell address , eisenhower warned of the dangers posed by the growing influence of the `` military-industrial complex , '' but was unable to slow the arms race. $ ^9 $ what do you think ? what were the assumptions underlying the national security council 's recommendations in nsc-68 ? were those assumptions justified ? did civil defense films like duck and cover comfort or traumatize american children ? would it have been possible to halt nuclear development , or was the creation of more and deadlier atomic bombs unavoidable ?
|
when the clock first appeared , the scientists predicted that humankind was mere seven minutes to midnight. $ ^1 $ but by 1953 , the scientists had revised their estimate to just two minutes to midnight . their reason for this panicked prognosis was the united states ' decision to develop and test a hydrogen bomb , or h-bomb , a nuclear weapon one thousand times more powerful than the atomic bomb that had leveled hiroshima at the end of world war ii . although scientists and some government officials argued against it , us officials ultimately reasoned that it would be imprudent for them not to develop any weapon that the soviet union might possess. $ ^2 $ the development of the h-bomb committed the us to an arms race with the ussr .
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and how does the nuclear bomb work ?
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