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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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also , how are photons absorbed ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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and how do atoms and molecules emit photons ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ .
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but since frequency can have basically any numerical value , would n't that make the energy of a photon continuous then ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation .
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is there a difference between these notations ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light .
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what is this photon made of ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation .
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what exactly is electromagnetic radiation ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation .
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but where does photon get its energy from ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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does n't gamma stand for photons ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field .
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does that mean cathode rays are also electromagnetic waves ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century .
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as there is both electric and magnetic waves ( which are involved with electrons ) , does light wave carry electrons ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa .
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is n't herz cycles per second.. ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave .
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does this mean that the amount of energy in each photon is different depending on the frequency of the electromagnetic wave ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe .
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since different frequencies can be shown in a spectrum ( continuous ) , does that mean the amount of energy one photon can have can be described using a spectrum as well ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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are photons basically `` energy packets '' ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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also , do photons only come from atoms that lose energy ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ?
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why are both f and v symbols being used for the frequency of an electromagnetic wave ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule .
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is emr also moving back and forth ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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are photons are basically packets of energy ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ?
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einstein 's equation e=mc^2 and e^2=p^2*c^2+m^2*c^4 have mass components ( including p ) then , what kind of energy does it have ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation .
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how does the arrangement of the electrons change the absorption of electromagnetic radiation or the emission of electromagnetic radiation ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example .
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if light travels more slowly in water , glass and other materials , than it does in air and changes wavelength when it goes from one medium to another , how come the frequency does not change ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ .
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i would think that 'more slowly ' means a change in frequency ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy .
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if amplitude is more then wavelength will be less ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) .
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does the wavelength and the frequency changes while refraction ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted .
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why ca n't the anode emit electrons ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy .
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how is amplitude related to brightness ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation .
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so does this mean that electromagnetic radiations/waves is not matter ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted .
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in planck 's research , what sort of waves were emitted by the blackbodies ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves .
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how many photons does an atom have to emit ( with energy corresponding to any of the waves of the visible spectrum ) for the human eye to see light ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves .
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in rainbow , how come the refraction of light through droplets in atmosphere create a continious visible spectrum of light ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ?
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what is the highest frequency a light wave can have ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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what is the source of photons in an atom of an element ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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does this mean that electromagnetic waves are produced only when atoms and molecules release photons ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon .
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how do you pronounce the greek symbol that looks like the letter v ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter .
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just need a little help , what exaclty is a magnetic , or electric field ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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so are photons the source of energy for all em waves ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low .
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are em waves produced from photons and if so , always ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined .
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does light bend from one place to other ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons .
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why do they say energy is quantized if in the equation e = hv , v the frequency is continuous ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation .
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if so does that mean that a packet of electromagnetic wave flowing through space can have any level of energy ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon .
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i did n't get how ''planck 's discovery that electromagnetic radiation is quantised '' meant that light also has particle like nature ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength .
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would the speed of light coming from the flashlight be equal to the speed of the spaceship plus the speed of light coming from the flashlight ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century .
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so how fast is light ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules .
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if photon is a particle .why is mass of photon zero ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ .
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if photon is a particle , so , what is meant by its energy in terms of frequency ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted .
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is black hole radiation similar to black body radiation or else it is shows any principle and i also want if there is any another principle ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules .
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a photon does not even have a mass , how is it a particle ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude .
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in the graph representing amplitude of a wave how can crest+trough be wavelength when the axis represents time ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ .
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and what happens to a photon once it 's absorbed ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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are photons used in case of lights and with reference to other radiations quanta is used ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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when atoms absorb energy from photons what does it do to them/what does it allow them to do ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed .
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say an iron atom absorbs a bunch of photons , does it start glowing , or what 's the outcome ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy .
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a wavelength with more crests over a given period will oscillate slower than a wavelength with less crests over the same period ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true .
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what happens to the photon after transfer of energy ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light .
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what is the mass of a photon ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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also , if an atom/molecule receives more photons , does that increase its amount of electrons ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties .
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why does an x-ray sheet turn black if used to wrap uranium ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter .
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is the amplitude of the electrical field and magnetic field of a electromagnetic wave always same ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties .
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could someone tell me how max planck discovered quantized nature of light ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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$ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . )
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what do you mean by energetic in the question asked in concept check ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light .
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what is the formula for momentum of a photon ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave .
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so the force , like tension , is a kind of incontinuous energy ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) .
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wave is just a graph of the intensity of energy at the given point in space right ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light .
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and 'on the graph only ' the wavelength concept is explained right ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true .
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but with what instrument was this up and down of energy level detected ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter .
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how did we know that there is an electric field and a magnetic field ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount .
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when planck discovered that the energy emitted/absorbed were multiples of 'hv ' , that is a constant times frequency , what frequency did he take into account ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ .
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when energy is absorbed/emitted , thousands of light waves are involved and each wave has a different frequency , which one did he take ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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$ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) .
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is n't the wavelength measured on the spatial axis of the wave , rather than on its time axis , where its equivalent is the period ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted .
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or is it just that the axis should have been `` space '' ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true .
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is only energy of em waves quantised or even other forms of energy i.e in projectile motion or rectilinear motion or any other motion , ca n't m ( mass ) and v ( velocitie ) and take any value giving any value for energy e= ( mv^2 ) /2 ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century .
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what is effect of light with eye ?
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introduction to electromagnetic waves electromagnetic radiation is one of the many ways that energy travels through space . the heat from a burning fire , the light from the sun , the x-rays used by your doctor , as well as the energy used to cook food in a microwave are all forms of electromagnetic radiation . while these forms of energy might seem quite different from one another , they are related in that they all exhibit wavelike properties . if you ’ ve ever gone swimming in the ocean , you are already familiar with waves . waves are simply disturbances in a particular physical medium or a field , resulting in a vibration or oscillation . the swell of a wave in the ocean , and the subsequent dip that follows , is simply a vibration or oscillation of the water at the ocean ’ s surface . electromagnetic waves are similar , but they are also distinct in that they actually consist of $ 2 $ waves oscillating perpendicular to one another . one of the waves is an oscillating magnetic field ; the other is an oscillating electric field . this can be visualized as follows : while it ’ s good to have a basic understanding of what electromagnetic radiation is , most chemists are less interested in the physics behind this type of energy , and are far more interested in how these waves interact with matter . more specifically , chemists study how different forms of electromagnetic radiation interact with atoms and molecules . from these interactions , a chemist can get information about a molecule ’ s structure , as well as the types of chemical bonds it contains . before we talk about that , however , it ’ s necessary to talk a little bit more about the physical properties of light waves . basic properties of waves : amplitude , wavelength , and frequency as you might already know , a wave has a trough ( lowest point ) and a crest ( highest point ) . the vertical distance between the tip of a crest and the wave ’ s central axis is known as its amplitude . this is the property associated with the brightness , or intensity , of the wave . the horizontal distance between two consecutive troughs or crests is known as the wavelength of the wave . these lengths can be visualized as follows : keep in mind that some waves ( including electromagnetic waves ) also oscillate in space , and therefore they are oscillating at a given position as time passes . the quantity known as the wave ’ s frequency refers to the number of full wavelengths that pass by a given point in space every second ; the si unit for frequency is hertz $ ( \text { hz } ) $ , which is equivalent to “ per seconds ” $ \big ( $ written as $ \dfrac { 1 } { \text { s } } $ or $ \text { s } ^ { -1 } \big ) $ . as you might imagine , wavelength and frequency are inversely proportional : that is , the shorter the wavelength , the higher the frequency , and vice versa . this relationship is given by the following equation : $ c=\lambda \nu $ where $ \lambda $ ( the greek lambda ) is the wavelength ( in meters , $ \text { m } $ ) and $ \nu $ ( the greek nu ) is the frequency ( in hertz , $ \text { hz } $ ) . their product is the constant $ c $ , the speed of light , which is equal to $ 3.00\times10^8 \text { m/s } $ . this relationship reflects an important fact : all electromagnetic radiation , regardless of wavelength or frequency , travels at the speed of light . to illustrate the relationship between frequency and wavelength , let ’ s consider an example . example : calculating the wavelength of a light wave a particular wave of electromagnetic radiation has a frequency of $ 1.5\times10^ { 14 } \text { hz } $ . what is the wavelength of this wave ? we can start with our equation that relates frequency , wavelength , and the speed of light . $ c=\lambda \nu $ next , we rearrange the equation to solve for wavelength . $ \lambda=\dfrac { c } { \nu } $ lastly , we plug in our given values and solve . $ \lambda=\dfrac { 3.00\times10^8\dfrac { \text { m } } { \cancel { \text { s } } } } { 1.5\times10^ { 14 } \dfrac { 1 } { \cancel { \text { s } } } } =2.00\times10^ { -6 } \text { m } $ concept check : what would you expect to happen to the frequency of a light wave if its wavelength were increased by a factor of $ 10 $ ? period the last quantity we will consider is the period of a wave . a wave ’ s period is the length of time it takes for one wavelength to pass by a given point in space . mathematically , the period ( $ t $ ) is simply the reciprocal of the wave ’ s frequency ( $ f $ ) : $ t=\dfrac { 1 } { f } $ the units of period are seconds ( $ \text { s } $ ) . now that we have an understanding of some basic properties of waves , we ’ ll look at the different types of electromagnetic radiation . the electromagnetic spectrum electromagnetic waves can be classified and arranged according to their various wavelengths/frequencies ; this classification is known as the electromagnetic spectrum . the following table shows us this spectrum , which consists of all the types of electromagnetic radiation that exist in our universe . as we can see , the visible spectrum—that is , light that we can see with our eyes—makes up only a small fraction of the different types of radiation that exist . to the right of the visible spectrum , we find the types of energy that are lower in frequency ( and thus longer in wavelength ) than visible light . these types of energy include infrared ( ir ) rays ( heat waves given off by thermal bodies ) , microwaves , and radio waves . these types of radiation surround us constantly , and are not harmful , because their frequencies are so low . as we will see in the section , “ the photon , ” lower frequency waves are lower in energy , and thus are not dangerous to our health . to the left of the visible spectrum , we have ultraviolet ( uv ) rays , x-rays , and gamma rays . these types of radiation are harmful to living organisms , due to their extremely high frequencies ( and thus , high energies ) . it is for this reason that we wear suntan lotion at the beach ( to block the uv rays from the sun ) and why an x-ray technician will place a lead shield over us , in order to prevent the x-rays from penetrating anything other than the area of our body being imaged . gamma rays , being the highest in frequency and energy , are the most damaging . luckily though , our atmosphere absorbs gamma rays from outer space , thereby protecting us from harm . next , we will talk about the relationship between a wave ’ s frequency and its energy . quantization of energy and the dual nature of light we have already described how light travels through space as a wave . this has been well-known for quite some time ; in fact , the dutch physicist christiaan huygens first described the wave nature of light as far back as the late seventeenth century . for about $ 200 $ years after huygens , physicists assumed that light waves and matter were quite distinct from one another . according to classical physics , matter was composed of particles that had mass , and whose position in space could be known ; light waves , on the other hand , were considered to have zero mass , and their position in space could not be determined . because they were considered to be in different categories , scientists did not have a good understanding of how light and matter interacted . this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted . this was a shocking discovery , because it challenged the idea that energy was continuous , and could be transferred in any amount . the reality , which planck discovered , is that energy is not continuous but quantized—meaning that it can only be transferred in individual “ packets ” ( or particles ) of the size $ h\nu $ . each of these energy packets is known as a quantum ( plural : quanta ) . while this might sound confusing , we are actually already very familiar with quantized systems . the money we use daily , for example , is quantized . for instance , when you go into a store , you will not see anything on sale for a price of one dollar and two and a half cents $ ( \ $ 1.025 ) $ . this is because the smallest possible monetary unit is the penny—it is impossible to transfer money in any smaller amount than this . just as we can not pay the cashier at the store half of a cent , energy can not be transferred in anything less than a single quantum . we can think of quanta as being like “ pennies ” of electromagnetic energy—the smallest possible units by which such energy can be transferred . planck ’ s discovery that electromagnetic radiation is quantized forever changed the idea that light behaves purely as a wave . in actuality , light seemed to have both wavelike and particle-like properties . the photon planck ’ s discoveries paved the way for the discovery of the photon . a photon is the elementary particle , or quantum , of light . as we will soon see , photons can be absorbed or emitted by atoms and molecules . when a photon is absorbed , its energy is transferred to that atom or molecule . because energy is quantized , the photon ’ s entire energy is transferred ( remember that we can not transfer fractions of quanta , which are the smallest possible individual “ energy packets ” ) . the reverse of this process is also true . when an atom or molecule loses energy , it emits a photon that carries an energy exactly equal to the loss in energy of the atom or molecule . this change in energy is directly proportional to the frequency of photon emitted or absorbed . this relationship is given by planck ’ s famous equation : $ e=h\nu $ where $ e $ is the energy of the photon absorbed or emitted ( given in joules , $ \text { j } $ ) , $ \nu $ is frequency of the photon ( given in hertz , $ \text { hz } $ ) , and $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ . example : calculating the energy of a photon a photon has a frequency of $ 2.0\times10^ { 24 } \text { hz } $ . what is the energy of this photon ? first , we can apply planck 's equation . $ e=h\nu $ next , we plug in our given value for the frequency , as well as the value for planck 's constant , $ h $ , and solve . $ e= ( 6.626\times10^ { -34 } \text { j } \cdot\cancel { \text { s } } ) \times ( 2.0\times 10^ { 24 } \cancel { \text { s } ^ { -1 } } ) =1.3\times10^ { -9 } \text { j } $ concept check : the wavelength of orange light is about $ 590-635\text { nm } $ , and the wavelength of green light is about $ 520-560\text { nm } $ . which color of light is more energetic , orange or green ? ( hint : keep in mind what you have already learned about the relationship between wavelength and frequency . ) conclusion electromagnetic radiation can be described by its amplitude ( brightness ) , wavelength , frequency , and period . by the equation $ e=h\nu $ , we have seen how the frequency of a light wave is proportional to its energy . at the beginning of the twentieth century , the discovery that energy is quantized led to the revelation that light is not only a wave , but can also be described as a collection of particles known as photons . photons carry discrete amounts of energy called quanta . this energy can be transferred to atoms and molecules when photons are absorbed . atoms and molecules can also lose energy by emitting photons .
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this all changed in $ 1900 $ , however , when the physicist max planck began studying blackbodies – bodies heated until they began to glow . planck found that the electromagnetic radiation emitted by blackbodies could not be explained by classical physics , which postulated that matter could absorb or emit any quantity of electromagnetic radiation . planck observed that matter actually absorbed or emitted energy only in whole-number multiples of the value $ h\nu $ , where $ h $ is planck ’ s constant , $ 6.626\times10^ { -34 } \text { j } \cdot\text { s } $ , and $ \nu $ is the frequency of the light absorbed or emitted .
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what type of radiation is this ?
