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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron .
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is the requirement for light to free electron a minimum amount of energy , or is it a range ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved .
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why do we have to think about an electron as particle in photo effect not a wave ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared .
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of electron is knocked out then wo n't it change the configuration of the metal ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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is it possible for a photon to knock out multiple electrons ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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energy of a photon is e=hf not hv right ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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does a photon have a finite energy or a finite momentum ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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how does light `` hit '' the electron and have an effect on it if on a subatomic level it has no mass ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved .
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how can a massless particle knock out an electron ( which has a mass ) ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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what will be the consequence if the work function is equal o the initial energy of the photon ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 .
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in the calculation , does the mass of the photoelectron needs to be converted to grams since 9.11 x 10^31 is in kg ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is .
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also is the velocity calculated a vector so how do we represent the direction ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced .
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this might sound like a stupid question but what happens to the electron once it 's freed out of the metal surface and what happens to the photon ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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if f = m x a , and a photon is massless , than how can it knock off an electron ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus .
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so if enough energy is passed to the atoms in that metal plate , would all the atoms inside become cations and change the properties of that metal ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared .
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how does sal know the mass of the electron ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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why does a photon travel 1,000 times faster ( in this example , anyway ) than a photo-electron ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is .
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so is the velocity of the photoelectron 0m/s or what ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron .
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what happens to the part of the energy 'expended ' to do the work function ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about .
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is the work function affected by heat ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced .
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if i put enough photons who have enough energy to remove all the electrons then at the very last , the metal will be without electron ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced .
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what is photo-electron rather than being photon partial with electron ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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how is the photoelectric effect evidence that light has particle nature ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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why ca n't wave nature of light explain photoelectric effect ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced .
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how do you know if it is just one photon with an energy of say , x or multiple photons with a cumulative energy of x which dislodges the electron ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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also we are talking about classical mechanics is n't the photons motion supposed to be studied by quantum mechanics ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ?
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if the wavelength of the photon was 625 nm then what would 've happened ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here .
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would the photons just pass through cesium without affecting it or would cesium be transparent for the 625 nm wavelength light ( probably orange ) or would something else happen entirely ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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if so then what exactly does happen when the energy of the photon is less than the work function of the metal it hits ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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if the photon does not have enough energy to knock the electron free , that is if the energy of the photon is less than the work function , what happens then ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared .
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does the electron have a negative velocity in that case ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle .
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could you fine tune the frequency of the light so the electrons velocity is visible to the human eye ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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how would the photon knock the electron without any mass ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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does a photon with a smaller wavelength cause an electron on the metal surface to be ejected with a greater velocity ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ?
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do photons ever emerge or combine like waves do ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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but sal , what exactly happens to the photon ( and its energy ) when its energy is less than the work function ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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who decided that a photon was massless ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle .
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does this mean we can generate electric current using electromagnetic radiation ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here .
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what is planck 's constant ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers .
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can wavelength be expressed in any other form like m , cm , km ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers .
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why is wavelength expressed in nm ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons .
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why ca n't we explain photo effect in terms of wave nature of light ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle .
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so if you shine white light on a metal , it will knock electrons off for sure , because white light contains all wavelengths of visible light ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron .
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so my question is after this stage of we still supply ( sufficient ) energy photons , then from where will the electrons be emitted- from the next orbit or from the next layer of atoms ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that .
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when a photon collides with an electron to crate a photo electron , is the energy in the photon being transferred to the electron in quanta so that the atom is in the excited state for a moment and the resulting light is spectra ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron .
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or is the electron totally freed from its atom making a positive ion before it loses enough to kinetic energy to be brought into another orbital ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron .
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there is a usage of the term photoelectron , what does it actually mean ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ?
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if i were to say i had to convert all my meters of wavelength to nanometers , how would i convert meters to nanometers ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here .
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what kind of equation would be used ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us .
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so the battery is connected to keep the plates at different potential , and still the circuit is incomplete unless photons are bombarded , right ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here .
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also , does it ever happen that the cathode gets much positive charge and anode , negative charge , so that the current decreases in the given direction , or even stops ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle .
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if you have a really bright , really massive purple light compared to a small , dim purple light would the larger , brighter one cause more electrons to be liberated ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron .
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if the energy of the photon is lesser than the work function , why ca n't the electron absorb another photon to meet it 's energy requirements ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron .
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for what energy level is work function valid ?