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1 . describe the plate motions along the himalayan mountains . do you think these mountains are getting larger , smaller , or staying the same ? explain your answer . answer : along the himalayan mountains , two plates are pushing into each other . since both plates have continental crust at this boundary , they crumple and fold up , forming a mountain range . the plates are still moving , so the mountains continue to grow taller . 2 . given earth ’ s history , do you think there will ever be another supercontinent like pangea ? explain your answer . answer : over earth ’ s 4.5 billion year history , the continents have come together and spread apart at least three times . this motion is driven by convection in earth ’ s mantle . since earth ’ s mantle will continue to flow , the plates will continue to move . given earth ’ s history and the flow of the mantle , it is likely that there will be another supercontinent like pangea . 3 . write a caption for this map . answer : the pacific plate is sinking beneath the north american plate , forming a subduction zone along the plate boundary shown as the red line with triangles . the sinking pacific plate causes the mantle above it to melt and form magma , which rises to form the aleutian island arc , a chain of volcanoes shown as red triangles . 4 . provide two kinds of evidence that support the theory of plate tectonics . answer may include : the shapes of continents fit together like a puzzle . the matching coastlines show where the continents broke apart . identical rocks that formed over 200 million years ago have been found on different continents . the minerals and textures of the rocks indicate that they formed in the same place before the continents separated . identical fossils have been found in south america and africa . this supports the explanation that these animals lived on the same continent before it separated . 5 . explain how scientists are using seismic data to learn about the geologic activity and earth ’ s interior under yellowstone national park . ( hint : describe how the speed of seismic waves relates to temperature in the mantle . ) © usgs , © ineel answer : using seismic data , scientists can see where seismic waves move faster and slower . since the speed of waves increases with temperature , scientists can identify areas in the mantle that are hotter and cooler and build three-dimensional models of the temperature in the mantle . these models show that yellowstone is over a hotspot—where a column of hot material is rising from deep in the mantle .
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write a caption for this map . answer : the pacific plate is sinking beneath the north american plate , forming a subduction zone along the plate boundary shown as the red line with triangles . the sinking pacific plate causes the mantle above it to melt and form magma , which rises to form the aleutian island arc , a chain of volcanoes shown as red triangles .
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what factors can cause the land at one convergent plate boundary to look very different from that at another convergent plate boundary ?
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1 . describe the plate motions along the himalayan mountains . do you think these mountains are getting larger , smaller , or staying the same ? explain your answer . answer : along the himalayan mountains , two plates are pushing into each other . since both plates have continental crust at this boundary , they crumple and fold up , forming a mountain range . the plates are still moving , so the mountains continue to grow taller . 2 . given earth ’ s history , do you think there will ever be another supercontinent like pangea ? explain your answer . answer : over earth ’ s 4.5 billion year history , the continents have come together and spread apart at least three times . this motion is driven by convection in earth ’ s mantle . since earth ’ s mantle will continue to flow , the plates will continue to move . given earth ’ s history and the flow of the mantle , it is likely that there will be another supercontinent like pangea . 3 . write a caption for this map . answer : the pacific plate is sinking beneath the north american plate , forming a subduction zone along the plate boundary shown as the red line with triangles . the sinking pacific plate causes the mantle above it to melt and form magma , which rises to form the aleutian island arc , a chain of volcanoes shown as red triangles . 4 . provide two kinds of evidence that support the theory of plate tectonics . answer may include : the shapes of continents fit together like a puzzle . the matching coastlines show where the continents broke apart . identical rocks that formed over 200 million years ago have been found on different continents . the minerals and textures of the rocks indicate that they formed in the same place before the continents separated . identical fossils have been found in south america and africa . this supports the explanation that these animals lived on the same continent before it separated . 5 . explain how scientists are using seismic data to learn about the geologic activity and earth ’ s interior under yellowstone national park . ( hint : describe how the speed of seismic waves relates to temperature in the mantle . ) © usgs , © ineel answer : using seismic data , scientists can see where seismic waves move faster and slower . since the speed of waves increases with temperature , scientists can identify areas in the mantle that are hotter and cooler and build three-dimensional models of the temperature in the mantle . these models show that yellowstone is over a hotspot—where a column of hot material is rising from deep in the mantle .
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1 . describe the plate motions along the himalayan mountains .
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what is the tectonic setting of the u.s. ?
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high school is full of activity . whether you play sports , act in school plays , have a job , take care of siblings , or are taking hard classes - or even doing more than one of these things ! - you have almost certainly looked at the clock before and been shocked by how little time you have to get everything done . throw sat prep into the mix , and it can seem like there just aren ’ t enough hours in the day . while you may not be able to cut down on all of your responsibilities during sat practice time , there are some ways you can structure your planning and studying to keep things going smoothly and ensuring that nothing gets left by the wayside . several high school students offered up some of their time management suggestions : big tip # 1 : make a study plan study a little bit at a time : “ the first thing i did was take out a calendar and chart out the type of section i was going to study each day . i tried to study a little bit every day of the week and take off weekends , but adjusted this as needed . i personally think doing well is about forming habits - studying a little each day for a month or two is much more effective than cramming the same material in a week. ” – aneesh figure out your system : “ i like to have certain times throughout the week dedicated to studying . i 've gotten into the habit of sleeping early ( 10pm ) and waking up early ( 7am ) to do work instead of doing work at 1am . the work i do in the morning is lower-priority homework or assignments to help me wake up . my committees and extracurriculars occur after school and change times often , so i fit my more important homework around it . essentially , creating a system and a schedule that works is key . i do n't use an agenda or a planner , but i get around just fine because i have a system . it 's about experimenting and finding one that will keep you sane through the busiest times. ” – eric go after the low-hanging fruit first : “ when possible , i stay after school or go to a coffee shop right after school with a friend in order to get some homework out of the way immediately . i always find that when i get home after a long day at school , i do n't have motivation to start my work , and am more likely to procrastinate and not try as hard . working/studying right after school before i go home allows me to get small assignments out of the way , so i have more time at home to study and do other assignments . at home , i break up my work time and give myself many breaks . i usually try to work for 45mins to an hour and then give myself a 10 minute break . i switch subjects , and if something is taking a long time i 'll take a break from it , work on something else , and then come back to it. ” – fariha prioritize , prioritize , prioritize : “ make a list of things that are most to least important ( ex : 1. math , 2. english studying , 3. music practice , etc . ) . write down the main things you need to get done in those subjects . concentrate on the most important one first . sometimes i tend to get pretty overwhelmed by certain projects and assignments and studying so when i go through each subject i split up the work into very simple steps , then i 'm not nearly as worried about an assignment ( example : to write an essay : 1 ) brainstorm for 4 minutes 2 ) cross out ideas that wo n't work 3 ) write basic outline ... ) this always keeps me from procrastinating . give yourself 5 minute breaks now and then , usually for breaks i make some tea or listen to music . refocusing is not too hard when you give yourself simple steps to do after the break. ” – elyse listen to yourself : “ check in with yourself to see how you feel before starting to study ; do you feel like memorizing math formulas right now ? do you want to go ahead and write that paper ? or maybe you 'd rather just read ? do what you feel will be most productive . just make sure that you really stick to the time limits and follow your study guide once you 've made it . feel free to come back to assignments after taking a small break or working on another task. ” – emily big tip # 2 : keep yourself on track stick to your schedule : “ yes , we all deal with the temptation of procrastination . it 's like a cupcake that later gives us food poisoning . we can avoid the costs of procrastination by making a schedule , and committing to that schedule . sometimes i will purposely write deadlines for myself that are a couple days before the actual assignment is due as a way of `` tricking myself . '' it 's a pretend due date ! that way , if i procrastinate , it wo n't be so harmful. ” – eillen estimate the time you need : “ i plan out what homework i have and how long i think it will take me . i usually work for an hour to and hour and a half and take a 10 minute break . during a break , i play basketball , listen to music , or read. ” – sahil start with mini-deadlines : “ setting a deadline usually is n't enough for a study plan - go through what you need to cover and make mini-deadlines for each section. ” – jody take breaks : “ it 's definitely important that you take some sort of break ( s ) during your study sessions . some people say that your brain can only focus for 20 minutes at a time , so do n't push your study sessions if you find that you ca n't focus or you are n't retaining any information . make sure that you are doing something that you find enjoyable so that you find some balance . you want to feel refreshed and truly rested when you return to your studying because you 've worked hard ! ” – emily big tip # 3 : stay organized put everything in writing : “ i always write everything that i have to do each day in a physical agenda , and i write reminders of test dates and due dates in as well to remind me of what 's coming in days to come . having all of my tasks laid out keeps me organized and gives me incentive to finish everything , just so i can check things off ! ” – heeju set yourself up for rewards : “ always make a to do list . i make a to do list with the smallest tasks such as `` email ___ '' so that i am able to cross out something . having a planner or a to do list gives me a specific set of things that i need to do and nothing feels better than physically crossing something off that list . when i finish a medium to large sized task , i allow myself a specific amount of time to go outside , go on social media , or go into the kitchen to get food . these little breaks serve as mini rewards for completing tasks. ” – tiffany think ahead : each sunday , i write out all the homework or mandatory work i anticipate to receive over the next week , because most of the times , teachers assign regular problem sets or papers that are predictable in advance . each daily plan that i formulate includes a portion of this list of homework . this helps me keep track of due dates so that i do n't miss any homework , and gives me the joy of erasing completed items from the long list to eventually make it blank . if i keep my set schedule , then i know i wo n't have to worry about late work or time management. ” – gaeun
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write down the main things you need to get done in those subjects . concentrate on the most important one first . sometimes i tend to get pretty overwhelmed by certain projects and assignments and studying so when i go through each subject i split up the work into very simple steps , then i 'm not nearly as worried about an assignment ( example : to write an essay : 1 ) brainstorm for 4 minutes 2 ) cross out ideas that wo n't work 3 ) write basic outline ... ) this always keeps me from procrastinating .
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also , is it important to take the psat/nmsqt ?
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high school is full of activity . whether you play sports , act in school plays , have a job , take care of siblings , or are taking hard classes - or even doing more than one of these things ! - you have almost certainly looked at the clock before and been shocked by how little time you have to get everything done . throw sat prep into the mix , and it can seem like there just aren ’ t enough hours in the day . while you may not be able to cut down on all of your responsibilities during sat practice time , there are some ways you can structure your planning and studying to keep things going smoothly and ensuring that nothing gets left by the wayside . several high school students offered up some of their time management suggestions : big tip # 1 : make a study plan study a little bit at a time : “ the first thing i did was take out a calendar and chart out the type of section i was going to study each day . i tried to study a little bit every day of the week and take off weekends , but adjusted this as needed . i personally think doing well is about forming habits - studying a little each day for a month or two is much more effective than cramming the same material in a week. ” – aneesh figure out your system : “ i like to have certain times throughout the week dedicated to studying . i 've gotten into the habit of sleeping early ( 10pm ) and waking up early ( 7am ) to do work instead of doing work at 1am . the work i do in the morning is lower-priority homework or assignments to help me wake up . my committees and extracurriculars occur after school and change times often , so i fit my more important homework around it . essentially , creating a system and a schedule that works is key . i do n't use an agenda or a planner , but i get around just fine because i have a system . it 's about experimenting and finding one that will keep you sane through the busiest times. ” – eric go after the low-hanging fruit first : “ when possible , i stay after school or go to a coffee shop right after school with a friend in order to get some homework out of the way immediately . i always find that when i get home after a long day at school , i do n't have motivation to start my work , and am more likely to procrastinate and not try as hard . working/studying right after school before i go home allows me to get small assignments out of the way , so i have more time at home to study and do other assignments . at home , i break up my work time and give myself many breaks . i usually try to work for 45mins to an hour and then give myself a 10 minute break . i switch subjects , and if something is taking a long time i 'll take a break from it , work on something else , and then come back to it. ” – fariha prioritize , prioritize , prioritize : “ make a list of things that are most to least important ( ex : 1. math , 2. english studying , 3. music practice , etc . ) . write down the main things you need to get done in those subjects . concentrate on the most important one first . sometimes i tend to get pretty overwhelmed by certain projects and assignments and studying so when i go through each subject i split up the work into very simple steps , then i 'm not nearly as worried about an assignment ( example : to write an essay : 1 ) brainstorm for 4 minutes 2 ) cross out ideas that wo n't work 3 ) write basic outline ... ) this always keeps me from procrastinating . give yourself 5 minute breaks now and then , usually for breaks i make some tea or listen to music . refocusing is not too hard when you give yourself simple steps to do after the break. ” – elyse listen to yourself : “ check in with yourself to see how you feel before starting to study ; do you feel like memorizing math formulas right now ? do you want to go ahead and write that paper ? or maybe you 'd rather just read ? do what you feel will be most productive . just make sure that you really stick to the time limits and follow your study guide once you 've made it . feel free to come back to assignments after taking a small break or working on another task. ” – emily big tip # 2 : keep yourself on track stick to your schedule : “ yes , we all deal with the temptation of procrastination . it 's like a cupcake that later gives us food poisoning . we can avoid the costs of procrastination by making a schedule , and committing to that schedule . sometimes i will purposely write deadlines for myself that are a couple days before the actual assignment is due as a way of `` tricking myself . '' it 's a pretend due date ! that way , if i procrastinate , it wo n't be so harmful. ” – eillen estimate the time you need : “ i plan out what homework i have and how long i think it will take me . i usually work for an hour to and hour and a half and take a 10 minute break . during a break , i play basketball , listen to music , or read. ” – sahil start with mini-deadlines : “ setting a deadline usually is n't enough for a study plan - go through what you need to cover and make mini-deadlines for each section. ” – jody take breaks : “ it 's definitely important that you take some sort of break ( s ) during your study sessions . some people say that your brain can only focus for 20 minutes at a time , so do n't push your study sessions if you find that you ca n't focus or you are n't retaining any information . make sure that you are doing something that you find enjoyable so that you find some balance . you want to feel refreshed and truly rested when you return to your studying because you 've worked hard ! ” – emily big tip # 3 : stay organized put everything in writing : “ i always write everything that i have to do each day in a physical agenda , and i write reminders of test dates and due dates in as well to remind me of what 's coming in days to come . having all of my tasks laid out keeps me organized and gives me incentive to finish everything , just so i can check things off ! ” – heeju set yourself up for rewards : “ always make a to do list . i make a to do list with the smallest tasks such as `` email ___ '' so that i am able to cross out something . having a planner or a to do list gives me a specific set of things that i need to do and nothing feels better than physically crossing something off that list . when i finish a medium to large sized task , i allow myself a specific amount of time to go outside , go on social media , or go into the kitchen to get food . these little breaks serve as mini rewards for completing tasks. ” – tiffany think ahead : each sunday , i write out all the homework or mandatory work i anticipate to receive over the next week , because most of the times , teachers assign regular problem sets or papers that are predictable in advance . each daily plan that i formulate includes a portion of this list of homework . this helps me keep track of due dates so that i do n't miss any homework , and gives me the joy of erasing completed items from the long list to eventually make it blank . if i keep my set schedule , then i know i wo n't have to worry about late work or time management. ” – gaeun
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while you may not be able to cut down on all of your responsibilities during sat practice time , there are some ways you can structure your planning and studying to keep things going smoothly and ensuring that nothing gets left by the wayside . several high school students offered up some of their time management suggestions : big tip # 1 : make a study plan study a little bit at a time : “ the first thing i did was take out a calendar and chart out the type of section i was going to study each day . i tried to study a little bit every day of the week and take off weekends , but adjusted this as needed .