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- sometimes light seems to act as a wave , and sometimes light seems to act as a particle . and , an example of this , would be the photoelectric effect , as described by einstein . so let 's say you had a piece of metal , and we know the metal has electrons . i 'm gon na go ahead and draw one electron in here , and this electron is bound to the metal because it 's attracted to the positive charges in the nucleus . if you shine a light on the metal , so the right kind of light with the right kind of frequency , you can actually knock some of those electrons loose , which causes a current of electrons to flow . so this is kind of like a collision between two particles , if we think about light as being a particle . so i 'm gon na draw in a particle of light which we call a photon , so this is massless , and the photon is going to hit this electron , and if the photon has enough energy , it can free the electron , right ? so we can knock it loose , and so let me go ahead and show that . so here , we 're showing the electron being knocked loose and so the electron 's moving in , let 's just say , this direction , with some velocity , v , and if the electron has mass , m , we know that there 's a kinetic energy . the kinetic energy of the electron would be equal to one half mv squared . this freed electron is usually referred to now as a photoelectron . so one photon creates one photoelectron . so one particle hits another particle . and , if you think about this in terms of classical physics , you could think about energy being conserved . so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced . so , kinetic energy of the photoelectron . so let 's say you wanted to solve for the kinetic energy of that photoelectron . so that would be very simple , it would just be kinetic energy would be equal to the energy of the photon , energy of the photon , minus the energy that was necessary to free the electron from the metallic surface . and this e naught , here i 'm calling it e naught , you might see it written differently , a different symbol , but this is the work function . let me go ahead and write work function here , and the work function is different for every kind of metal . so , it 's the minimum amount of energy that 's necessary to free the electron , and so obviously that 's going to be different depending on what metal you 're talking about . all right , let 's do a problem . now that we understand the general idea of the photoelectric effect , let 's look at what this problem asks us . so the problem says , `` if a photon of wavelength `` 525 nm hits metallic cesium ... '' and so here 's the work function for metallic cesium . `` what is the velocity of the photoelectron produced ? '' so they want to know the velocity of the photoelectron produced , which we know is hiding in the kinetic energy right here , and we also know what the work function is . so we know what e naught is here . what we do n't know is the energy of the photon so that 's what we need to calculate first . and so the energy of the photon , energy of the photon , is equal to h , which is planck 's constant , times the frequency , which is usually symbolized by nu . so , we got the frequency , but they gave us the wavelength in the problem here . they gave us wavelength , so we need to relate frequency to wavelength , and that 's related by c , which is the speed of light , is equal to lambda times nu . so , c is the speed of light , and that 's equal to the frequency times the wavelength . so we can substitute n for the frequency , all right , 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength . the frequency is equal to speed of light over lambda , so we can plug that into here , and so now we have the energy of the photon is equal to hc over lambda , and we can plug in those numbers . h is planck 's constant , which is 6.626 times 10 to the negative 34 . so , times 10 to the negative 34 here . c is the speed of light , which is 2.998 times 10 to the 8th meters over seconds , and all over lambda . lambda is the wavelength . that 's 525 nanometers . so 525 times 10 to the negative 9th meters . all right , so let 's get out our calculator and calculate the energy of the photon here . so , let 's go ahead and do that math , so we have 6.626 times 10 to the negative 34 , and we 're going to multiply that number by the speed of light , 2.998 times 10 to the 8th , and we get that number . we 're gon na divide it by the wavelength , 525 times 10 to the negative 9 , and we get 3.78 times 10 to the negative 19 . so , let me go ahead and write that down here . 3.78 times 10 to the negative 19 , and if you did you units up here , you would get joules , and so let 's think about this number for a second , 3.78 times 10 to the negative 19 is the energy of the photon . and that energy of the photon is greater than the work function , which means that that 's a high-energy photon . it 's able to knock the electron free , 'cause remember , this number right here , is the minimum amount of energy needed to free the electron and so we 've exceeded that minimum amount of energy , and so we will produce a photoelectron . so , this photon is high-energy enough to produce a photoelectron . so let 's go ahead and find the kinetic energy of the photoelectron that 's produced . so we 're gon na use this equation right up here . so let me just go and get some more room , and i will rewrite that equation . so we have the kinetic energy of the photoelectron , kinetic energy of the photoelectron , is equal to the energy of the photon , energy of the photon , minus the work function . so let 's plug in our numbers . the energy of the photon was 3.78 times 10 the negative 19 joules , and then the work function is right up here again , it 's 3.43 , so minus 3.43 times 10 to the negative 19 joules . so let 's get out the calculator again . so , from that we 're going to subtract the work function 3.43 times 10 to the negative 19 and we get 3.5 times 10 to the negative 20 . so let 's go ahead and write that . this is equal to 3.5 times 10 to the negative 20 joules . this is equal to the kinetic energy of the photoelectron , and we know that kinetic energy is equal to one half mv squared . the problem asked us to solve for the velocity of the photoelectron . so all we have to do is plug in the mass of an electron , which is 9.11 times 10 to the negative 31st kilograms , times v squared . this is equal to 3.5 times 10 to the negative 20 . so , let 's do that math . so we take 3.5 times 10 to the negative 20 , we multiply that by 2 , and then we divide by the mass of an electron , 9.11 times 10 to the negative 31st , and this gives us that number , which we need to take the square root of . so , square root of our answer gives us the velocity of the electron , 2.8 times 10 to the 5th . so if you look at your decimal place here , this 'll be one , two , three , four , five , so 2.8 times 10 to the 5th meters per second . so here 's the velocity of the photoelectron produced , 2.8 times 10 to the 5th meters per second , and if you increased the intensity of this light , so you had more photons , they would produce more photoelectrons . so one photon knocks out one photoelectron if it has enough energy to do so . so let 's think about this same problem , but let 's change the wavelength . so , what if your wavelength changed to 625 nanometers . so what would happen now ? well , to save time , i wo n't do the calculation , but all we would have to do is plug in 625 up here . so instead of 525 , just plug in 625 to calculate your energy , and if you did that , so if you used 625 times 10 to the negative 9 here , i 'll go ahead and give you the answer just to save some time , you would get 3.2 times 10 to the negative 19 joules . and that is lower than the work function . so let me go ahead and highlight that here . so this number is not as high as the work function . the work function was how much energy we needed to free that electron , and since this is lower than the work function that means we do not get a photoelectron . so , you have to have a high enough energy photon in order to produce a photoelectron . it would n't even matter if we increased the intensity . so if we had more and more and more of these photons at this wavelength , we still would n't produce any photoelectrons . and so , this is the idea of the photoelectric effect , which is best explained by thinking about light as a particle .
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so the energy of the photon , the energy that went in , so let me go ahead and write this here , so the energy of the photon , the energy that went in , what happened to that energy ? some of that energy was needed to free the electron . so the electron was bound , and some of the energy freed the electron . i 'm gon na call that e naught , the energy that freed the electron , and then the rest of that energy must have gone into the kinetic energy of the electron , and so we can write here kinetic energy of the photoelectron that was produced .
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if the photon has enough energy to knock out 2 electron , so will it knock electron with higher speed or will it knock out two electron ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way .
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what is the ph level of soil from the sahara desert ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions .
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why does dave insert the negative sign on the top of the o instead of at the end of oh ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head .
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is there any way to calculate mathemetically that the ph becomes 7 when 20 ml of naoh neutralizes 20 ml of hcl ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o .
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how do we know that all the hydrogen ions and hydroxide ions will react to form water ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride .
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would n't the concentration of h+ be zero and therefore the ph = - log [ 0 ] ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven .
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how do we know that the sodium ions and the chloride anions do n't interact with water to affect ph ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids .
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what are some of the acids and bases that are mostly used in titration ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here .
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is equivalence pt the same as end point ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point .
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is the equivalence point for a strong acid and strong base always a ph of 7 ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over .
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how do you know that the h30 does n't remain , but that there is some base left over ?
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- we 've been looking at the titration curve for the titration of a strong acid , hcl , with a strong base , naoh . in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ? so how many moles of hydroxide ions are we adding to our original acid solution ? we can figure that out by this concentration rate here . so the concentration of sodium hydroxide is .500 molar . that 's also the concentration of hydroxide ions in solution , since we 're talking about a strong base , so the concentration of hydroxide ions in solution is equal to .500 molar . remember : molarity is moles over liters . so this would be equal to moles over liters . how many liters do we have ? we have 20 milliliters , so 20 milliliters would be equal to , move our decimal place , one , two , three ; that 's .02 liters . so to find how many moles , just multiply .5 by .02 and you will get .01 so we have .01 moles of hydroxide ions . so that 's how many moles of hydroxide ions we 're adding to our original acid solution . in the previous video , we already calculated the moles of hydronium ions in solution , and it was the same number as this : .0100 moles of h3o+ so you could watch the previous video , or you can just look at , it 's the same numbers : 20 milliliters here , 20 milliliters here , .500 molar here , .500 molar here . so it 's the same calculation to give us moles of h3o+ , hydronium , or you could just consider that to be moles of h+ . so we have an equal number of moles of base as we do of acid , and the base that we 're adding is going to neutralize the acid that 's present . so the h3o+ , the hydronium that 's present , is neutralized by the base that we add . and so h3o+ donates a proton to oh- , so we get h2o , and then if h3o+ donates a proton , we also get another molecule of h2o . so we get two molecules of h2o here , and we are starting with .01 moles of oh- so let 's go ahead and write that in here . so we have : .01 moles of base , and that 's the same number of moles of acid that we have . so .01 moles of acids . so , this time , we have enough base to completely neutralize our acids . so everything is reacting in a 1:1 ratio here . so all of our base is going to react , and it 's going to completely neutralize our acids . so when that happens , the ph should be just the ph of water . the ph of our solution should be the ph of water , which we know is equal to seven , so 7.00 i could have written this another way . i could have written : hcl + naoh , right ? this would give us , this would give us h2o , 'cause h+ and oh- give us h2o , and then we would have nacl left , right ? we would have a solution of sodium chloride . so , an aqueous solution of sodium chloride . and , if our acid and our base completely neutralize each other , we 're just left with an aqueous solution of sodium chloride , and so the ph is just the ph of water , because sodium and ions and chloride anions do n't interact with water enough to change the ph . so the ph , after we 've added 20 mls of our base , is equal to seven . so we can find that here on our titration curve . so 20 mls of base added , the ph should be seven , so we can find this point on our titration curve . this is the equivalence point . so let me go ahead and draw a line down here . so right here is our equivalence point . let me write that . so , our equivalence point has been reached . we 've added enough moles of base to completely neutralize the acid present , so we 've reached the equivalence point . finally , in part d , they want us to find the ph after the addition of 20.2 mls of a .500 molar solution of sodium hydroxide . so just like before , we need to find the moles of hydroxide ions that we 're adding . and so the concentration of hydroxide ions is , once again , .5 , so .500 molar . molarity is moles over liters , so we wan na find moles . how many liters are we adding ? well , 20.20 mls , is the same thing as .02020 liters . so , we just need to solve for moles ; and you can probably do this in your head . i 'm just going to use the calculator here to show you the answer . so : .5 x .02020 , gives us .0101 so that 's how many moles of hydroxide ions we have : .0101 moles of hydroxide ions . okay , remember : the hydroxide ions reacted with the hydronium ions . we talked about the fact that h3o+ plus oh- gives us 2h2o . this time , we 're starting with .0101 moles of hydroxide ions . so let 's write : .0101 moles . and hydronium , we only started with .01 moles of hydronium , so , .01 moles of hydronium ions . and so , this time we have more base than we do acid , so all of the acid is going to be neutralized , right ? so the acid is going to be completely neutralized . we 're gon na be left with nothing . so all the acid is gone , and most of the base is going to react . so we 're gon na get the same , we 're gon na lose the same amount of base , so we 're gon na lose .0100 moles of base , and so we 're left with a very small amount of base . we 're left with .0001 moles of base left over . so all of the acid has been completely neutralized and we have a small amount of base left over . next , let 's think about the total volume . we started with 20 mls of our acid solution , right ? we started our titration with 20 mls , and at this point of the titration , we 've added 20.2 mls more . so we 've added 20.2 mls more . this gives us a total volume of 40.20 mls . so we have 40.20 mls here . and now we can calculate the concentration of hydroxide ions in solution . so what 's the concentration of hydroxide ions ? concentration is moles over liters , and so we have .0001 moles of hydroxide , and the volume would be , this is in milliliters , so that 's the same thing as .04020 liters . so we can go ahead and do that calculation . take out the calculator here . so we have .0001 divided by .04020 , and we get .002 so our concentration of hydroxide ions is equal to .002 molar . our goal was to find the ph , but right now , we just have to find the poh . so , the poh is equal to the negative log of the concentration of hydroxide ions . so this is the negative log of .002 so : -log ( .002 ) let 's see what that gives us on the calculator . - log ( .002 ) gives us a poh of 2.7 so the poh is equal to 2.7 and finally , to find the ph , we need to know one more equation . the ph plus the poh is equal to 14 . so if we plug in 2.7 into here , the ph is equal to 14 - 2.7 , which is , of course , 11.3 so we finally found the ph . so let 's think about where this point is on our titration curve . we 've added 20.20 mls of our base , let me go ahead and use blue for this so we can see it a little better , we 've added 20.20 mls of our base , and the ph , we just found to be 11.3 so we 're just barely past this 20 here . it 's really hard to draw a straight line . i 'm not doing a very good job . but our ph should be 11.3 so that allows us to find this point on our titration curve , so somewhere around there .
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in the previous video , we 've already found the ph at two points on our titration curve , so we found the ph before we 'd added any of our base , we found the ph at this point , and we also found the ph after we added 10 mls of our base , we found the ph at this point . this is part a of our question , this is part b of our question . now we 're on part c. what is the ph after the addition of 20 mls of a .500 molar solution of sodium hydroxide ?
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are the significant figures correct in the calculation of part d ?
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let 's say there are two communities , an orange community and a purple community , and they 're separate from each other . and your job is to go into these communities , and find out what the most common influenza type is that 's circulating among the people . so you do this , and the first thing you discover is something that 's pretty interesting , which is that , in the orange community , turns out that they really only have influenza type a . remember that there are three types of influenza , and , over here , the only one that seems to be affecting people is type a . so let me actually write that over here , type a . and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b . so these people over here are having influenza type b . and influenza type b also has eight strands of rna . and let me write in purple then , type b . so that 's what you learn in the first kind of day on the job . now there are many different types of type a that are affecting the orange community , and what i 've drawn for you is just the dominant strain . so there may be a handful of type a 's affecting the orange people , but this is the dominant strain . and you know , actually the same is true over here in the purple community . they have a few different type b 's circulating , but the dominant strain is the one that i 've drawn for your . so now , let me make a little bit of space , and let me tell you what you 're going to have to do . over the course of the next year , over the course of the next 12 months , you 're going to actually have to follow these two communities . and what you 're going to do is basically track out over that year what 's happening with the dominant strain . so that 's all we care about -- not all the strains , but just the dominant strain . and you want to know how genetically different is it compared to what it was like on day one of your job ? so when i say genetic change , i 'm really comparing it to what it was like on the first day of your job -- comparing to initial strain . so , over the 12 months , you 'll get a real good idea of how much change happened while you were on the job . so let 's say you start out , and you live close to the purple people . so , of course , initially , there 's no change . you 're doing the type b strain , and you 're saying , well , yep , it has n't changed yet . but some time passes . let 's say you spend some time away , and you come back , and you visit the purple community . and you ask them , hey , what is the common type b strain that you guys are seeing nowadays ? and they say , well , it 's basically the same as it used to be , it has n't really changed a lot , but there are two point mutations that have happened . so the dominant strain now has a couple of point mutations , so it 's a little bit different than it used to be . and you say , a-ha , there is some genetic change happening here . the dominant strain is changing a little bit . and then you go , and you visit again sometime later , and they say , yep , thanks for visiting again . a couple more changes have happened since you last were here . and you say , ah , interesting . let 's plot that a little bit higher . so now the virus , the type b virus , is looking slightly different from how it was when you first started the job . and you keep going with this process , and you know , there 's a mutation here , another one over here . so mutations kind of pile up . and basically what you get is kind of a staggered line -- something like this , where it kind of goes like that , all the way to the end of the year . so the end of the year comes , and you look back at your virus , and you say , ah , there are a few mutations . it 's a little different than what it was like when i started . and those little mutations you can see with the yellow x 's . so what would we call this process ? we call it genetic drift . this is genetic drift . this is kind of the normal process that happens with many , many types of viruses and bacteria . really all viruses and bacteria make mistakes when they replicate , and so you 're going to see some degree of genetic drift over time . so now here 's the cool part . you go to the orange community , the orange county , if you want to call it that . and you say , hey , i 'm here to do the exact same thing with your type a influenza virus . and , in the beginning , of course , it 's not any different . but you come back a little bit later , and you notice that this one has had a couple of changes , a few mutations , just like you saw before . so you say , ok , well , so far so good . it looks like it 's a little changed . and then , you find out that , you know , there 's one more mutation , when you come back on another trip . so you say , ok , looks like it 's a little changed further . and then , a really interesting thing happens . what you find out is on a third trip , that this entire segment is gone , and it 's replaced by this . so you see a huge , new chunk of rna . so how do you plot that on your genetic change axis ? well , it 's really different , is n't it ? so you 'd say , ok , well , gosh , now that 1/8 of the entire thing is different , that would be something like this . that 's a huge jump . so you 'd say , ok , well now there 's been a huge genetic change . and then , you come back on another trip , and you find out that there 's a little mutation in this green rna , and maybe one over there . so , again , you 've got a little bit of change . and you go , and you find out that there was another mutation here , maybe one over here . and so , you keep plotting -- you 're very loyal to your job -- you keep plotting . and then , it turns out that there 's another big shift . let 's say this piece gets changed out for this one . and so , again , you have a big , big jump . something like that . and finally , by the end of the year , it kind of goes up again , because you 've got a couple more mutations . so let 's say , there 's another mutation there and there . so that 's what it looks like . right ? the genetic change over time for the orange one , the type a , is actually looking quite different . and this one actually has elements of what i would call genetic drift and shift . and , more specifically , this part would be kind of a big shift . this is where a whole chunk of rna got kind of incorporated into the dominant virus . these are two shifts that might have happened that year . and these other parts -- let me circle with a different color , let 's say , over here -- this and this is actually looking more similar to what we talked about before . these are just kind of steady changes , steady mutations over time . and this is kind of what we have come to know as genetic drift . so with type a influenza , done in orange , you can see that there is some drift and some shift happening . and with type b influenza , there 's only genetic drift . now what happens , and this is kind of the scary part about type a influenza , is that whenever you have these giant shifts , there are two here , whenever you have these shifts , the entire community has n't really experienced that new type a influenza . they 're not used to it . their immune systems do n't know how to deal with it . and so , many , many people can get sick . and what we call it is a pandemic . so in the past , we 've had a few pandemics . and each time , it 's usually because of a big genetic shift that happens , and many , many people , as i said , get sick , go to the hospital , and can even die .