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i have just under two and a half months before my fourth and final sat , what should my study plan look like ?
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high school is full of activity . whether you play sports , act in school plays , have a job , take care of siblings , or are taking hard classes - or even doing more than one of these things ! - you have almost certainly looked at the clock before and been shocked by how little time you have to get everything done . throw sat prep into the mix , and it can seem like there just aren ’ t enough hours in the day . while you may not be able to cut down on all of your responsibilities during sat practice time , there are some ways you can structure your planning and studying to keep things going smoothly and ensuring that nothing gets left by the wayside . several high school students offered up some of their time management suggestions : big tip # 1 : make a study plan study a little bit at a time : “ the first thing i did was take out a calendar and chart out the type of section i was going to study each day . i tried to study a little bit every day of the week and take off weekends , but adjusted this as needed . i personally think doing well is about forming habits - studying a little each day for a month or two is much more effective than cramming the same material in a week. ” – aneesh figure out your system : “ i like to have certain times throughout the week dedicated to studying . i 've gotten into the habit of sleeping early ( 10pm ) and waking up early ( 7am ) to do work instead of doing work at 1am . the work i do in the morning is lower-priority homework or assignments to help me wake up . my committees and extracurriculars occur after school and change times often , so i fit my more important homework around it . essentially , creating a system and a schedule that works is key . i do n't use an agenda or a planner , but i get around just fine because i have a system . it 's about experimenting and finding one that will keep you sane through the busiest times. ” – eric go after the low-hanging fruit first : “ when possible , i stay after school or go to a coffee shop right after school with a friend in order to get some homework out of the way immediately . i always find that when i get home after a long day at school , i do n't have motivation to start my work , and am more likely to procrastinate and not try as hard . working/studying right after school before i go home allows me to get small assignments out of the way , so i have more time at home to study and do other assignments . at home , i break up my work time and give myself many breaks . i usually try to work for 45mins to an hour and then give myself a 10 minute break . i switch subjects , and if something is taking a long time i 'll take a break from it , work on something else , and then come back to it. ” – fariha prioritize , prioritize , prioritize : “ make a list of things that are most to least important ( ex : 1. math , 2. english studying , 3. music practice , etc . ) . write down the main things you need to get done in those subjects . concentrate on the most important one first . sometimes i tend to get pretty overwhelmed by certain projects and assignments and studying so when i go through each subject i split up the work into very simple steps , then i 'm not nearly as worried about an assignment ( example : to write an essay : 1 ) brainstorm for 4 minutes 2 ) cross out ideas that wo n't work 3 ) write basic outline ... ) this always keeps me from procrastinating . give yourself 5 minute breaks now and then , usually for breaks i make some tea or listen to music . refocusing is not too hard when you give yourself simple steps to do after the break. ” – elyse listen to yourself : “ check in with yourself to see how you feel before starting to study ; do you feel like memorizing math formulas right now ? do you want to go ahead and write that paper ? or maybe you 'd rather just read ? do what you feel will be most productive . just make sure that you really stick to the time limits and follow your study guide once you 've made it . feel free to come back to assignments after taking a small break or working on another task. ” – emily big tip # 2 : keep yourself on track stick to your schedule : “ yes , we all deal with the temptation of procrastination . it 's like a cupcake that later gives us food poisoning . we can avoid the costs of procrastination by making a schedule , and committing to that schedule . sometimes i will purposely write deadlines for myself that are a couple days before the actual assignment is due as a way of `` tricking myself . '' it 's a pretend due date ! that way , if i procrastinate , it wo n't be so harmful. ” – eillen estimate the time you need : “ i plan out what homework i have and how long i think it will take me . i usually work for an hour to and hour and a half and take a 10 minute break . during a break , i play basketball , listen to music , or read. ” – sahil start with mini-deadlines : “ setting a deadline usually is n't enough for a study plan - go through what you need to cover and make mini-deadlines for each section. ” – jody take breaks : “ it 's definitely important that you take some sort of break ( s ) during your study sessions . some people say that your brain can only focus for 20 minutes at a time , so do n't push your study sessions if you find that you ca n't focus or you are n't retaining any information . make sure that you are doing something that you find enjoyable so that you find some balance . you want to feel refreshed and truly rested when you return to your studying because you 've worked hard ! ” – emily big tip # 3 : stay organized put everything in writing : “ i always write everything that i have to do each day in a physical agenda , and i write reminders of test dates and due dates in as well to remind me of what 's coming in days to come . having all of my tasks laid out keeps me organized and gives me incentive to finish everything , just so i can check things off ! ” – heeju set yourself up for rewards : “ always make a to do list . i make a to do list with the smallest tasks such as `` email ___ '' so that i am able to cross out something . having a planner or a to do list gives me a specific set of things that i need to do and nothing feels better than physically crossing something off that list . when i finish a medium to large sized task , i allow myself a specific amount of time to go outside , go on social media , or go into the kitchen to get food . these little breaks serve as mini rewards for completing tasks. ” – tiffany think ahead : each sunday , i write out all the homework or mandatory work i anticipate to receive over the next week , because most of the times , teachers assign regular problem sets or papers that are predictable in advance . each daily plan that i formulate includes a portion of this list of homework . this helps me keep track of due dates so that i do n't miss any homework , and gives me the joy of erasing completed items from the long list to eventually make it blank . if i keep my set schedule , then i know i wo n't have to worry about late work or time management. ” – gaeun
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whether you play sports , act in school plays , have a job , take care of siblings , or are taking hard classes - or even doing more than one of these things ! - you have almost certainly looked at the clock before and been shocked by how little time you have to get everything done . throw sat prep into the mix , and it can seem like there just aren ’ t enough hours in the day . while you may not be able to cut down on all of your responsibilities during sat practice time , there are some ways you can structure your planning and studying to keep things going smoothly and ensuring that nothing gets left by the wayside . several high school students offered up some of their time management suggestions : big tip # 1 : make a study plan study a little bit at a time : “ the first thing i did was take out a calendar and chart out the type of section i was going to study each day .
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how much time should we devote daily for the preparation of sat for a year ?
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in ancient rome equestrian statues of emperors would not have been uncommon sights in the city—late antique sources suggest that at least 22 of these “ great horses ” ( equi magni ) were to be seen—as they were official devices for honoring the emperor for singular military and civic achievements . the statues themselves were , in turn , copied in other media , including coins , for even wider distribution . few examples of these equestrian statues survive from antiquity , however , making the equestrian statue of marcus aurelius a singular artifact of roman antiquity , one that has borne quiet witness to the ebb and flow of the city of rome for nearly 1,900 years . a gilded bronze monument of the 170s c.e . that was originally dedicated to the emperor marcus aurelius antoninus augustus , referred to commonly as marcus aurelius ( reigned 161-180 c.e . ) , the statue is an important object not only for the study of official roman portraiture , but also for the consideration of monumental dedications . further , the use of the statue in the medieval , renaissance , modern , and post-modern city of rome has important implications for the connectivity that exists between the past and the present . description the statue is an over life-size depiction of the emperor elegantly mounted atop his horse while participating in a public ritual or ceremony ; the statue stands approximately 4.24 meters tall . a gilded bronze statue , the piece was originally cast using the lost-wax technique , with horse and rider cast in multiple pieces and then soldered together after casting . the horse the emperor ’ s horse is a magnificent example of dynamism captured in the sculptural medium . the horse , caught in motion , raises its right foreleg at the knee while planting its left foreleg on the ground , its motion checked by the application of reins , which the emperor originally held in his left hand . the horse ’ s body—in particular its musculature—has been modeled very carefully by the artist , resulting in a powerful rendering . in keeping with the motion of the horse ’ s body , its head turns to its right , with its mouth opened slightly . the horse wears a harness , some elements of which have not survived . the horse is saddled with a persian-style saddlecloth of several layers , as opposed to a rigid saddle . it should be noted that the horse is an important and expressive element of the overall composition . the horseman the horseman sits astride the steed , with his left hand guiding the reins and his right arm raised to shoulder level , the hand outstretched . portrait types there are approximately 110 known portraits of marcus aurelius and these have been grouped into four typological groupings . the first two types belong to the emperor ’ s youth , before he assumed the duties of the principate . in the roman world it was standard practice to create official portrait types of high-ranking officials , such as emperors that would then circulate in various media , notably sculpture in the round and coin portraits . these portrait types are vital in several respects , especially for determining the chronology of monuments and coins , since the portrait types can usually be placed in a fairly accurate and legible chronological order . the interpretation of these portraits relies on various key elements , especially the reading of hairstyle and the examination of facial physiognomy . the second portrait type was made when marcus was in his late 20s , c. 147 c.e . and shows a still youthful type , although marcus now has light facial hair ( left ) . in the case of the equestrian statue , the portrait typology offers the best means of assigning an approximate date to the object since it does not otherwise offer another means of dating . the earliest portrait of marcus aurelius dates to c. 140 c.e . and is best represented by the capitoline galleria 28 type , where the youth wears a cloak fastened at the shoulder ( paludamentum ) ; this portrait was widely circulated , with approximately 25 known copies ( above , left ) . marcus aurelius became emperor in 161 c.e. , when he was forty years of age ; this was the occasion for the creation of his third and most important portrait type . this mature type ( type iii , left ) shows the emperor fully bearded with a full head of tightly curled , voluminous hair ; he retains the characteristic oval-shaped face and heavy eyelids from his earlier portraits . his coiffure forms a distinctive arc over his forehead . this third type is known from approximately 50 copies . the emperor ’ s fourth portrait type ( below , left ) , created between 170 and 180 c.e. , retains most of the features of the third type , but shows the emperor slightly more advanced in age with a very full beard that is divided in the center at the chin , showing parallel locks of hair . dating of the equestrian portrait the statue of the horseman is carefully composed by the artist and depicts a figure that is simultaneously dynamic and a bit passive and removed , by virtue of his facial expression ( see image below ) . the locks of hair are curly and compact and distributed evenly ; the beard is also curly , covering the cheeks and upper lip , and is worn longer at the chin . the pose of the body shows the rider ’ s head turned slightly to his right , in the direction of his outstretched right arm . the left hand originally held the reins ( no longer preserved ) between the index and middle fingers , with the palm facing upwards . scholars continue to debate whether he originally held some attached figure or object in the palm of the left hand ; possible suggestions have included a scepter , a globe , a statue of victory – but there is no clear indication of any attachment point for such an object . on the left hand the rider does wear the senatorial ring . the rider is clad in civic garb , including a short-sleeved tunic that is gathered at the waist by a knotted belt ( cingulum ) . over the tunic the rider wears a cloak ( paludamentum ) that is clasped at the right shoulder . on his feet marcus aurelius wears the senatorial boots of the patrician class , known as calcei patricii . interpretation and chronology the interpretation and chronology of the equestrian statue must rely on the statue itself , as no ancient literary testimony or other evidence survives to aid in the interpretation . it is obvious that the statue is part of an elaborate public monument , no doubt commissioned to mark an important occasion in the emperor ’ s reign . with that said , however , it must also be noted that scholars continue to debate its precise dating , the occasion for its creation , and its likely original location in the city of rome . starting with the portrait typology it is possible to determine a range of likely dates for the statue ’ s creation . the portrait is clearly an adult type of the emperor , meaning the statue must have been created after 161 c.e. , the year of marcus aurelius ’ accession and the creation of his third portrait type . this provides a terminus post quem ( the limit after which ) for the equestrian statue . art historians have debated whether the portrait head most resembles the type iii or the type iv portrait . recent scholarly thinking , based on the work of klaus fittschen , holds that the equestrian portrait represents a unique variant of the standard type iii portrait , created as an improvisation by the artist who was commissioned to create the equestrian statue . in the end the precise chronology of the portrait head—and indeed the typology—remains a matter of scholarly debate . the pose of the horseman is also helpful . the emperor stretches his right hand outward , the palm facing toward the ground ; a pose that could be interpreted as the posture of adlocutio , indicating that the emperor is about to speak . however , more likely in this case we may read it as the gesture of clemency ( clementia ) , offered to a vanquished enemy , or of restitutio pacis , the `` restoration of peace . '' richard brilliant has noted that since the emperor appears in civic garb as opposed to the general ’ s armor , the overall impression of the statue is one of peace rather than of the immediate post-war celebration of military victory . some art historians reconstruct a now-missing barbarian on the right side of the horse , as seen in a surviving panel relief sculpture that originally belonged to a now-lost triumphal arch dedicated to marcus aurelius ( left ) . we know that marcus aurelius celebrated a triumph in 176 c.e . for his victories over german and sarmatian tribes , leading some to suggest that year as the occasion for the creation of the equestrian monument . history the original location of the equestrian monument also remains debated , with some supporting a location on the caelian hill near the barracks of the imperial cavalry ( equites singulares ) , while others favor the campus martius ( a low-lying alluvial plain of the tiber river ) as a possible location . a text known as the liber pontificalis that dates to the middle of the tenth century c.e . mentions the equestrian monument , referring to it as “ caballus constantini ” or the “ horse of constantine. ” according to the text , the urban prefect of rome was condemned following an uprising against pope john xii and , as punishment , was hung by the hair from the equestrian monument . at this time the equestrian statue was located in the lateran quarter of the city of rome near the lateran palace , where it may have been since at least the eighth century c.e . popular theories at the time held that the bearded emperor was in fact constantine i , thus sparing the statue from being melted down . in 1538 the statue was relocated from the lateran quarter to the capitoline hill to become the centerpiece for michelangelo ’ s new design for the campidoglio ( a piazza , or public square , at the top of the capitoline hill ) . the statue was set atop a pedestal at the center of an intricately designed piazza flanked by three palazzi ( image above ) . it became the centerpiece of the main piazza of secular rome and , as such , an icon of the city , a role that its still retains . the equestrian statue still plays a role as an official symbol of the city of rome , even being incorporated into the reverse image of the italian version of the € 0.50 coin ( image above ) . the statue itself remained where michelangelo positioned it until it was moved indoors in 1981 for conservation reasons ; a high-tech copy of the original was placed on the pedestal . the ancient statue is now housed within the musei capitolini where it can be visited and viewed today . the equestrian statue of marcus aurelius is an enduring monument , one that links the city ’ s many phases , ancient and modern . it has borne witness to the city ’ s imperial glory , post-imperial decline , its renaissance resurgence , and even its quotidian experience in the twenty-first century . in so doing it reminds us about the role of public art in creating and reinforcing cultural identity as it relates to specific events and locations . in the ancient world the equestrian statue would have evoked powerful memories from the viewer , not only reinforcing the identity and appearance of the emperor but also calling to mind the key events , achievements , and celebrations of his administration . the statue is , like the city , eternal , as reflected by the romanesco poet giuseppe belli who reflects in his sonnet campidojjo ( 1830 ) that the gilded statue is directly linked to the long sweep of rome ’ s history . text by dr. jeffrey a. becker additional resources : j. bergemann , römische reiterstatuen : ehrendenkmäler im öffentlichen bereich ( mainz am rhein : ph . von zabern , 1990 ) . a. birley , marcus aurelius : a biography ( london : routledge , 2002 ) . p.j.e . davies , death and the emperor : roman imperial funerary monuments , from augustus to marcus aurelius ( austin : university of texas press , 2004 ) p. fehl , “ the placement of the equestrian statue of marcus aurelius in the middle ages. ” journal of the warburg and courtauld institutes 37 , 1974 , pp . 362-67 . k. fittschen and p. zanker , katalog der römischen porträts in den capitolinischen museen und den anderen kommunalen sammlungen der stadt rom . 3 v. ( berlin : p. von zabern , 1983-2010 ) . d. e. e. kleiner , roman sculpture ( new haven : yale university press , 1992 ) . m. nimmo , marco aurelio , mostra di cantiere : le indagini in corso sul monumento ( rome : arti grafiche pedanesi , 1984 ) . c. p. presicce , and a. m. sommella , the equestrian statue of marcus aurelius in campidoglio ( milan : silvana , 1990 ) . i. s. ryberg , '' rites of the state religion in roman art '' ( memoirs of the american academy in rome ; 22 ) ( rome : american academy in rome , 1955 ) . i. s. ryberg , panel reliefs of marcus aurelius ( new york : archaeological institute of america , 1967 ) . k. stemmer , ed . kaiser , marc aurel und seine zeit : das römische reich im umbruch ( berlin : abguss-sammlung antiker plastik , 1988 ) . d. e. strong , roman art ( new haven : yale university press , 1976 ) . a. m. vaccaro , et al. , marco aurelio : storia di un monumento e del suo restauro ( milan : silvana , 1989 ) . m. van ackeren , ed. , a companion to marcus aurelius ( malden ma : wiley-blackwell , 2012 ) . capitoline museums - marcus aurelius exedra
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and shows a still youthful type , although marcus now has light facial hair ( left ) . in the case of the equestrian statue , the portrait typology offers the best means of assigning an approximate date to the object since it does not otherwise offer another means of dating . the earliest portrait of marcus aurelius dates to c. 140 c.e .