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and those little mutations you can see with the yellow x 's . so what would we call this process ? we call it genetic drift .
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would the swine flu ( h1n1 ) that happened at around 2008-09 be considered a pandemic ?
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let 's say there are two communities , an orange community and a purple community , and they 're separate from each other . and your job is to go into these communities , and find out what the most common influenza type is that 's circulating among the people . so you do this , and the first thing you discover is something that 's pretty interesting , which is that , in the orange community , turns out that they really only have influenza type a . remember that there are three types of influenza , and , over here , the only one that seems to be affecting people is type a . so let me actually write that over here , type a . and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b . so these people over here are having influenza type b . and influenza type b also has eight strands of rna . and let me write in purple then , type b . so that 's what you learn in the first kind of day on the job . now there are many different types of type a that are affecting the orange community , and what i 've drawn for you is just the dominant strain . so there may be a handful of type a 's affecting the orange people , but this is the dominant strain . and you know , actually the same is true over here in the purple community . they have a few different type b 's circulating , but the dominant strain is the one that i 've drawn for your . so now , let me make a little bit of space , and let me tell you what you 're going to have to do . over the course of the next year , over the course of the next 12 months , you 're going to actually have to follow these two communities . and what you 're going to do is basically track out over that year what 's happening with the dominant strain . so that 's all we care about -- not all the strains , but just the dominant strain . and you want to know how genetically different is it compared to what it was like on day one of your job ? so when i say genetic change , i 'm really comparing it to what it was like on the first day of your job -- comparing to initial strain . so , over the 12 months , you 'll get a real good idea of how much change happened while you were on the job . so let 's say you start out , and you live close to the purple people . so , of course , initially , there 's no change . you 're doing the type b strain , and you 're saying , well , yep , it has n't changed yet . but some time passes . let 's say you spend some time away , and you come back , and you visit the purple community . and you ask them , hey , what is the common type b strain that you guys are seeing nowadays ? and they say , well , it 's basically the same as it used to be , it has n't really changed a lot , but there are two point mutations that have happened . so the dominant strain now has a couple of point mutations , so it 's a little bit different than it used to be . and you say , a-ha , there is some genetic change happening here . the dominant strain is changing a little bit . and then you go , and you visit again sometime later , and they say , yep , thanks for visiting again . a couple more changes have happened since you last were here . and you say , ah , interesting . let 's plot that a little bit higher . so now the virus , the type b virus , is looking slightly different from how it was when you first started the job . and you keep going with this process , and you know , there 's a mutation here , another one over here . so mutations kind of pile up . and basically what you get is kind of a staggered line -- something like this , where it kind of goes like that , all the way to the end of the year . so the end of the year comes , and you look back at your virus , and you say , ah , there are a few mutations . it 's a little different than what it was like when i started . and those little mutations you can see with the yellow x 's . so what would we call this process ? we call it genetic drift . this is genetic drift . this is kind of the normal process that happens with many , many types of viruses and bacteria . really all viruses and bacteria make mistakes when they replicate , and so you 're going to see some degree of genetic drift over time . so now here 's the cool part . you go to the orange community , the orange county , if you want to call it that . and you say , hey , i 'm here to do the exact same thing with your type a influenza virus . and , in the beginning , of course , it 's not any different . but you come back a little bit later , and you notice that this one has had a couple of changes , a few mutations , just like you saw before . so you say , ok , well , so far so good . it looks like it 's a little changed . and then , you find out that , you know , there 's one more mutation , when you come back on another trip . so you say , ok , looks like it 's a little changed further . and then , a really interesting thing happens . what you find out is on a third trip , that this entire segment is gone , and it 's replaced by this . so you see a huge , new chunk of rna . so how do you plot that on your genetic change axis ? well , it 's really different , is n't it ? so you 'd say , ok , well , gosh , now that 1/8 of the entire thing is different , that would be something like this . that 's a huge jump . so you 'd say , ok , well now there 's been a huge genetic change . and then , you come back on another trip , and you find out that there 's a little mutation in this green rna , and maybe one over there . so , again , you 've got a little bit of change . and you go , and you find out that there was another mutation here , maybe one over here . and so , you keep plotting -- you 're very loyal to your job -- you keep plotting . and then , it turns out that there 's another big shift . let 's say this piece gets changed out for this one . and so , again , you have a big , big jump . something like that . and finally , by the end of the year , it kind of goes up again , because you 've got a couple more mutations . so let 's say , there 's another mutation there and there . so that 's what it looks like . right ? the genetic change over time for the orange one , the type a , is actually looking quite different . and this one actually has elements of what i would call genetic drift and shift . and , more specifically , this part would be kind of a big shift . this is where a whole chunk of rna got kind of incorporated into the dominant virus . these are two shifts that might have happened that year . and these other parts -- let me circle with a different color , let 's say , over here -- this and this is actually looking more similar to what we talked about before . these are just kind of steady changes , steady mutations over time . and this is kind of what we have come to know as genetic drift . so with type a influenza , done in orange , you can see that there is some drift and some shift happening . and with type b influenza , there 's only genetic drift . now what happens , and this is kind of the scary part about type a influenza , is that whenever you have these giant shifts , there are two here , whenever you have these shifts , the entire community has n't really experienced that new type a influenza . they 're not used to it . their immune systems do n't know how to deal with it . and so , many , many people can get sick . and what we call it is a pandemic . so in the past , we 've had a few pandemics . and each time , it 's usually because of a big genetic shift that happens , and many , many people , as i said , get sick , go to the hospital , and can even die .
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so let me actually write that over here , type a . and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b .
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where can we go to find out which strain is in the population ?
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let 's say there are two communities , an orange community and a purple community , and they 're separate from each other . and your job is to go into these communities , and find out what the most common influenza type is that 's circulating among the people . so you do this , and the first thing you discover is something that 's pretty interesting , which is that , in the orange community , turns out that they really only have influenza type a . remember that there are three types of influenza , and , over here , the only one that seems to be affecting people is type a . so let me actually write that over here , type a . and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b . so these people over here are having influenza type b . and influenza type b also has eight strands of rna . and let me write in purple then , type b . so that 's what you learn in the first kind of day on the job . now there are many different types of type a that are affecting the orange community , and what i 've drawn for you is just the dominant strain . so there may be a handful of type a 's affecting the orange people , but this is the dominant strain . and you know , actually the same is true over here in the purple community . they have a few different type b 's circulating , but the dominant strain is the one that i 've drawn for your . so now , let me make a little bit of space , and let me tell you what you 're going to have to do . over the course of the next year , over the course of the next 12 months , you 're going to actually have to follow these two communities . and what you 're going to do is basically track out over that year what 's happening with the dominant strain . so that 's all we care about -- not all the strains , but just the dominant strain . and you want to know how genetically different is it compared to what it was like on day one of your job ? so when i say genetic change , i 'm really comparing it to what it was like on the first day of your job -- comparing to initial strain . so , over the 12 months , you 'll get a real good idea of how much change happened while you were on the job . so let 's say you start out , and you live close to the purple people . so , of course , initially , there 's no change . you 're doing the type b strain , and you 're saying , well , yep , it has n't changed yet . but some time passes . let 's say you spend some time away , and you come back , and you visit the purple community . and you ask them , hey , what is the common type b strain that you guys are seeing nowadays ? and they say , well , it 's basically the same as it used to be , it has n't really changed a lot , but there are two point mutations that have happened . so the dominant strain now has a couple of point mutations , so it 's a little bit different than it used to be . and you say , a-ha , there is some genetic change happening here . the dominant strain is changing a little bit . and then you go , and you visit again sometime later , and they say , yep , thanks for visiting again . a couple more changes have happened since you last were here . and you say , ah , interesting . let 's plot that a little bit higher . so now the virus , the type b virus , is looking slightly different from how it was when you first started the job . and you keep going with this process , and you know , there 's a mutation here , another one over here . so mutations kind of pile up . and basically what you get is kind of a staggered line -- something like this , where it kind of goes like that , all the way to the end of the year . so the end of the year comes , and you look back at your virus , and you say , ah , there are a few mutations . it 's a little different than what it was like when i started . and those little mutations you can see with the yellow x 's . so what would we call this process ? we call it genetic drift . this is genetic drift . this is kind of the normal process that happens with many , many types of viruses and bacteria . really all viruses and bacteria make mistakes when they replicate , and so you 're going to see some degree of genetic drift over time . so now here 's the cool part . you go to the orange community , the orange county , if you want to call it that . and you say , hey , i 'm here to do the exact same thing with your type a influenza virus . and , in the beginning , of course , it 's not any different . but you come back a little bit later , and you notice that this one has had a couple of changes , a few mutations , just like you saw before . so you say , ok , well , so far so good . it looks like it 's a little changed . and then , you find out that , you know , there 's one more mutation , when you come back on another trip . so you say , ok , looks like it 's a little changed further . and then , a really interesting thing happens . what you find out is on a third trip , that this entire segment is gone , and it 's replaced by this . so you see a huge , new chunk of rna . so how do you plot that on your genetic change axis ? well , it 's really different , is n't it ? so you 'd say , ok , well , gosh , now that 1/8 of the entire thing is different , that would be something like this . that 's a huge jump . so you 'd say , ok , well now there 's been a huge genetic change . and then , you come back on another trip , and you find out that there 's a little mutation in this green rna , and maybe one over there . so , again , you 've got a little bit of change . and you go , and you find out that there was another mutation here , maybe one over here . and so , you keep plotting -- you 're very loyal to your job -- you keep plotting . and then , it turns out that there 's another big shift . let 's say this piece gets changed out for this one . and so , again , you have a big , big jump . something like that . and finally , by the end of the year , it kind of goes up again , because you 've got a couple more mutations . so let 's say , there 's another mutation there and there . so that 's what it looks like . right ? the genetic change over time for the orange one , the type a , is actually looking quite different . and this one actually has elements of what i would call genetic drift and shift . and , more specifically , this part would be kind of a big shift . this is where a whole chunk of rna got kind of incorporated into the dominant virus . these are two shifts that might have happened that year . and these other parts -- let me circle with a different color , let 's say , over here -- this and this is actually looking more similar to what we talked about before . these are just kind of steady changes , steady mutations over time . and this is kind of what we have come to know as genetic drift . so with type a influenza , done in orange , you can see that there is some drift and some shift happening . and with type b influenza , there 's only genetic drift . now what happens , and this is kind of the scary part about type a influenza , is that whenever you have these giant shifts , there are two here , whenever you have these shifts , the entire community has n't really experienced that new type a influenza . they 're not used to it . their immune systems do n't know how to deal with it . and so , many , many people can get sick . and what we call it is a pandemic . so in the past , we 've had a few pandemics . and each time , it 's usually because of a big genetic shift that happens , and many , many people , as i said , get sick , go to the hospital , and can even die .
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so what would we call this process ? we call it genetic drift . this is genetic drift . this is kind of the normal process that happens with many , many types of viruses and bacteria .
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if a genetic shift is responsible for pandemics , then why was the swine flu ( h1n1 ) in 2009 a pandemic ?
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let 's say there are two communities , an orange community and a purple community , and they 're separate from each other . and your job is to go into these communities , and find out what the most common influenza type is that 's circulating among the people . so you do this , and the first thing you discover is something that 's pretty interesting , which is that , in the orange community , turns out that they really only have influenza type a . remember that there are three types of influenza , and , over here , the only one that seems to be affecting people is type a . so let me actually write that over here , type a . and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b . so these people over here are having influenza type b . and influenza type b also has eight strands of rna . and let me write in purple then , type b . so that 's what you learn in the first kind of day on the job . now there are many different types of type a that are affecting the orange community , and what i 've drawn for you is just the dominant strain . so there may be a handful of type a 's affecting the orange people , but this is the dominant strain . and you know , actually the same is true over here in the purple community . they have a few different type b 's circulating , but the dominant strain is the one that i 've drawn for your . so now , let me make a little bit of space , and let me tell you what you 're going to have to do . over the course of the next year , over the course of the next 12 months , you 're going to actually have to follow these two communities . and what you 're going to do is basically track out over that year what 's happening with the dominant strain . so that 's all we care about -- not all the strains , but just the dominant strain . and you want to know how genetically different is it compared to what it was like on day one of your job ? so when i say genetic change , i 'm really comparing it to what it was like on the first day of your job -- comparing to initial strain . so , over the 12 months , you 'll get a real good idea of how much change happened while you were on the job . so let 's say you start out , and you live close to the purple people . so , of course , initially , there 's no change . you 're doing the type b strain , and you 're saying , well , yep , it has n't changed yet . but some time passes . let 's say you spend some time away , and you come back , and you visit the purple community . and you ask them , hey , what is the common type b strain that you guys are seeing nowadays ? and they say , well , it 's basically the same as it used to be , it has n't really changed a lot , but there are two point mutations that have happened . so the dominant strain now has a couple of point mutations , so it 's a little bit different than it used to be . and you say , a-ha , there is some genetic change happening here . the dominant strain is changing a little bit . and then you go , and you visit again sometime later , and they say , yep , thanks for visiting again . a couple more changes have happened since you last were here . and you say , ah , interesting . let 's plot that a little bit higher . so now the virus , the type b virus , is looking slightly different from how it was when you first started the job . and you keep going with this process , and you know , there 's a mutation here , another one over here . so mutations kind of pile up . and basically what you get is kind of a staggered line -- something like this , where it kind of goes like that , all the way to the end of the year . so the end of the year comes , and you look back at your virus , and you say , ah , there are a few mutations . it 's a little different than what it was like when i started . and those little mutations you can see