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is there a process for chemically or otherwise scientifically dating metal ?
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in ancient rome equestrian statues of emperors would not have been uncommon sights in the city—late antique sources suggest that at least 22 of these “ great horses ” ( equi magni ) were to be seen—as they were official devices for honoring the emperor for singular military and civic achievements . the statues themselves were , in turn , copied in other media , including coins , for even wider distribution . few examples of these equestrian statues survive from antiquity , however , making the equestrian statue of marcus aurelius a singular artifact of roman antiquity , one that has borne quiet witness to the ebb and flow of the city of rome for nearly 1,900 years . a gilded bronze monument of the 170s c.e . that was originally dedicated to the emperor marcus aurelius antoninus augustus , referred to commonly as marcus aurelius ( reigned 161-180 c.e . ) , the statue is an important object not only for the study of official roman portraiture , but also for the consideration of monumental dedications . further , the use of the statue in the medieval , renaissance , modern , and post-modern city of rome has important implications for the connectivity that exists between the past and the present . description the statue is an over life-size depiction of the emperor elegantly mounted atop his horse while participating in a public ritual or ceremony ; the statue stands approximately 4.24 meters tall . a gilded bronze statue , the piece was originally cast using the lost-wax technique , with horse and rider cast in multiple pieces and then soldered together after casting . the horse the emperor ’ s horse is a magnificent example of dynamism captured in the sculptural medium . the horse , caught in motion , raises its right foreleg at the knee while planting its left foreleg on the ground , its motion checked by the application of reins , which the emperor originally held in his left hand . the horse ’ s body—in particular its musculature—has been modeled very carefully by the artist , resulting in a powerful rendering . in keeping with the motion of the horse ’ s body , its head turns to its right , with its mouth opened slightly . the horse wears a harness , some elements of which have not survived . the horse is saddled with a persian-style saddlecloth of several layers , as opposed to a rigid saddle . it should be noted that the horse is an important and expressive element of the overall composition . the horseman the horseman sits astride the steed , with his left hand guiding the reins and his right arm raised to shoulder level , the hand outstretched . portrait types there are approximately 110 known portraits of marcus aurelius and these have been grouped into four typological groupings . the first two types belong to the emperor ’ s youth , before he assumed the duties of the principate . in the roman world it was standard practice to create official portrait types of high-ranking officials , such as emperors that would then circulate in various media , notably sculpture in the round and coin portraits . these portrait types are vital in several respects , especially for determining the chronology of monuments and coins , since the portrait types can usually be placed in a fairly accurate and legible chronological order . the interpretation of these portraits relies on various key elements , especially the reading of hairstyle and the examination of facial physiognomy . the second portrait type was made when marcus was in his late 20s , c. 147 c.e . and shows a still youthful type , although marcus now has light facial hair ( left ) . in the case of the equestrian statue , the portrait typology offers the best means of assigning an approximate date to the object since it does not otherwise offer another means of dating . the earliest portrait of marcus aurelius dates to c. 140 c.e . and is best represented by the capitoline galleria 28 type , where the youth wears a cloak fastened at the shoulder ( paludamentum ) ; this portrait was widely circulated , with approximately 25 known copies ( above , left ) . marcus aurelius became emperor in 161 c.e. , when he was forty years of age ; this was the occasion for the creation of his third and most important portrait type . this mature type ( type iii , left ) shows the emperor fully bearded with a full head of tightly curled , voluminous hair ; he retains the characteristic oval-shaped face and heavy eyelids from his earlier portraits . his coiffure forms a distinctive arc over his forehead . this third type is known from approximately 50 copies . the emperor ’ s fourth portrait type ( below , left ) , created between 170 and 180 c.e. , retains most of the features of the third type , but shows the emperor slightly more advanced in age with a very full beard that is divided in the center at the chin , showing parallel locks of hair . dating of the equestrian portrait the statue of the horseman is carefully composed by the artist and depicts a figure that is simultaneously dynamic and a bit passive and removed , by virtue of his facial expression ( see image below ) . the locks of hair are curly and compact and distributed evenly ; the beard is also curly , covering the cheeks and upper lip , and is worn longer at the chin . the pose of the body shows the rider ’ s head turned slightly to his right , in the direction of his outstretched right arm . the left hand originally held the reins ( no longer preserved ) between the index and middle fingers , with the palm facing upwards . scholars continue to debate whether he originally held some attached figure or object in the palm of the left hand ; possible suggestions have included a scepter , a globe , a statue of victory – but there is no clear indication of any attachment point for such an object . on the left hand the rider does wear the senatorial ring . the rider is clad in civic garb , including a short-sleeved tunic that is gathered at the waist by a knotted belt ( cingulum ) . over the tunic the rider wears a cloak ( paludamentum ) that is clasped at the right shoulder . on his feet marcus aurelius wears the senatorial boots of the patrician class , known as calcei patricii . interpretation and chronology the interpretation and chronology of the equestrian statue must rely on the statue itself , as no ancient literary testimony or other evidence survives to aid in the interpretation . it is obvious that the statue is part of an elaborate public monument , no doubt commissioned to mark an important occasion in the emperor ’ s reign . with that said , however , it must also be noted that scholars continue to debate its precise dating , the occasion for its creation , and its likely original location in the city of rome . starting with the portrait typology it is possible to determine a range of likely dates for the statue ’ s creation . the portrait is clearly an adult type of the emperor , meaning the statue must have been created after 161 c.e. , the year of marcus aurelius ’ accession and the creation of his third portrait type . this provides a terminus post quem ( the limit after which ) for the equestrian statue . art historians have debated whether the portrait head most resembles the type iii or the type iv portrait . recent scholarly thinking , based on the work of klaus fittschen , holds that the equestrian portrait represents a unique variant of the standard type iii portrait , created as an improvisation by the artist who was commissioned to create the equestrian statue . in the end the precise chronology of the portrait head—and indeed the typology—remains a matter of scholarly debate . the pose of the horseman is also helpful . the emperor stretches his right hand outward , the palm facing toward the ground ; a pose that could be interpreted as the posture of adlocutio , indicating that the emperor is about to speak . however , more likely in this case we may read it as the gesture of clemency ( clementia ) , offered to a vanquished enemy , or of restitutio pacis , the `` restoration of peace . '' richard brilliant has noted that since the emperor appears in civic garb as opposed to the general ’ s armor , the overall impression of the statue is one of peace rather than of the immediate post-war celebration of military victory . some art historians reconstruct a now-missing barbarian on the right side of the horse , as seen in a surviving panel relief sculpture that originally belonged to a now-lost triumphal arch dedicated to marcus aurelius ( left ) . we know that marcus aurelius celebrated a triumph in 176 c.e . for his victories over german and sarmatian tribes , leading some to suggest that year as the occasion for the creation of the equestrian monument . history the original location of the equestrian monument also remains debated , with some supporting a location on the caelian hill near the barracks of the imperial cavalry ( equites singulares ) , while others favor the campus martius ( a low-lying alluvial plain of the tiber river ) as a possible location . a text known as the liber pontificalis that dates to the middle of the tenth century c.e . mentions the equestrian monument , referring to it as “ caballus constantini ” or the “ horse of constantine. ” according to the text , the urban prefect of rome was condemned following an uprising against pope john xii and , as punishment , was hung by the hair from the equestrian monument . at this time the equestrian statue was located in the lateran quarter of the city of rome near the lateran palace , where it may have been since at least the eighth century c.e . popular theories at the time held that the bearded emperor was in fact constantine i , thus sparing the statue from being melted down . in 1538 the statue was relocated from the lateran quarter to the capitoline hill to become the centerpiece for michelangelo ’ s new design for the campidoglio ( a piazza , or public square , at the top of the capitoline hill ) . the statue was set atop a pedestal at the center of an intricately designed piazza flanked by three palazzi ( image above ) . it became the centerpiece of the main piazza of secular rome and , as such , an icon of the city , a role that its still retains . the equestrian statue still plays a role as an official symbol of the city of rome , even being incorporated into the reverse image of the italian version of the € 0.50 coin ( image above ) . the statue itself remained where michelangelo positioned it until it was moved indoors in 1981 for conservation reasons ; a high-tech copy of the original was placed on the pedestal . the ancient statue is now housed within the musei capitolini where it can be visited and viewed today . the equestrian statue of marcus aurelius is an enduring monument , one that links the city ’ s many phases , ancient and modern . it has borne witness to the city ’ s imperial glory , post-imperial decline , its renaissance resurgence , and even its quotidian experience in the twenty-first century . in so doing it reminds us about the role of public art in creating and reinforcing cultural identity as it relates to specific events and locations . in the ancient world the equestrian statue would have evoked powerful memories from the viewer , not only reinforcing the identity and appearance of the emperor but also calling to mind the key events , achievements , and celebrations of his administration . the statue is , like the city , eternal , as reflected by the romanesco poet giuseppe belli who reflects in his sonnet campidojjo ( 1830 ) that the gilded statue is directly linked to the long sweep of rome ’ s history . text by dr. jeffrey a. becker additional resources : j. bergemann , römische reiterstatuen : ehrendenkmäler im öffentlichen bereich ( mainz am rhein : ph . von zabern , 1990 ) . a. birley , marcus aurelius : a biography ( london : routledge , 2002 ) . p.j.e . davies , death and the emperor : roman imperial funerary monuments , from augustus to marcus aurelius ( austin : university of texas press , 2004 ) p. fehl , “ the placement of the equestrian statue of marcus aurelius in the middle ages. ” journal of the warburg and courtauld institutes 37 , 1974 , pp . 362-67 . k. fittschen and p. zanker , katalog der römischen porträts in den capitolinischen museen und den anderen kommunalen sammlungen der stadt rom . 3 v. ( berlin : p. von zabern , 1983-2010 ) . d. e. e. kleiner , roman sculpture ( new haven : yale university press , 1992 ) . m. nimmo , marco aurelio , mostra di cantiere : le indagini in corso sul monumento ( rome : arti grafiche pedanesi , 1984 ) . c. p. presicce , and a. m. sommella , the equestrian statue of marcus aurelius in campidoglio ( milan : silvana , 1990 ) . i. s. ryberg , '' rites of the state religion in roman art '' ( memoirs of the american academy in rome ; 22 ) ( rome : american academy in rome , 1955 ) . i. s. ryberg , panel reliefs of marcus aurelius ( new york : archaeological institute of america , 1967 ) . k. stemmer , ed . kaiser , marc aurel und seine zeit : das römische reich im umbruch ( berlin : abguss-sammlung antiker plastik , 1988 ) . d. e. strong , roman art ( new haven : yale university press , 1976 ) . a. m. vaccaro , et al. , marco aurelio : storia di un monumento e del suo restauro ( milan : silvana , 1989 ) . m. van ackeren , ed. , a companion to marcus aurelius ( malden ma : wiley-blackwell , 2012 ) . capitoline museums - marcus aurelius exedra
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it is obvious that the statue is part of an elaborate public monument , no doubt commissioned to mark an important occasion in the emperor ’ s reign . with that said , however , it must also be noted that scholars continue to debate its precise dating , the occasion for its creation , and its likely original location in the city of rome . starting with the portrait typology it is possible to determine a range of likely dates for the statue ’ s creation .
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we know ways of carbon dating as well as ring counting on wood objects for dating , but what about metal ?