with the yellow x 's . so what would we call this process ? we call it genetic drift . this is genetic drift . this is kind of the normal process that happens with many , many types of viruses and bacteria . really all viruses and bacteria make mistakes when they replicate , and so you 're going to see some degree of genetic drift over time . so now here 's the cool part . you go to the orange community , the orange county , if you want to call it that . and you say , hey , i 'm here to do the exact same thing with your type a influenza virus . and , in the beginning , of course , it 's not any different . but you come back a little bit later , and you notice that this one has had a couple of changes , a few mutations , just like you saw before . so you say , ok , well , so far so good . it looks like it 's a little changed . and then , you find out that , you know , there 's one more mutation , when you come back on another trip . so you say , ok , looks like it 's a little changed further . and then , a really interesting thing happens . what you find out is on a third trip , that this entire segment is gone , and it 's replaced by this . so you see a huge , new chunk of rna . so how do you plot that on your genetic change axis ? well , it 's really different , is n't it ? so you 'd say , ok , well , gosh , now that 1/8 of the entire thing is different , that would be something like this . that 's a huge jump . so you 'd say , ok , well now there 's been a huge genetic change . and then , you come back on another trip , and you find out that there 's a little mutation in this green rna , and maybe one over there . so , again , you 've got a little bit of change . and you go , and you find out that there was another mutation here , maybe one over here . and so , you keep plotting -- you 're very loyal to your job -- you keep plotting . and then , it turns out that there 's another big shift . let 's say this piece gets changed out for this one . and so , again , you have a big , big jump . something like that . and finally , by the end of the year , it kind of goes up again , because you 've got a couple more mutations . so let 's say , there 's another mutation there and there . so that 's what it looks like . right ? the genetic change over time for the orange one , the type a , is actually looking quite different . and this one actually has elements of what i would call genetic drift and shift . and , more specifically , this part would be kind of a big shift . this is where a whole chunk of rna got kind of incorporated into the dominant virus . these are two shifts that might have happened that year . and these other parts -- let me circle with a different color , let 's say , over here -- this and this is actually looking more similar to what we talked about before . these are just kind of steady changes , steady mutations over time . and this is kind of what we have come to know as genetic drift . so with type a influenza , done in orange , you can see that there is some drift and some shift happening . and with type b influenza , there 's only genetic drift . now what happens , and this is kind of the scary part about type a influenza , is that whenever you have these giant shifts , there are two here , whenever you have these shifts , the entire community has n't really experienced that new type a influenza . they 're not used to it . their immune systems do n't know how to deal with it . and so , many , many people can get sick . and what we call it is a pandemic . so in the past , we 've had a few pandemics . and each time , it 's usually because of a big genetic shift that happens , and many , many people , as i said , get sick , go to the hospital , and can even die .
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let 's plot that a little bit higher . so now the virus , the type b virus , is looking slightly different from how it was when you first started the job . and you keep going with this process , and you know , there 's a mutation here , another one over here .
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if it were impossible for two different strains of a virus to attack the same cell would it then be impossible for a virus to shift/drift ?
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let 's say there are two communities , an orange community and a purple community , and they 're separate from each other . and your job is to go into these communities , and find out what the most common influenza type is that 's circulating among the people . so you do this , and the first thing you discover is something that 's pretty interesting , which is that , in the orange community , turns out that they really only have influenza type a . remember that there are three types of influenza , and , over here , the only one that seems to be affecting people is type a . so let me actually write that over here , type a . and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b . so these people over here are having influenza type b . and influenza type b also has eight strands of rna . and let me write in purple then , type b . so that 's what you learn in the first kind of day on the job . now there are many different types of type a that are affecting the orange community , and what i 've drawn for you is just the dominant strain . so there may be a handful of type a 's affecting the orange people , but this is the dominant strain . and you know , actually the same is true over here in the purple community . they have a few different type b 's circulating , but the dominant strain is the one that i 've drawn for your . so now , let me make a little bit of space , and let me tell you what you 're going to have to do . over the course of the next year , over the course of the next 12 months , you 're going to actually have to follow these two communities . and what you 're going to do is basically track out over that year what 's happening with the dominant strain . so that 's all we care about -- not all the strains , but just the dominant strain . and you want to know how genetically different is it compared to what it was like on day one of your job ? so when i say genetic change , i 'm really comparing it to what it was like on the first day of your job -- comparing to initial strain . so , over the 12 months , you 'll get a real good idea of how much change happened while you were on the job . so let 's say you start out , and you live close to the purple people . so , of course , initially , there 's no change . you 're doing the type b strain , and you 're saying , well , yep , it has n't changed yet . but some time passes . let 's say you spend some time away , and you come back , and you visit the purple community . and you ask them , hey , what is the common type b strain that you guys are seeing nowadays ? and they say , well , it 's basically the same as it used to be , it has n't really changed a lot , but there are two point mutations that have happened . so the dominant strain now has a couple of point mutations , so it 's a little bit different than it used to be . and you say , a-ha , there is some genetic change happening here . the dominant strain is changing a little bit . and then you go , and you visit again sometime later , and they say , yep , thanks for visiting again . a couple more changes have happened since you last were here . and you say , ah , interesting . let 's plot that a little bit higher . so now the virus , the type b virus , is looking slightly different from how it was when you first started the job . and you keep going with this process , and you know , there 's a mutation here , another one over here . so mutations kind of pile up . and basically what you get is kind of a staggered line -- something like this , where it kind of goes like that , all the way to the end of the year . so the end of the year comes , and you look back at your virus , and you say , ah , there are a few mutations . it 's a little different than what it was like when i started . and those little mutations you can see with the yellow x 's . so what would we call this process ? we call it genetic drift . this is genetic drift . this is kind of the normal process that happens with many , many types of viruses and bacteria . really all viruses and bacteria make mistakes when they replicate , and so you 're going to see some degree of genetic drift over time . so now here 's the cool part . you go to the orange community , the orange county , if you want to call it that . and you say , hey , i 'm here to do the exact same thing with your type a influenza virus . and , in the beginning , of course , it 's not any different . but you come back a little bit later , and you notice that this one has had a couple of changes , a few mutations , just like you saw before . so you say , ok , well , so far so good . it looks like it 's a little changed . and then , you find out that , you know , there 's one more mutation , when you come back on another trip . so you say , ok , looks like it 's a little changed further . and then , a really interesting thing happens . what you find out is on a third trip , that this entire segment is gone , and it 's replaced by this . so you see a huge , new chunk of rna . so how do you plot that on your genetic change axis ? well , it 's really different , is n't it ? so you 'd say , ok , well , gosh , now that 1/8 of the entire thing is different , that would be something like this . that 's a huge jump . so you 'd say , ok , well now there 's been a huge genetic change . and then , you come back on another trip , and you find out that there 's a little mutation in this green rna , and maybe one over there . so , again , you 've got a little bit of change . and you go , and you find out that there was another mutation here , maybe one over here . and so , you keep plotting -- you 're very loyal to your job -- you keep plotting . and then , it turns out that there 's another big shift . let 's say this piece gets changed out for this one . and so , again , you have a big , big jump . something like that . and finally , by the end of the year , it kind of goes up again , because you 've got a couple more mutations . so let 's say , there 's another mutation there and there . so that 's what it looks like . right ? the genetic change over time for the orange one , the type a , is actually looking quite different . and this one actually has elements of what i would call genetic drift and shift . and , more specifically , this part would be kind of a big shift . this is where a whole chunk of rna got kind of incorporated into the dominant virus . these are two shifts that might have happened that year . and these other parts -- let me circle with a different color , let 's say , over here -- this and this is actually looking more similar to what we talked about before . these are just kind of steady changes , steady mutations over time . and this is kind of what we have come to know as genetic drift . so with type a influenza , done in orange , you can see that there is some drift and some shift happening . and with type b influenza , there 's only genetic drift . now what happens , and this is kind of the scary part about type a influenza , is that whenever you have these giant shifts , there are two here , whenever you have these shifts , the entire community has n't really experienced that new type a influenza . they 're not used to it . their immune systems do n't know how to deal with it . and so , many , many people can get sick . and what we call it is a pandemic . so in the past , we 've had a few pandemics . and each time , it 's usually because of a big genetic shift that happens , and many , many people , as i said , get sick , go to the hospital , and can even die .
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and if you go over to the purple community , you actually find quite the opposite . you find that over here , people are also getting the flu , but it 's always because of type b . so these people over here are having influenza type b .
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or is it possible for a strain of type a flu to genetically change/mutate without mixing with another ?
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the illustration below shows the graph of y as a function of x . so that 's this graph right over here . and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis . horizontal axis is x-axis . initially , as x increases -- so let 's think about it . initially , so when we start from x equals 0 and x is increasing , what 's happening to y ? well , y is decreasing . so y decreases . so as x increases initially , y decreases . the slope of the graph is equal to blank for all x between x equals 0 and x equals 3 . so x equals 0 and x equals 3 , what 's the slope ? well , every time we move 1 in the x direction , we move down in the y direction . we go negative 1 in the y direction . move up 1 in the x direction , we go negative 1 in the y direction . so our change in y over our change in x -- our change in y is negative 1 whenever our change in x is 1 . so our change in y over our change in x , which is the definition of slope , is negative 1/1 . so it 's negative 1 . and we see that . every time x increases by 1 , y decreases by 1 . starting at x equals 3 , y blank as x increases . so starting at x equals 3 , y increases as x increases . as x increases , y is increasing . so y increases as x increases . the slope of the graph is equal to blank for x between 3 and 5 . so when x increases by 1 , y is increasing by 3 . so change in y is 3 , change in x is 1 . slope is change in y over change in x , which is 3/1 . so the slope here is 3 . every time x increases by 1 , y increases by 3 . for x between x equals 0 and x equals 4 , y -- let 's see , we can pick less than or equal to , greater than or equal to , or equal . so for x equals 0 and x equals 4 , y is less than or equal to 0 . so let 's do less than or equal to 0 . and then they say , for x between x equals 4 and x equals 8 -- well , then y is greater than or equal to 0 . so let 's make sure that we did n't make any careless mistakes here . let 's check our answer . we got it right .
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so as x increases initially , y decreases . the slope of the graph is equal to blank for all x between x equals 0 and x equals 3 . so x equals 0 and x equals 3 , what 's the slope ? well , every time we move 1 in the x direction , we move down in the y direction .
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what 's the slope of sal 's function when x is 3 ?
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the illustration below shows the graph of y as a function of x . so that 's this graph right over here . and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis . horizontal axis is x-axis . initially , as x increases -- so let 's think about it . initially , so when we start from x equals 0 and x is increasing , what 's happening to y ? well , y is decreasing . so y decreases . so as x increases initially , y decreases . the slope of the graph is equal to blank for all x between x equals 0 and x equals 3 . so x equals 0 and x equals 3 , what 's the slope ? well , every time we move 1 in the x direction , we move down in the y direction . we go negative 1 in the y direction . move up 1 in the x direction , we go negative 1 in the y direction . so our change in y over our change in x -- our change in y is negative 1 whenever our change in x is 1 . so our change in y over our change in x , which is the definition of slope , is negative 1/1 . so it 's negative 1 . and we see that . every time x increases by 1 , y decreases by 1 . starting at x equals 3 , y blank as x increases . so starting at x equals 3 , y increases as x increases . as x increases , y is increasing . so y increases as x increases . the slope of the graph is equal to blank for x between 3 and 5 . so when x increases by 1 , y is increasing by 3 . so change in y is 3 , change in x is 1 . slope is change in y over change in x , which is 3/1 . so the slope here is 3 . every time x increases by 1 , y increases by 3 . for x between x equals 0 and x equals 4 , y -- let 's see , we can pick less than or equal to , greater than or equal to , or equal . so for x equals 0 and x equals 4 , y is less than or equal to 0 . so let 's do less than or equal to 0 . and then they say , for x between x equals 4 and x equals 8 -- well , then y is greater than or equal to 0 . so let 's make sure that we did n't make any careless mistakes here . let 's check our answer . we got it right .
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and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis .
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what is a `` constant function '' ?
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the illustration below shows the graph of y as a function of x . so that 's this graph right over here . and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis . horizontal axis is x-axis . initially , as x increases -- so let 's think about it . initially , so when we start from x equals 0 and x is increasing , what 's happening to y ? well , y is decreasing . so y decreases . so as x increases initially , y decreases . the slope of the graph is equal to blank for all x between x equals 0 and x equals 3 . so x equals 0 and x equals 3 , what 's the slope ? well , every time we move 1 in the x direction , we move down in the y direction . we go negative 1 in the y direction . move up 1 in the x direction , we go negative 1 in the y direction . so our change in y over our change in x -- our change in y is negative 1 whenever our change in x is 1 . so our change in y over our change in x , which is the definition of slope , is negative 1/1 . so it 's negative 1 . and we see that . every time x increases by 1 , y decreases by 1 . starting at x equals 3 , y blank as x increases . so starting at x equals 3 , y increases as x increases . as x increases , y is increasing . so y increases as x increases . the slope of the graph is equal to blank for x between 3 and 5 . so when x increases by 1 , y is increasing by 3 . so change in y is 3 , change in x is 1 . slope is change in y over change in x , which is 3/1 . so the slope here is 3 . every time x increases by 1 , y increases by 3 . for x between x equals 0 and x equals 4 , y -- let 's see , we can pick less than or equal to , greater than or equal to , or equal . so for x equals 0 and x equals 4 , y is less than or equal to 0 . so let 's do less than or equal to 0 . and then they say , for x between x equals 4 and x equals 8 -- well , then y is greater than or equal to 0 . so let 's make sure that we did n't make any careless mistakes here . let 's check our answer . we got it right .
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and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis .
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can different style of line graphs affect how you interpret the function ?
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the illustration below shows the graph of y as a function of x . so that 's this graph right over here . and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis . horizontal axis is x-axis . initially , as x increases -- so let 's think about it . initially , so when we start from x equals 0 and x is increasing , what 's happening to y ? well , y is decreasing . so y decreases . so as x increases initially , y decreases . the slope of the graph is equal to blank for all x between x equals 0 and x equals 3 . so x equals 0 and x equals 3 , what 's the slope ? well , every time we move 1 in the x direction , we move down in the y direction . we go negative 1 in the y direction . move up 1 in the x direction , we go negative 1 in the y direction . so our change in y over our change in x -- our change in y is negative 1 whenever our change in x is 1 . so our change in y over our change in x , which is the definition of slope , is negative 1/1 . so it 's negative 1 . and we see that . every time x increases by 1 , y decreases by 1 . starting at x equals 3 , y blank as x increases . so starting at x equals 3 , y increases as x increases . as x increases , y is increasing . so y increases as x increases . the slope of the graph is equal to blank for x between 3 and 5 . so when x increases by 1 , y is increasing by 3 . so change in y is 3 , change in x is 1 . slope is change in y over change in x , which is 3/1 . so the slope here is 3 . every time x increases by 1 , y increases by 3 . for x between x equals 0 and x equals 4 , y -- let 's see , we can pick less than or equal to , greater than or equal to , or equal . so for x equals 0 and x equals 4 , y is less than or equal to 0 . so let 's do less than or equal to 0 . and then they say , for x between x equals 4 and x equals 8 -- well , then y is greater than or equal to 0 . so let 's make sure that we did n't make any careless mistakes here . let 's check our answer . we got it right .