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in ancient rome equestrian statues of emperors would not have been uncommon sights in the city—late antique sources suggest that at least 22 of these “ great horses ” ( equi magni ) were to be seen—as they were official devices for honoring the emperor for singular military and civic achievements . the statues themselves were , in turn , copied in other media , including coins , for even wider distribution . few examples of these equestrian statues survive from antiquity , however , making the equestrian statue of marcus aurelius a singular artifact of roman antiquity , one that has borne quiet witness to the ebb and flow of the city of rome for nearly 1,900 years . a gilded bronze monument of the 170s c.e . that was originally dedicated to the emperor marcus aurelius antoninus augustus , referred to commonly as marcus aurelius ( reigned 161-180 c.e . ) , the statue is an important object not only for the study of official roman portraiture , but also for the consideration of monumental dedications . further , the use of the statue in the medieval , renaissance , modern , and post-modern city of rome has important implications for the connectivity that exists between the past and the present . description the statue is an over life-size depiction of the emperor elegantly mounted atop his horse while participating in a public ritual or ceremony ; the statue stands approximately 4.24 meters tall . a gilded bronze statue , the piece was originally cast using the lost-wax technique , with horse and rider cast in multiple pieces and then soldered together after casting . the horse the emperor ’ s horse is a magnificent example of dynamism captured in the sculptural medium . the horse , caught in motion , raises its right foreleg at the knee while planting its left foreleg on the ground , its motion checked by the application of reins , which the emperor originally held in his left hand . the horse ’ s body—in particular its musculature—has been modeled very carefully by the artist , resulting in a powerful rendering . in keeping with the motion of the horse ’ s body , its head turns to its right , with its mouth opened slightly . the horse wears a harness , some elements of which have not survived . the horse is saddled with a persian-style saddlecloth of several layers , as opposed to a rigid saddle . it should be noted that the horse is an important and expressive element of the overall composition . the horseman the horseman sits astride the steed , with his left hand guiding the reins and his right arm raised to shoulder level , the hand outstretched . portrait types there are approximately 110 known portraits of marcus aurelius and these have been grouped into four typological groupings . the first two types belong to the emperor ’ s youth , before he assumed the duties of the principate . in the roman world it was standard practice to create official portrait types of high-ranking officials , such as emperors that would then circulate in various media , notably sculpture in the round and coin portraits . these portrait types are vital in several respects , especially for determining the chronology of monuments and coins , since the portrait types can usually be placed in a fairly accurate and legible chronological order . the interpretation of these portraits relies on various key elements , especially the reading of hairstyle and the examination of facial physiognomy . the second portrait type was made when marcus was in his late 20s , c. 147 c.e . and shows a still youthful type , although marcus now has light facial hair ( left ) . in the case of the equestrian statue , the portrait typology offers the best means of assigning an approximate date to the object since it does not otherwise offer another means of dating . the earliest portrait of marcus aurelius dates to c. 140 c.e . and is best represented by the capitoline galleria 28 type , where the youth wears a cloak fastened at the shoulder ( paludamentum ) ; this portrait was widely circulated , with approximately 25 known copies ( above , left ) . marcus aurelius became emperor in 161 c.e. , when he was forty years of age ; this was the occasion for the creation of his third and most important portrait type . this mature type ( type iii , left ) shows the emperor fully bearded with a full head of tightly curled , voluminous hair ; he retains the characteristic oval-shaped face and heavy eyelids from his earlier portraits . his coiffure forms a distinctive arc over his forehead . this third type is known from approximately 50 copies . the emperor ’ s fourth portrait type ( below , left ) , created between 170 and 180 c.e. , retains most of the features of the third type , but shows the emperor slightly more advanced in age with a very full beard that is divided in the center at the chin , showing parallel locks of hair . dating of the equestrian portrait the statue of the horseman is carefully composed by the artist and depicts a figure that is simultaneously dynamic and a bit passive and removed , by virtue of his facial expression ( see image below ) . the locks of hair are curly and compact and distributed evenly ; the beard is also curly , covering the cheeks and upper lip , and is worn longer at the chin . the pose of the body shows the rider ’ s head turned slightly to his right , in the direction of his outstretched right arm . the left hand originally held the reins ( no longer preserved ) between the index and middle fingers , with the palm facing upwards . scholars continue to debate whether he originally held some attached figure or object in the palm of the left hand ; possible suggestions have included a scepter , a globe , a statue of victory – but there is no clear indication of any attachment point for such an object . on the left hand the rider does wear the senatorial ring . the rider is clad in civic garb , including a short-sleeved tunic that is gathered at the waist by a knotted belt ( cingulum ) . over the tunic the rider wears a cloak ( paludamentum ) that is clasped at the right shoulder . on his feet marcus aurelius wears the senatorial boots of the patrician class , known as calcei patricii . interpretation and chronology the interpretation and chronology of the equestrian statue must rely on the statue itself , as no ancient literary testimony or other evidence survives to aid in the interpretation . it is obvious that the statue is part of an elaborate public monument , no doubt commissioned to mark an important occasion in the emperor ’ s reign . with that said , however , it must also be noted that scholars continue to debate its precise dating , the occasion for its creation , and its likely original location in the city of rome . starting with the portrait typology it is possible to determine a range of likely dates for the statue ’ s creation . the portrait is clearly an adult type of the emperor , meaning the statue must have been created after 161 c.e. , the year of marcus aurelius ’ accession and the creation of his third portrait type . this provides a terminus post quem ( the limit after which ) for the equestrian statue . art historians have debated whether the portrait head most resembles the type iii or the type iv portrait . recent scholarly thinking , based on the work of klaus fittschen , holds that the equestrian portrait represents a unique variant of the standard type iii portrait , created as an improvisation by the artist who was commissioned to create the equestrian statue . in the end the precise chronology of the portrait head—and indeed the typology—remains a matter of scholarly debate . the pose of the horseman is also helpful . the emperor stretches his right hand outward , the palm facing toward the ground ; a pose that could be interpreted as the posture of adlocutio , indicating that the emperor is about to speak . however , more likely in this case we may read it as the gesture of clemency ( clementia ) , offered to a vanquished enemy , or of restitutio pacis , the `` restoration of peace . '' richard brilliant has noted that since the emperor appears in civic garb as opposed to the general ’ s armor , the overall impression of the statue is one of peace rather than of the immediate post-war celebration of military victory . some art historians reconstruct a now-missing barbarian on the right side of the horse , as seen in a surviving panel relief sculpture that originally belonged to a now-lost triumphal arch dedicated to marcus aurelius ( left ) . we know that marcus aurelius celebrated a triumph in 176 c.e . for his victories over german and sarmatian tribes , leading some to suggest that year as the occasion for the creation of the equestrian monument . history the original location of the equestrian monument also remains debated , with some supporting a location on the caelian hill near the barracks of the imperial cavalry ( equites singulares ) , while others favor the campus martius ( a low-lying alluvial plain of the tiber river ) as a possible location . a text known as the liber pontificalis that dates to the middle of the tenth century c.e . mentions the equestrian monument , referring to it as “ caballus constantini ” or the “ horse of constantine. ” according to the text , the urban prefect of rome was condemned following an uprising against pope john xii and , as punishment , was hung by the hair from the equestrian monument . at this time the equestrian statue was located in the lateran quarter of the city of rome near the lateran palace , where it may have been since at least the eighth century c.e . popular theories at the time held that the bearded emperor was in fact constantine i , thus sparing the statue from being melted down . in 1538 the statue was relocated from the lateran quarter to the capitoline hill to become the centerpiece for michelangelo ’ s new design for the campidoglio ( a piazza , or public square , at the top of the capitoline hill ) . the statue was set atop a pedestal at the center of an intricately designed piazza flanked by three palazzi ( image above ) . it became the centerpiece of the main piazza of secular rome and , as such , an icon of the city , a role that its still retains . the equestrian statue still plays a role as an official symbol of the city of rome , even being incorporated into the reverse image of the italian version of the € 0.50 coin ( image above ) . the statue itself remained where michelangelo positioned it until it was moved indoors in 1981 for conservation reasons ; a high-tech copy of the original was placed on the pedestal . the ancient statue is now housed within the musei capitolini where it can be visited and viewed today . the equestrian statue of marcus aurelius is an enduring monument , one that links the city ’ s many phases , ancient and modern . it has borne witness to the city ’ s imperial glory , post-imperial decline , its renaissance resurgence , and even its quotidian experience in the twenty-first century . in so doing it reminds us about the role of public art in creating and reinforcing cultural identity as it relates to specific events and locations . in the ancient world the equestrian statue would have evoked powerful memories from the viewer , not only reinforcing the identity and appearance of the emperor but also calling to mind the key events , achievements , and celebrations of his administration . the statue is , like the city , eternal , as reflected by the romanesco poet giuseppe belli who reflects in his sonnet campidojjo ( 1830 ) that the gilded statue is directly linked to the long sweep of rome ’ s history . text by dr. jeffrey a. becker additional resources : j. bergemann , römische reiterstatuen : ehrendenkmäler im öffentlichen bereich ( mainz am rhein : ph . von zabern , 1990 ) . a. birley , marcus aurelius : a biography ( london : routledge , 2002 ) . p.j.e . davies , death and the emperor : roman imperial funerary monuments , from augustus to marcus aurelius ( austin : university of texas press , 2004 ) p. fehl , “ the placement of the equestrian statue of marcus aurelius in the middle ages. ” journal of the warburg and courtauld institutes 37 , 1974 , pp . 362-67 . k. fittschen and p. zanker , katalog der römischen porträts in den capitolinischen museen und den anderen kommunalen sammlungen der stadt rom . 3 v. ( berlin : p. von zabern , 1983-2010 ) . d. e. e. kleiner , roman sculpture ( new haven : yale university press , 1992 ) . m. nimmo , marco aurelio , mostra di cantiere : le indagini in corso sul monumento ( rome : arti grafiche pedanesi , 1984 ) . c. p. presicce , and a. m. sommella , the equestrian statue of marcus aurelius in campidoglio ( milan : silvana , 1990 ) . i. s. ryberg , '' rites of the state religion in roman art '' ( memoirs of the american academy in rome ; 22 ) ( rome : american academy in rome , 1955 ) . i. s. ryberg , panel reliefs of marcus aurelius ( new york : archaeological institute of america , 1967 ) . k. stemmer , ed . kaiser , marc aurel und seine zeit : das römische reich im umbruch ( berlin : abguss-sammlung antiker plastik , 1988 ) . d. e. strong , roman art ( new haven : yale university press , 1976 ) . a. m. vaccaro , et al. , marco aurelio : storia di un monumento e del suo restauro ( milan : silvana , 1989 ) . m. van ackeren , ed. , a companion to marcus aurelius ( malden ma : wiley-blackwell , 2012 ) . capitoline museums - marcus aurelius exedra
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the horse wears a harness , some elements of which have not survived . the horse is saddled with a persian-style saddlecloth of several layers , as opposed to a rigid saddle . it should be noted that the horse is an important and expressive element of the overall composition .
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why would the roman emperor have a persian-style saddlecloth ?
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in ancient rome equestrian statues of emperors would not have been uncommon sights in the city—late antique sources suggest that at least 22 of these “ great horses ” ( equi magni ) were to be seen—as they were official devices for honoring the emperor for singular military and civic achievements . the statues themselves were , in turn , copied in other media , including coins , for even wider distribution . few examples of these equestrian statues survive from antiquity , however , making the equestrian statue of marcus aurelius a singular artifact of roman antiquity , one that has borne quiet witness to the ebb and flow of the city of rome for nearly 1,900 years . a gilded bronze monument of the 170s c.e . that was originally dedicated to the emperor marcus aurelius antoninus augustus , referred to commonly as marcus aurelius ( reigned 161-180 c.e . ) , the statue is an important object not only for the study of official roman portraiture , but also for the consideration of monumental dedications . further , the use of the statue in the medieval , renaissance , modern , and post-modern city of rome has important implications for the connectivity that exists between the past and the present . description the statue is an over life-size depiction of the emperor elegantly mounted atop his horse while participating in a public ritual or ceremony ; the statue stands approximately 4.24 meters tall . a gilded bronze statue , the piece was originally cast using the lost-wax technique , with horse and rider cast in multiple pieces and then soldered together after casting . the horse the emperor ’ s horse is a magnificent example of dynamism captured in the sculptural medium . the horse , caught in motion , raises its right foreleg at the knee while planting its left foreleg on the ground , its motion checked by the application of reins , which the emperor originally held in his left hand . the horse ’ s body—in particular its musculature—has been modeled very carefully by the artist , resulting in a powerful rendering . in keeping with the motion of the horse ’ s body , its head turns to its right , with its mouth opened slightly . the horse wears a harness , some elements of which have not survived . the horse is saddled with a persian-style saddlecloth of several layers , as opposed to a rigid saddle . it should be noted that the horse is an important and expressive element of the overall composition . the horseman the horseman sits astride the steed , with his left hand guiding the reins and his right arm raised to shoulder level , the hand outstretched . portrait types there are approximately 110 known portraits of marcus aurelius and these have been grouped into four typological groupings . the first two types belong to the emperor ’ s youth , before he assumed the duties of the principate . in the roman world it was standard practice to create official portrait types of high-ranking officials , such as emperors that would then circulate in various media , notably sculpture in the round and coin portraits . these portrait types are vital in several respects , especially for determining the chronology of monuments and coins , since the portrait types can usually be placed in a fairly accurate and legible chronological order . the interpretation of these portraits relies on various key elements , especially the reading of hairstyle and the examination of facial physiognomy . the second portrait type was made when marcus was in his late 20s , c. 147 c.e . and shows a still youthful type , although marcus now has light facial hair ( left ) . in the case of the equestrian statue , the portrait typology offers the best means of assigning an approximate date to the object since it does not otherwise offer another means of dating . the earliest portrait of marcus aurelius dates to c. 140 c.e . and is best represented by the capitoline galleria 28 type , where the youth wears a cloak fastened at the shoulder ( paludamentum ) ; this portrait was widely circulated , with approximately 25 known copies ( above , left ) . marcus aurelius became emperor in 161 c.e. , when he was forty years of age ; this was the occasion for the creation of his third and most important portrait type . this mature type ( type iii , left ) shows the emperor fully bearded with a full head of tightly curled , voluminous hair ; he retains the characteristic oval-shaped face and heavy eyelids from his earlier portraits . his coiffure forms a distinctive arc over his forehead . this third type is known from approximately 50 copies . the emperor ’ s fourth portrait type ( below , left ) , created between 170 and 180 c.e. , retains most of the features of the third type , but shows the emperor slightly more advanced in age with a very full beard that is divided in the center at the chin , showing parallel locks of hair . dating of the equestrian portrait the statue of the horseman is carefully composed by the artist and depicts a figure that is simultaneously dynamic and a bit passive and removed , by virtue of his facial expression ( see image below ) . the locks of hair are curly and compact and distributed evenly ; the beard is also curly , covering the cheeks and upper lip , and is worn longer at the chin . the pose of the body shows the rider ’ s head turned slightly to his right , in the direction of his outstretched right arm . the left hand originally held the reins ( no longer preserved ) between the index and middle fingers , with the palm facing upwards . scholars continue to debate whether he originally held some attached figure or object in the palm of the left hand ; possible suggestions have included a scepter , a globe , a statue of victory – but there is no clear indication of any attachment point for such an object . on the left hand the rider does wear the senatorial ring . the rider is clad in civic garb , including a short-sleeved tunic that is gathered at the waist by a knotted belt ( cingulum ) . over the tunic the rider wears a cloak ( paludamentum ) that is clasped at the right shoulder . on his feet marcus aurelius wears the senatorial boots of the patrician class , known as calcei patricii . interpretation and chronology the interpretation and chronology of the equestrian statue must rely on the statue itself , as no ancient literary testimony or other evidence survives to aid in the interpretation . it is obvious that the statue is part of an elaborate public monument , no doubt commissioned to mark an important occasion in the emperor ’ s reign . with that said , however , it must also be noted that scholars continue to debate its precise dating , the occasion for its creation , and its likely original location in the city of rome . starting with the portrait typology it is possible to determine a range of likely dates for the statue ’ s creation . the portrait is clearly an adult type of the emperor , meaning the statue must have been created after 161 c.e. , the year of marcus aurelius ’ accession and the creation of his third portrait type . this provides a terminus post quem ( the limit after which ) for the equestrian statue . art historians have debated whether the portrait head most resembles the type iii or the type iv portrait . recent scholarly thinking , based on the work of klaus fittschen , holds that the equestrian portrait represents a unique variant of the standard type iii portrait , created as an improvisation by the artist who was commissioned to create the equestrian statue . in the end the precise chronology of the portrait head—and indeed the typology—remains a matter of scholarly debate . the pose of the horseman is also helpful . the emperor stretches his right hand outward , the palm facing toward the ground ; a pose that could be interpreted as the posture of adlocutio , indicating that the emperor is about to speak . however , more likely in this case we may read it as the gesture of clemency ( clementia ) , offered to a vanquished enemy , or of restitutio pacis , the `` restoration of peace . '' richard brilliant has noted that since the emperor appears in civic garb as opposed to the general ’ s armor , the overall impression of the statue is one of peace rather than of the immediate post-war celebration of military victory . some art historians reconstruct a now-missing barbarian on the right side of the horse , as seen in a surviving panel relief sculpture that originally belonged to a now-lost triumphal arch dedicated to marcus aurelius ( left ) . we know that marcus aurelius celebrated a triumph in 176 c.e . for his victories over german and sarmatian tribes , leading some to suggest that year as the occasion for the creation of the equestrian monument . history the original location of the equestrian monument also remains debated , with some supporting a location on the caelian hill near the barracks of the imperial cavalry ( equites singulares ) , while others favor the campus martius ( a low-lying alluvial plain of the tiber river ) as a possible location . a text known as the liber pontificalis that dates to the middle of the tenth century c.e . mentions the equestrian monument , referring to it as “ caballus constantini ” or the “ horse of constantine. ” according to the text , the urban prefect of rome was condemned following an uprising against pope john xii and , as punishment , was hung by the hair from the equestrian monument . at this time the equestrian statue was located in the lateran quarter of the city of rome near the lateran palace , where it may have been since at least the eighth century c.e . popular theories at the time held that the bearded emperor was in fact constantine i , thus sparing the statue from being melted down . in 1538 the statue was relocated from the lateran quarter to the capitoline hill to become the centerpiece for michelangelo ’ s new design for the campidoglio ( a piazza , or public square , at the top of the capitoline hill ) . the statue was set atop a pedestal at the center of an intricately designed piazza flanked by three palazzi ( image above ) . it became the centerpiece of the main piazza of secular rome and , as such , an icon of the city , a role that its still retains . the equestrian statue still plays a role as an official symbol of the city of rome , even being incorporated into the reverse image of the italian version of the € 0.50 coin ( image above ) . the statue itself remained where michelangelo positioned it until it was moved indoors in 1981 for conservation reasons ; a high-tech copy of the original was placed on the pedestal . the ancient statue is now housed within the musei capitolini where it can be visited and viewed today . the equestrian statue of marcus aurelius is an enduring monument , one that links the city ’ s many phases , ancient and modern . it has borne witness to the city ’ s imperial glory , post-imperial decline , its renaissance resurgence , and even its quotidian experience in the twenty-first century . in so doing it reminds us about the role of public art in creating and reinforcing cultural identity as it relates to specific events and locations . in the ancient world the equestrian statue would have evoked powerful memories from the viewer , not only reinforcing the identity and appearance of the emperor but also calling to mind the key events , achievements , and celebrations of his administration . the statue is , like the city , eternal , as reflected by the romanesco poet giuseppe belli who reflects in his sonnet campidojjo ( 1830 ) that the gilded statue is directly linked to the long sweep of rome ’ s history . text by dr. jeffrey a. becker additional resources : j. bergemann , römische reiterstatuen : ehrendenkmäler im öffentlichen bereich ( mainz am rhein : ph . von zabern , 1990 ) . a. birley , marcus aurelius : a biography ( london : routledge , 2002 ) . p.j.e . davies , death and the emperor : roman imperial funerary monuments , from augustus to marcus aurelius ( austin : university of texas press , 2004 ) p. fehl , “ the placement of the equestrian statue of marcus aurelius in the middle ages. ” journal of the warburg and courtauld institutes 37 , 1974 , pp . 362-67 . k. fittschen and p. zanker , katalog der römischen porträts in den capitolinischen museen und den anderen kommunalen sammlungen der stadt rom . 3 v. ( berlin : p. von zabern , 1983-2010 ) . d. e. e. kleiner , roman sculpture ( new haven : yale university press , 1992 ) . m. nimmo , marco aurelio , mostra di cantiere : le indagini in corso sul monumento ( rome : arti grafiche pedanesi , 1984 ) . c. p. presicce , and a. m. sommella , the equestrian statue of marcus aurelius in campidoglio ( milan : silvana , 1990 ) . i. s. ryberg , '' rites of the state religion in roman art '' ( memoirs of the american academy in rome ; 22 ) ( rome : american academy in rome , 1955 ) . i. s. ryberg , panel reliefs of marcus aurelius ( new york : archaeological institute of america , 1967 ) . k. stemmer , ed . kaiser , marc aurel und seine zeit : das römische reich im umbruch ( berlin : abguss-sammlung antiker plastik , 1988 ) . d. e. strong , roman art ( new haven : yale university press , 1976 ) . a. m. vaccaro , et al. , marco aurelio : storia di un monumento e del suo restauro ( milan : silvana , 1989 ) . m. van ackeren , ed. , a companion to marcus aurelius ( malden ma : wiley-blackwell , 2012 ) . capitoline museums - marcus aurelius exedra
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scholars continue to debate whether he originally held some attached figure or object in the palm of the left hand ; possible suggestions have included a scepter , a globe , a statue of victory – but there is no clear indication of any attachment point for such an object . on the left hand the rider does wear the senatorial ring . the rider is clad in civic garb , including a short-sleeved tunic that is gathered at the waist by a knotted belt ( cingulum ) .
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what evidence supports the statement that it is a senatorial ring ?
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in ancient rome equestrian statues of emperors would not have been uncommon sights in the city—late antique sources suggest that at least 22 of these “ great horses ” ( equi magni ) were to be seen—as they were official devices for honoring the emperor for singular military and civic achievements . the statues themselves were , in turn , copied in other media , including coins , for even wider distribution . few examples of these equestrian statues survive from antiquity , however , making the equestrian statue of marcus aurelius a singular artifact of roman antiquity , one that has borne quiet witness to the ebb and flow of the city of rome for nearly 1,900 years . a gilded bronze monument of the 170s c.e . that was originally dedicated to the emperor marcus aurelius antoninus augustus , referred to commonly as marcus aurelius ( reigned 161-180 c.e . ) , the statue is an important object not only for the study of official roman portraiture , but also for the consideration of monumental dedications . further , the use of the statue in the medieval , renaissance , modern , and post-modern city of rome has important implications for the connectivity that exists between the past and the present . description the statue is an over life-size depiction of the emperor elegantly mounted atop his horse while participating in a public ritual or ceremony ; the statue stands approximately 4.24 meters tall . a gilded bronze statue , the piece was originally cast using the lost-wax technique , with horse and rider cast in multiple pieces and then soldered together after casting . the horse the emperor ’ s horse is a magnificent example of dynamism captured in the sculptural medium . the horse , caught in motion , raises its right foreleg at the knee while planting its left foreleg on the ground , its motion checked by the application of reins , which the emperor originally held in his left hand . the horse ’ s body—in particular its musculature—has been modeled very carefully by the artist , resulting in a powerful rendering . in keeping with the motion of the horse ’ s body , its head turns to its right , with its mouth opened slightly . the horse wears a harness , some elements of which have not survived . the horse is saddled with a persian-style saddlecloth of several layers , as opposed to a rigid saddle . it should be noted that the horse is an important and expressive element of the overall composition . the horseman the horseman sits astride the steed , with his left hand guiding the reins and his right arm raised to shoulder level , the hand outstretched . portrait types there are approximately 110 known portraits of marcus aurelius and these have been grouped into four typological groupings . the first two types belong to the emperor ’ s youth , before he assumed the duties of the principate . in the roman world it was standard practice to create official portrait types of high-ranking officials , such as emperors that would then circulate in various media , notably sculpture in the round and coin portraits . these portrait types are vital in several respects , especially for determining the chronology of monuments and coins , since the portrait types can usually be placed in a fairly accurate and legible chronological order . the interpretation of these portraits relies on various key elements , especially the reading of hairstyle and the examination of facial physiognomy . the second portrait type was made when marcus was in his late 20s , c. 147 c.e . and shows a still youthful type , although marcus now has light facial hair ( left ) . in the case of the equestrian statue , the portrait typology offers the best means of assigning an approximate date to the object since it does not otherwise offer another means of dating . the earliest portrait of marcus aurelius dates to c. 140 c.e . and is best represented by the capitoline galleria 28 type , where the youth wears a cloak fastened at the shoulder ( paludamentum ) ; this portrait was widely circulated , with approximately 25 known copies ( above , left ) . marcus aurelius became emperor in 161 c.e. , when he was forty years of age ; this was the occasion for the creation of his third and most important portrait type . this mature type ( type iii , left ) shows the emperor fully bearded with a full head of tightly curled , voluminous hair ; he retains the characteristic oval-shaped face and heavy eyelids from his earlier portraits . his coiffure forms a distinctive arc over his forehead . this third type is known from approximately 50 copies . the emperor ’ s fourth portrait type ( below , left ) , created between 170 and 180 c.e. , retains most of the features of the third type , but shows the emperor slightly more advanced in age with a very full beard that is divided in the center at the chin , showing parallel locks of hair . dating of the equestrian portrait the statue of the horseman is carefully composed by the artist and depicts a figure that is simultaneously dynamic and a bit passive and removed , by virtue of his facial expression ( see image below ) . the locks of hair are curly and compact and distributed evenly ; the beard is also curly , covering the cheeks and upper lip , and is worn longer at the chin . the pose of the body shows the rider ’ s head turned slightly to his right , in the direction of his outstretched right arm . the left hand originally held the reins ( no longer preserved ) between the index and middle fingers , with the palm facing upwards . scholars continue to debate whether he originally held some attached figure or object in the palm of the left hand ; possible suggestions have included a scepter , a globe , a statue of victory – but there is no clear indication of any attachment point for such an object . on the left hand the rider does wear the senatorial ring . the rider is clad in civic garb , including a short-sleeved tunic that is gathered at the waist by a knotted belt ( cingulum ) . over the tunic the rider wears a cloak ( paludamentum ) that is clasped at the right shoulder . on his feet marcus aurelius wears the senatorial boots of the patrician class , known as calcei patricii . interpretation and chronology the interpretation and chronology of the equestrian statue must rely on the statue itself , as no ancient literary testimony or other evidence survives to aid in the interpretation . it is obvious that the statue is part of an elaborate public monument , no doubt commissioned to mark an important occasion in the emperor ’ s reign . with that said , however , it must also be noted that scholars continue to debate its precise dating , the occasion for its creation , and its likely original location in the city of rome . starting with the portrait typology it is possible to determine a range of likely dates for the statue ’ s creation . the portrait is clearly an adult type of the emperor , meaning the statue must have been created after 161 c.e. , the year of marcus aurelius ’ accession and the creation of his third portrait type . this provides a terminus post quem ( the limit after which ) for the equestrian statue . art historians have debated whether the portrait head most resembles the type iii or the type iv portrait . recent scholarly thinking , based on the work of klaus fittschen , holds that the equestrian portrait represents a unique variant of the standard type iii portrait , created as an improvisation by the artist who was commissioned to create the equestrian statue . in the end the precise chronology of the portrait head—and indeed the typology—remains a matter of scholarly debate . the pose of the horseman is also helpful . the emperor stretches his right hand outward , the palm facing toward the ground ; a pose that could be interpreted as the posture of adlocutio , indicating that the emperor is about to speak . however , more likely in this case we may read it as the gesture of clemency ( clementia ) , offered to a vanquished enemy , or of restitutio pacis , the `` restoration of peace . '' richard brilliant has noted that since the emperor appears in civic garb as opposed to the general ’ s armor , the overall impression of the statue is one of peace rather than of the immediate post-war celebration of military victory . some art historians reconstruct a now-missing barbarian on the right side of the horse , as seen in a surviving panel relief sculpture that originally belonged to a now-lost triumphal arch dedicated to marcus aurelius ( left ) . we know that marcus aurelius celebrated a triumph in 176 c.e . for his victories over german and sarmatian tribes , leading some to suggest that year as the occasion for the creation of the equestrian monument . history the original location of the equestrian monument also remains debated , with some supporting a location on the caelian hill near the barracks of the imperial cavalry ( equites singulares ) , while others favor the campus martius ( a low-lying alluvial plain of the tiber river ) as a possible location . a text known as the liber pontificalis that dates to the middle of the tenth century c.e . mentions the equestrian monument , referring to it as “ caballus constantini ” or the “ horse of constantine. ” according to the text , the urban prefect of rome was condemned following an uprising against pope john xii and , as punishment , was hung by the hair from the equestrian monument . at this time the equestrian statue was located in the lateran quarter of the city of rome near the lateran palace , where it may have been since at least the eighth century c.e . popular theories at the time held that the bearded emperor was in fact constantine i , thus sparing the statue from being melted down . in 1538 the statue was relocated from the lateran quarter to the capitoline hill to become the centerpiece for michelangelo ’ s new design for the campidoglio ( a piazza , or public square , at the top of the capitoline hill ) . the statue was set atop a pedestal at the center of an intricately designed piazza flanked by three palazzi ( image above ) . it became the centerpiece of the main piazza of secular rome and , as such , an icon of the city , a role that its still retains . the equestrian statue still plays a role as an official symbol of the city of rome , even being incorporated into the reverse image of the italian version of the € 0.50 coin ( image above ) . the statue itself remained where michelangelo positioned it until it was moved indoors in 1981 for conservation reasons ; a high-tech copy of the original was placed on the pedestal . the ancient statue is now housed within the musei capitolini where it can be visited and viewed today . the equestrian statue of marcus aurelius is an enduring monument , one that links the city ’ s many phases , ancient and modern . it has borne witness to the city ’ s imperial glory , post-imperial decline , its renaissance resurgence , and even its quotidian experience in the twenty-first century . in so doing it reminds us about the role of public art in creating and reinforcing cultural identity as it relates to specific events and locations . in the ancient world the equestrian statue would have evoked powerful memories from the viewer , not only reinforcing the identity and appearance of the emperor but also calling to mind the key events , achievements , and celebrations of his administration . the statue is , like the city , eternal , as reflected by the romanesco poet giuseppe belli who reflects in his sonnet campidojjo ( 1830 ) that the gilded statue is directly linked to the long sweep of rome ’ s history . text by dr. jeffrey a. becker additional resources : j. bergemann , römische reiterstatuen : ehrendenkmäler im öffentlichen bereich ( mainz am rhein : ph . von zabern , 1990 ) . a. birley , marcus aurelius : a biography ( london : routledge , 2002 ) . p.j.e . davies , death and the emperor : roman imperial funerary monuments , from augustus to marcus aurelius ( austin : university of texas press , 2004 ) p. fehl , “ the placement of the equestrian statue of marcus aurelius in the middle ages. ” journal of the warburg and courtauld institutes 37 , 1974 , pp . 362-67 . k. fittschen and p. zanker , katalog der römischen porträts in den capitolinischen museen und den anderen kommunalen sammlungen der stadt rom . 3 v. ( berlin : p. von zabern , 1983-2010 ) . d. e. e. kleiner , roman sculpture ( new haven : yale university press , 1992 ) . m. nimmo , marco aurelio , mostra di cantiere : le indagini in corso sul monumento ( rome : arti grafiche pedanesi , 1984 ) . c. p. presicce , and a. m. sommella , the equestrian statue of marcus aurelius in campidoglio ( milan : silvana , 1990 ) . i. s. ryberg , '' rites of the state religion in roman art '' ( memoirs of the american academy in rome ; 22 ) ( rome : american academy in rome , 1955 ) . i. s. ryberg , panel reliefs of marcus aurelius ( new york : archaeological institute of america , 1967 ) . k. stemmer , ed . kaiser , marc aurel und seine zeit : das römische reich im umbruch ( berlin : abguss-sammlung antiker plastik , 1988 ) . d. e. strong , roman art ( new haven : yale university press , 1976 ) . a. m. vaccaro , et al. , marco aurelio : storia di un monumento e del suo restauro ( milan : silvana , 1989 ) . m. van ackeren , ed. , a companion to marcus aurelius ( malden ma : wiley-blackwell , 2012 ) . capitoline museums - marcus aurelius exedra
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the equestrian statue still plays a role as an official symbol of the city of rome , even being incorporated into the reverse image of the italian version of the € 0.50 coin ( image above ) . the statue itself remained where michelangelo positioned it until it was moved indoors in 1981 for conservation reasons ; a high-tech copy of the original was placed on the pedestal . the ancient statue is now housed within the musei capitolini where it can be visited and viewed today .
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of what is the high tech modern copy composed ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber .
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in answering the problem at the bottom would the nations gdp who cut down the trees to make lumber and bookshelves be $ 400 ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ?
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would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp .
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if only new goods and services count toward gdp , does that mean that jobs and the salaries that they pay to get counted to gdp in the year the jobs are created and never again for as long as the jobs exist ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires !
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secondly , does an increase in the market value of a job over time not due to inflation also not count toward the gdps of the years other than that when the job was first created ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp .
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do music downloads contribute to the gdp ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories .
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why do we use the term `` net exports '' and group their calculation together , if we are really subtracting imports from consumption ( to avoid double counting ) ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total .
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other point : how can i define income ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply .
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does the inventory belongs to the investment ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp .
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what is chain weighted gdp and how to calculate it ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp .
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let 's have a look at the real-estate , they mainly just buy and sell old houses , which mean `` old products '' so can it be counted to gdp ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp .
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how is data that goes into calculating gdp collected ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone .
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data on production , sales , and the like are easy i guess , but what about things like yard sales or lemonade stands run by children ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ?
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about the problem at the bottom , i think the answer is 350 dollar gdp ( 100 for the tree and 250 for the bookshelves ) , is that right ?
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key points the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . introduction to understand macroeconomics , we first have to measure the economy . but how do we do that ? let 's start by taking a look at the economy of the united states . the size of a nation ’ s overall economy is typically measured by its gross domestic product , or gdp , which is the value of all final goods and services produced within a country in a given year . measuring gdp involves counting up the production of millions of different goods and services—smart phones , cars , music downloads , computers , steel , bananas , college educations , and all other new goods and services produced in the current year—and summing them into a total dollar value . the numbers are large , but the task is straightforward : step 1 : take the quantity of everything produced . step 2 : multiply it by the price at which each product sold . step 3 : add up the total . in 2014 , the gdp of the united states totaled \ $ 17.4 trillion , the largest gdp in the world . it 's important to remember that each of the market transactions that enter into gdp must involve both a buyer and a seller . the gdp of an economy can be measured by the total dollar value of what is purchased in the economy or by the total dollar value of what is produced . understanding how to measure gdp is important for analyzing connections in the macro economy and for thinking about macroeconomic policy tools . gdp measured by components of demand \ $ 17.4 trillion is a lot of money ! who buys all of this production ? let 's break it down by dividing demand into four main parts : consumer spending , or consumption business spending , or investment government spending on goods and services spending on net exports the table below shows how the four above components added up to the gdp for the united states in 2014 . it 's also important to think about how much of the gdp is made up of each of these components . you can analyze the percentages using either the table or the pie graph below it . || components of us gdp in 2014 : from the demand side || | components of gdp on the demand side in trillions of dollars | percentage of total - | - | - consumption | \ $ 11.9 | 68.4 % investment | \ $ 2.9 | 16.7 % government | \ $ 3.2 | 18.4 % exports | \ $ 2.3 | 13.2 % imports | –\ $ 2.9 | –16.7 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm a few patterns are worth noticing here . consumption expenditure by households was the largest component of the us gdp 2014 . in fact , consumption accounts for about two-thirds of the gdp in any given year . this tells us that consumers ’ spending decisions are a major driver of the economy . however , consumer spending is a gentle elephant—when viewed over time , it does n't jump around too much . investment demand accounts for a far smaller percentage of us gdp than consumption demand does , typically only about 15 to 18 % . investment can mean a lot of things , but here , investment expenditure refers to purchases of physical plants and equipment , primarily by businesses . for example , if starbucks builds a new store or amazon buys robots , these expenditures are counted under business investment . investment demand is very important for the economy because it is where jobs are created , but it fluctuates more noticeably than consumption . business investment is volatile . new technology or a new product can spur business investment , but then confidence can drop , and business investment can pull back sharply . if you 've noticed any infrastructure projects—like road construction—in your community or state , you 've seen how important government spending can be for the economy . government expenditure accounts for about 20 % of the gdp of the united states , including spending by federal , state , and local government . it 's important to remember that a significant portion of government budgets are transfer payments—like unemployment benefits , veteran ’ s benefits , and social security payments to retirees—that are excluded from gdp because the government does not receive a new good or service in return or exchange . the only part of government spending counted in demand is government purchases of goods or services produced in the economy—for example , a new fighter jet purchased for the air force ( federal government spending ) , construction of a new highway ( state government spending ) , or building of a new school ( local government spending ) . and finally , we must consider exports and imports when thinking about the demand for domestically produced goods in a global economy . first , we calculate spending on exports—domestically produced goods that are sold abroad . then , we subtract spending on imports—goods produced in other countries that are purchased by residents of this country . the net export component of gdp is equal to the dollar value of exports , $ \text { x } $ , minus the dollar value of imports $ \text { m } $ . the gap between exports and imports is called the trade balance . if a country ’ s exports are larger than its imports , then a country is said to have a trade surplus . if , however , imports exceed exports , the country is said to have a trade deficit . if exports and imports are equal , foreign trade has no effect on total gdp . however , even if exports and imports are balanced overall , foreign trade might still have powerful effects on particular industries and workers by causing nations to shift workers and physical capital investment toward one industry rather than another . based on the four components of demand discussed above—consumption , $ \text { c } $ , investment , $ \text { i } $ , government , $ \text { g } $ , and trade balance , $ \text { t } $ —gdp can be measured as follows : $ \text { gdp } = \text { c + i + g + ( x - m ) } $ gdp measured by what is produced everything that is purchased must be produced first . instead of trying to think about every single product produced , let 's break out five categories : durable goods , nondurable goods , services , structures , and change in inventories . you can see what percentage of the gdp each of these components contributes in the table and pie chart below . before we look at these categories in more detail , take a look at the table below and notice that total gdp measured according to what is produced is exactly the same as the gdp we measured by looking at the five components of demand above . since every market transaction must have both a buyer and a seller , gdp must be the same whether measured by what is demanded or by what is produced . || components of us gdp on the production side , 2014 || | components of gdp on the supply side in trillions of dollars | percentage of total - | - | - goods | | durable goods | \ $ 2.9 | 16.7 % nondurable goods | \ $ 2.3 | 13.2 % services | \ $ 10.8 | 62.1 % structures | \ $ 1.3 | 7.4 % change in inventories | \ $ 0.1 | 0.6 % total gdp | \ $ 17.4 | 100 % source : http : //bea.gov/itable/index_nipa.cfm let 's take a look at the graph above showing the five components of what is produced , expressed as a percentage of gdp , since 1960 . in thinking about what is produced in the economy , many non-economists immediately focus on solid , long-lasting goods—like cars and computers . by far the largest part of gdp , however , is services . additionally , services have been a growing share of gdp over time . you are probably already familiar with some of the leading service industries , like healthcare , education , legal services , and financial services . it has been decades since most of the us economy involved making solid objects . instead , the most common jobs in the modern us economy involve a worker looking at pieces of paper or a computer screen ; meeting with co-workers , customers , or suppliers ; or making phone calls . even if we look only at the goods category , long-lasting durable goods like cars and refrigerators are about the same share of the economy as short-lived nondurable goods like food and clothing . the category of structures includes everything from homes to office buildings , shopping malls , and factories . inventories is a small category that refers to the goods that have been produced by one business but have not yet been sold to consumers and are still sitting in warehouses and on shelves . the amount of inventories sitting on shelves tends to decline if business is better than expected or to rise if business is worse than expected . the problem of double counting gdp is defined as the current value of all final goods and services produced in a nation in a year . but what are final goods ? they are goods at the furthest stage of production at the end of a year . statisticians who calculate gdp must avoid the mistake of double counting—counting output more than once as it travels through the stages of production . for example , imagine what would happen if government statisticians first counted the value of tires produced by a tire manufacturer and then counted the value of a new truck sold by an automaker that contains those tires . the value of the tires would have been counted twice because the price of the truck includes the value of the tires ! to avoid this problem—which would overstate the size of the economy considerably—government statisticians count just the value of final goods and services in the chain of production that are sold for consumption , investment , government , and trade purposes . intermediate goods , which are goods that go into the production of other goods , are excluded from gdp calculations . this means that in the example above , only the value of the truck would be counted . the value of what businesses provide to other businesses is captured in the final products at the end of the production chain . || counting gdp || what is counted in gdp | what is not included in gdp - | - consumption | intermediate goods business investment | transfer payments and non-market activities government spending on goods and services | used goods net exports | illegal goods take a look at the table above showing which items get counted toward gdp and which do n't . the sales of used goods are not included because they were produced in a previous year and are part of that year ’ s gdp . the entire underground economy of services paid “ under the table ” and illegal sales should be counted—but is not—because it is impossible to track these sales . in a recent study by friedrich schneider of shadow economies , the underground economy in the united states was estimated to be 6.6 % of gdp , or close to \ $ 2 trillion dollars in 2013 alone . transfer payments , such as payment by the government to individuals , are not included , because they do not represent production . also , production of some goods—such as home production as when you make your breakfast—is not counted because these goods are not sold in the marketplace . summary the size of a nation ’ s economy is commonly expressed as its gross domestic product , or gdp , which measures the value of the output of all goods and services produced within the country in a year . gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports . what is produced in the economy can be divided into durable goods , nondurable goods , services , structures , and inventories . to avoid double counting—adding the value of output to the gdp more than once—gdp counts only final output of goods and services , not the production of intermediate goods or the value of labor in the chain of production . the gap between exports and imports is called the trade balance . if a nation 's imports exceed its exports , the nation is said to have a trade deficit . if a nation 's exports exceed its imports , it is said to have a trade surplus . self-check questions country a has export sales of \ $ 20 billion , government purchases of \ $ 1,000 billion , business investment is \ $ 50 billion , imports are \ $ 40 billion , and consumption spending is \ $ 2,000 billion . what is the dollar value of gdp ? which of the following are included in gdp , and which are not ? the cost of hospital stays the rise in life expectancy over time child care provided by a licensed day care center child care provided by a grandmother the sale of a used car the sale of a new car the greater variety of cheese available in supermarkets the iron that goes into the steel that goes into a refrigerator bought by a consumer review questions what are the main components of measuring gdp with what is demanded ? what are the main components of measuring gdp with what is produced ? would you usually expect gdp as measured by what is demanded to be greater than gdp measured by what is supplied , or the reverse ? why must double counting be avoided when measuring gdp ? problem last year , a small nation with abundant forests cut down \ $ 200 worth of trees . \ $ 100 worth of trees were then turned into \ $ 150 worth of lumber . \ $ 100 worth of that lumber was used to produce \ $ 250 worth of bookshelves . assuming the country produces no other outputs , and there are no other inputs used in the production of trees , lumber , and bookshelves , what is this nation 's gdp ? in other words , what is the value of the final goods produced including trees , lumber and bookshelves ?
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gdp is measured by taking the quantities of all goods and services produced , multiplying them by their prices , and summing the total . gdp can be measured either by the sum of what is purchased in the economy or by what is produced . demand can be divided into consumption , investment , government , exports , and imports .
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consumption , therefore meaning that the sum of what is purchased does not add up to that of what is produced ?
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animal hide painting painting on animal hides is a longstanding tradition of the great basin and great plains people of the united states , including the kiowa , lakota , shoshone , blackfeet , crow , dakota , and osage . while the earliest surviving hide paintings date to around 1800 , this tradition was undoubtedly practiced much earlier along with other forms of painting like petroglyphs ( rock engravings ) . painting , in tandem with oral traditions , functioned to record history . often artists like cotsiogo ( eastern shoshone ; pronounced “ co see ko ” ) , who is also known by his euro-american name , cadzi cody , painted on elk , deer , or buffalo hides using natural pigments like red ochre and chalk , and eventually paints and dyes obtained through trade . usually , artists decorated the hides with geometric or figural motifs . by the later nineteenth century certain hide artists like cotsiogo began depicting subject matter that “ affirmed native identity ” and appealed to tourists . the imagery placed on the hide was likely done with a combination of free-hand painting and stenciling . men and women both painted on hides , but men usually produced the scenes on tipis ( tepees ) , clothing , and shields . many of these scenes celebrated battles and other biographical details . the brooklyn museum ’ s hide painting by cotsiogo may have functioned as a wall hanging and has also been classified as a robe . the artist cotsiogo ( also codsiogo , katsikodi or cadzi cody ) , a member of the eastern shoshone tribe , painted many hides in addition to the two shown above . they represent his experiences during a period of immense change for the shoshone people . during his lifetime , cotsiogo was placed on the wind river reservation in central western wyoming . the wind river reservation is the size of rhode island and delaware combined and had been established by the fort bridger treaty of 1868 . prior to their placement on the wind river reservation , the shoshone moved with the seasons and the availability of natural resources . many shoshone traversed the geographic regions we now call the great plains and plateau regions . cotsiogo likely created the brooklyn museum hide painting ( above ) for euro-american tourists who visited the reservation . it might explain why there is a scene of buffalo hunting , a scene which was thought to be desirable to tourists . its production helped to support him after the shoshone were moved to the reservation . with newly established trade markets and the influx of new materials , artists like cotsiogo sometimes produced work that helped support themselves and their families . subject matter cotsiogo ’ s brooklyn museum hide painting combines history with the contemporary moment . it displays elements of several different dances , including the important and sacred sun dance and non-religious wolf dance ( tdsayuge or tásayùge ) . the sun dance surrounds a not-yet-raised buffalo head between two poles ( or a split tree ) , with an eagle above it . men dressed in feather bustles and headdresses—not to be confused with feathered war bonnets—dance around the poles , which represents the grass dance . with their arms akimbo and their bodies bent , cotsiogo shows these men in motion . men participating in this sacred , social ceremony refrained from eating or drinking . the sun dance was intended to honor the creator deity for the earth ’ s bounty and to ensure this bounty continued . it was a sacred ceremony that tourists and anthropologists often witnessed . however , the united states government deemed it unacceptable and forbid it . the u.s. government outlawed the sun dance until 1935 , in an effort to compel native americans to abandon their traditional ways . cotsiogo likely included references to the sun dance because he knew tourist consumers would find the scene attractive ; but he modified the scene combining it with the acceptable wolf dance , perhaps to avoid potential ramifications . the wolf dance eventually transformed into the grass dance which is performed today during pow wows ( ceremonial gatherings ) . the hide painting also shows activities of daily life . surrounding the sun dance , women rest near a fire and more men on horses hunt buffaloes . warriors on horses are also shown returning to camp , which was celebrated with the wolf dance . two tipis represent the camp , with the warriors appearing between them . some of the warriors wear feathered war bonnets made of eagle feathers . these headdresses communicated a warrior acted bravely in battle , and so they functioned as symbols of honor and power . not just anyone could wear a feathered war bonnet ! cotsiogo shows the warriors hunting with bows and arrows while riding , but in reality shoshone men had used rifles for some time . horses were introduced to the southwest by spaniards . horses made their way to some plains nations through trade with others like the ute , navajo , and apache . by the mid-eighteenth century , horses had become an important part of plains culture . buffaloes were sacred to the plains people because the animals were essential to their livelihood . some scenes display individuals skinning buffaloes and separating the animals ’ body parts into piles . all parts of the buffalo were used , as it was considered a way of honoring this sacred animal . at the time cotsiogo painted this hide , most buffalo had either been killed or displaced . buffaloes had largely disappeared from this area by the 1880s . cotsiogo ’ s hide thus marks past events and deeds rather than events occurring at the time it was created . essay by dr. lauren kilroy-ewbank editor 's note on the contemporary situation on the wind river reservation : according to the new york times , the 14,000 current residents of the wind river reservation suffer a crime rate more than five times the national average , a life expectancy of only 49 years , and an unemployment rate that may be above 80 percent . additional resources : information on cotsiogo , university of wyoming a song of the horse nation : horses in native american cultures , an exhibit at the nmai
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cotsiogo likely included references to the sun dance because he knew tourist consumers would find the scene attractive ; but he modified the scene combining it with the acceptable wolf dance , perhaps to avoid potential ramifications . the wolf dance eventually transformed into the grass dance which is performed today during pow wows ( ceremonial gatherings ) . the hide painting also shows activities of daily life .
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what is a `` pow wow '' ?
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animal hide painting painting on animal hides is a longstanding tradition of the great basin and great plains people of the united states , including the kiowa , lakota , shoshone , blackfeet , crow , dakota , and osage . while the earliest surviving hide paintings date to around 1800 , this tradition was undoubtedly practiced much earlier along with other forms of painting like petroglyphs ( rock engravings ) . painting , in tandem with oral traditions , functioned to record history . often artists like cotsiogo ( eastern shoshone ; pronounced “ co see ko ” ) , who is also known by his euro-american name , cadzi cody , painted on elk , deer , or buffalo hides using natural pigments like red ochre and chalk , and eventually paints and dyes obtained through trade . usually , artists decorated the hides with geometric or figural motifs . by the later nineteenth century certain hide artists like cotsiogo began depicting subject matter that “ affirmed native identity ” and appealed to tourists . the imagery placed on the hide was likely done with a combination of free-hand painting and stenciling . men and women both painted on hides , but men usually produced the scenes on tipis ( tepees ) , clothing , and shields . many of these scenes celebrated battles and other biographical details . the brooklyn museum ’ s hide painting by cotsiogo may have functioned as a wall hanging and has also been classified as a robe . the artist cotsiogo ( also codsiogo , katsikodi or cadzi cody ) , a member of the eastern shoshone tribe , painted many hides in addition to the two shown above . they represent his experiences during a period of immense change for the shoshone people . during his lifetime , cotsiogo was placed on the wind river reservation in central western wyoming . the wind river reservation is the size of rhode island and delaware combined and had been established by the fort bridger treaty of 1868 . prior to their placement on the wind river reservation , the shoshone moved with the seasons and the availability of natural resources . many shoshone traversed the geographic regions we now call the great plains and plateau regions . cotsiogo likely created the brooklyn museum hide painting ( above ) for euro-american tourists who visited the reservation . it might explain why there is a scene of buffalo hunting , a scene which was thought to be desirable to tourists . its production helped to support him after the shoshone were moved to the reservation . with newly established trade markets and the influx of new materials , artists like cotsiogo sometimes produced work that helped support themselves and their families . subject matter cotsiogo ’ s brooklyn museum hide painting combines history with the contemporary moment . it displays elements of several different dances , including the important and sacred sun dance and non-religious wolf dance ( tdsayuge or tásayùge ) . the sun dance surrounds a not-yet-raised buffalo head between two poles ( or a split tree ) , with an eagle above it . men dressed in feather bustles and headdresses—not to be confused with feathered war bonnets—dance around the poles , which represents the grass dance . with their arms akimbo and their bodies bent , cotsiogo shows these men in motion . men participating in this sacred , social ceremony refrained from eating or drinking . the sun dance was intended to honor the creator deity for the earth ’ s bounty and to ensure this bounty continued . it was a sacred ceremony that tourists and anthropologists often witnessed . however , the united states government deemed it unacceptable and forbid it . the u.s. government outlawed the sun dance until 1935 , in an effort to compel native americans to abandon their traditional ways . cotsiogo likely included references to the sun dance because he knew tourist consumers would find the scene attractive ; but he modified the scene combining it with the acceptable wolf dance , perhaps to avoid potential ramifications . the wolf dance eventually transformed into the grass dance which is performed today during pow wows ( ceremonial gatherings ) . the hide painting also shows activities of daily life . surrounding the sun dance , women rest near a fire and more men on horses hunt buffaloes . warriors on horses are also shown returning to camp , which was celebrated with the wolf dance . two tipis represent the camp , with the warriors appearing between them . some of the warriors wear feathered war bonnets made of eagle feathers . these headdresses communicated a warrior acted bravely in battle , and so they functioned as symbols of honor and power . not just anyone could wear a feathered war bonnet ! cotsiogo shows the warriors hunting with bows and arrows while riding , but in reality shoshone men had used rifles for some time . horses were introduced to the southwest by spaniards . horses made their way to some plains nations through trade with others like the ute , navajo , and apache . by the mid-eighteenth century , horses had become an important part of plains culture . buffaloes were sacred to the plains people because the animals were essential to their livelihood . some scenes display individuals skinning buffaloes and separating the animals ’ body parts into piles . all parts of the buffalo were used , as it was considered a way of honoring this sacred animal . at the time cotsiogo painted this hide , most buffalo had either been killed or displaced . buffaloes had largely disappeared from this area by the 1880s . cotsiogo ’ s hide thus marks past events and deeds rather than events occurring at the time it was created . essay by dr. lauren kilroy-ewbank editor 's note on the contemporary situation on the wind river reservation : according to the new york times , the 14,000 current residents of the wind river reservation suffer a crime rate more than five times the national average , a life expectancy of only 49 years , and an unemployment rate that may be above 80 percent . additional resources : information on cotsiogo , university of wyoming a song of the horse nation : horses in native american cultures , an exhibit at the nmai
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subject matter cotsiogo ’ s brooklyn museum hide painting combines history with the contemporary moment . it displays elements of several different dances , including the important and sacred sun dance and non-religious wolf dance ( tdsayuge or tásayùge ) . the sun dance surrounds a not-yet-raised buffalo head between two poles ( or a split tree ) , with an eagle above it .
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why did the government forbid the sun dance since it was a tradition to the tribe and it was a honor ?
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octet rule - matter always wants to be in the most stable form . for any atom , stability is achieved by following the octet rule , which is to say all atoms ( with a few exceptions ) want 8 electrons in their outermost electron shell ( just like noble gases ) . the electrons present in the outermost shell of an atom are called valence electrons . exceptions to the octet rule include hydrogen ( h ) and helium ( he ) that follow the duet rule instead . they are the first two elements of the periodic table and have a single electron shell which accommodates only 2 electrons . other exceptions include some group 3 elements like boron ( b ) that contain three valence electrons . theoretically , boron can accommodate five more electrons according to the octet rule , but boron is a very small atom and five non-metal atoms ( like hydrogen ) can not pack around the boron nucleus . thus , boron commonly forms three bonds , bh $ \text { } _ { 3 } $ , with a total of six electrons in the outermost shell . this also results in some anomalous properties for boron compounds because they are kind of “ short of electrons ” . it should be thus noted that covalent bonding between non-metals can occur to form compounds with less than an octet on each atom . in general , achieving the octet configuration ( i.e . 8 electrons in the outermost shell ) is the driving force for chemical bonding between atoms . take a look at the outer shell configuration ( i.e . number of valence electrons ) of three atoms – sodium ( na ) , chlorine ( cl ) and neon ( ne ) : ionic and covalent bonds let ’ s look at the following two scenarios a and b . there are two kids , emily and sarah . they both are very good friends . scenario a : scenario b : now let ’ s apply the above analogy to chemical bonding . assume that emily and sarah represent two atoms , and the blanket symbolizes their valence electrons . in scenario a , atom emily is willing to donate her electrons ( blanket ) to atom sarah because by doing so both achieve an octet configuration of 8 electrons in their respective outer shells , making them both happy and stable . this donation of electrons is called ionic bonding . example of an ionic bond in scenario b , both the atoms emily and sarah are equally electronegative . so , neither emily nor sarah is ready to part with her electrons ( blanket ) , and they instead share their valence electrons with each other . this is called a covalent bond . electronegativity is a measure of how strongly an atom attracts electrons from another atom in a chemical bond and this value is governed by where the particular atom is located in the periodic table ( francium is the least electronegative element while fluorine is the most electronegative ) . example of a covalent bond polar and non-polar covalent bond let ’ s go back to emily and sarah : scenario c : scenario d : let ’ s apply the above analogy to a covalent bond formation . in scenario c , both emily and sarah are equally cold ( in our analogy this translates to them having the same electronegativity ) . because they have the same electronegativity , they will share their valence electrons equally with each other . this type of a covalent bond where electrons are shared equally between two atoms is called a non-polar covalent bond . example of a non-polar covalent bond in scenario d , emily is cold but sarah is much colder ( no doubt mild hypothermia from playing outside in the rain too long ) ! together they share the blanket , but sarah has a tendency to keep pulling the blanket from emily in order to warm up more . in the atomic world , one atom ( sarah ) is more electronegative than another atom ( emily ) , and naturally pulls the shared electrons towards itself . this pulling of electrons creates slight polarity in the bond . covalent bonds where electrons are not shared equally between two atoms are called polar covalent bond . example of a polar covalent bond as shown above , the electrons in a covalent bond between two different atoms ( h and cl in this case ) are not equally shared by the atoms . this is due to the electronegativity difference between the two atoms . the more electronegative atom ( cl ) has greater share of the electrons than the less electronegative atom ( h ) . consequently , the atom that has the greater share of the bonding electrons bears a partial negative charge ( δ- ) and the other atom automatically bears a partial positive charge ( δ+ ) of equal magnitude . properties of non-polar covalent bonds : often occurs between atoms that are the same electronegativity difference between bonded atoms is small ( & lt ; 0.5 pauling units ) electrons are shared equally between atoms properties of polar covalent bond : always occurs between different atoms electronegativity difference between bonded atoms is moderate ( 0.5 and 1.9 pauling units ) electrons are not shared equally between atoms methane ( ch $ \text { } _ { 4 } $ ) is an example of a compound where non-polar covalent bonds are formed between two different atoms . one carbon atom forms four covalent bonds with four hydrogen atoms by sharing a pair of electron between itself and each hydrogen ( h ) atom . the electronegativity value for carbon ( c ) and hydrogen ( h ) is 2.55 and 2.1 respectively , so the difference in their electronegativity values is only 0.45 ( & lt ; 0.5 criteria ) ; the electrons are thus equally shared between carbon and hydrogen . so we can conveniently say that a molecule of methane has a total of four non-polar covalent bonds . single and multiple covalent bonds the number of pairs of electrons shared between two atoms determines the type of the covalent bond formed between them . number of electron pairs shared | type of covalent bond formed : - : | : - : 1 | single 2 | double 3 | triple now let ’ s move on to a couple of examples and try to determine the type of covalent bonds formed nitrogen atom can attain an octet configuration by sharing three electrons with another nitrogen atom , forming a triple bond ( three pairs of electrons shared ) consider the molecule carbon dioxide ( co $ \text { } _ { 2 } $ ) . let ’ s determine the type of covalent bonds it forms .
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consequently , the atom that has the greater share of the bonding electrons bears a partial negative charge ( δ- ) and the other atom automatically bears a partial positive charge ( δ+ ) of equal magnitude . properties of non-polar covalent bonds : often occurs between atoms that are the same electronegativity difference between bonded atoms is small ( & lt ; 0.5 pauling units ) electrons are shared equally between atoms properties of polar covalent bond : always occurs between different atoms electronegativity difference between bonded atoms is moderate ( 0.5 and 1.9 pauling units ) electrons are not shared equally between atoms methane ( ch $ \text { } _ { 4 } $ ) is an example of a compound where non-polar covalent bonds are formed between two different atoms . one carbon atom forms four covalent bonds with four hydrogen atoms by sharing a pair of electron between itself and each hydrogen ( h ) atom . the electronegativity value for carbon ( c ) and hydrogen ( h ) is 2.55 and 2.1 respectively , so the difference in their electronegativity values is only 0.45 ( & lt ; 0.5 criteria ) ; the electrons are thus equally shared between carbon and hydrogen .
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what is the max no of covalent bonds that an atom can form with other atoms ?
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