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the illustration below shows the graph of y as a function of x . so that 's this graph right over here .
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what is the difference between linear functions and nonlinear functions ?
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the illustration below shows the graph of y as a function of x . so that 's this graph right over here . and then they start to ask us some questions . complete the sentences based on the graph of the function . so this axis is our y-axis , the vertical axis . horizontal axis is x-axis . initially , as x increases -- so let 's think about it . initially , so when we start from x equals 0 and x is increasing , what 's happening to y ? well , y is decreasing . so y decreases . so as x increases initially , y decreases . the slope of the graph is equal to blank for all x between x equals 0 and x equals 3 . so x equals 0 and x equals 3 , what 's the slope ? well , every time we move 1 in the x direction , we move down in the y direction . we go negative 1 in the y direction . move up 1 in the x direction , we go negative 1 in the y direction . so our change in y over our change in x -- our change in y is negative 1 whenever our change in x is 1 . so our change in y over our change in x , which is the definition of slope , is negative 1/1 . so it 's negative 1 . and we see that . every time x increases by 1 , y decreases by 1 . starting at x equals 3 , y blank as x increases . so starting at x equals 3 , y increases as x increases . as x increases , y is increasing . so y increases as x increases . the slope of the graph is equal to blank for x between 3 and 5 . so when x increases by 1 , y is increasing by 3 . so change in y is 3 , change in x is 1 . slope is change in y over change in x , which is 3/1 . so the slope here is 3 . every time x increases by 1 , y increases by 3 . for x between x equals 0 and x equals 4 , y -- let 's see , we can pick less than or equal to , greater than or equal to , or equal . so for x equals 0 and x equals 4 , y is less than or equal to 0 . so let 's do less than or equal to 0 . and then they say , for x between x equals 4 and x equals 8 -- well , then y is greater than or equal to 0 . so let 's make sure that we did n't make any careless mistakes here . let 's check our answer . we got it right .
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so let 's make sure that we did n't make any careless mistakes here . let 's check our answer . we got it right .
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parcc test practice http : //parcc.pearson.com/resources/practice_tests/grade_8/math/pc194840-001_g8mathoptb_pt.pdf what is the answer of graph problem in page 7 ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language .
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has anyone ever wondered why so many languages have similar words for moms ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything .
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also , is `` learning theory '' interchangeable with `` behaviorist theory '' ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language .
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so if a child ( who has the ability to recognize and pick-up languages ) lived for short periods , perhaps a year in 3 different countries , would he/she be able to speak all three languages ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles .
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does anyone know if it is easier to acquire language for adults who already know a certain number of languages ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement .
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is there a climax number , after which learning becomes easier ( analogous to the activation energy of a reaction or hiking to the top of the mountain ) ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain .
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my question will be is there any ways to produce the lad to help people learn languages ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach .
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how can we disprove the idea within the learning theory that children will sometimes use words and/or phrases they 've never heard before ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach .
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more specifically , how can we be sure that these new words were not picked up passively from sources that the parents/observers/researchers were n't aware of ?
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so this might surprise you , but one of the most amazing feats you 'll ever accomplish as a human being already happened , and that is language development . i mean , think about it . when you 're a baby , all these sounds are coming at you , and somehow , you 're able to figure out which sounds are words , where there are breaks between the words , general grammatical rules , and you 're able to apply them without any real formal training . this is amazing . so naturally , a lot of research has been done into how this ability develops . and i 'm going to tell you about the three main theories that look at language development . so first , we start out with the nativist , or innatist perspective . and what this perspective says is that children are born with the ability to learn language . and the main guy associated with this theory is noam chomsky . and he thought the humans had something called a language acquisition device , or lad , in their brains that allowed them to learn language . and this is n't really supposed to be in a specific part of the brain . it 's just an idea that this ability exists . and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . '' the `` critical period '' is usually thought to be from birth until about age eight or nine , and it 's the period of time in which a child is most able to learn a language . so if you try to learn a language after that age , it 's a lot harder . it 's not impossible . it 's just a lot harder . and nativists like chomsky would say that that 's because the lad only operates during that critical period . once you start using it , then it specializes to your language , and it becomes unable to detect other sounds and grammar from other languages . the second theory i want to tell you about is the learning theory . learning theorists think that children are n't born with anything . they only acquire language through reinforcement . so a learning theorist would say that a child learns to say `` mama '' because every time it makes it sound that approaches that -- so `` ma-something '' -- then mom starts smiling , hugging the child , so over time , the child learns , oh , the more i make this sound , the more i get hugs and smiles . and so then , eventually , it learns to say `` ma , '' and then say it again , and learns to say `` mama . '' so this makes sense . but a strict learning theory does n't explain how children are able to produce words they 've never heard before or produce unique sentences . so we have another theory called the interactionist approach . sometimes this is called the social interactionist approach , because these theorists believe that biological and social factors have to interact in order for children to learn language . so they would say that children strongly desire to communicate with others , such as the adults in their lives , and that desire motivates them to learn to communicate via language . and the main theorist associated with this school of thought is vygotsky . he was a big proponent of the importance of social interaction in the development of children . all three of these theories have made big contributions to our understanding of how children develop language . so the next time you look at a baby , be impressed . they 're actually working really hard .
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and this works because he thought that all languages shared a universal grammar , or the same basic elements , so all languages would have nouns , verbs , things like that . so the language acquisition device enables the child to pick up on and understand those types of words and their organization within a sentence for any language . this goes along with the idea that there is a `` critical period '' or a `` sensitive period . ''
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which theory of language development you find the best in developing of the language of a child ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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let 's keep going . type the missing numbers . it says count the ladybugs .
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to count numbers in order , you basically just need to memorize the numbers and what order they come in right ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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do we have to count from zero ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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why do we count things ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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why is it important to count in order ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse !
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why did you use mice to count ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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let 's keep going . type the missing numbers . it says count the ladybugs .
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are there numbers after 100 ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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let 's keep going . type the missing numbers . it says count the ladybugs .
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why do we have numbers ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good .
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what is -5 divided by 2 , 2.5 or -10 or 10 or -2.5 ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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how do we know that we 're supposed to count flowers like americans count ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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why do we count in base 10 ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight .
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how do you cownt the to 20 ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight .
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what is the key to counting in order ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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is there an easier way to count in order ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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what is the easiest way to count in order ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there .
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i really want to know the history of the number zero ?
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how do we count the flowers ? so , this first choice , they go one , two , three , and then they do n't count this one and then they skip it and they go four , five , six , and then they skip this one again , and then they say seven , eight . that 's not how you count flowers ! you 'd say this is four , this is five , six , seven , eight , nine , 10 . so , this first choice is not right . now , the second one looks better . one , two , three , four , they did n't skip this one , five , six , seven , eight , nine , 10 . that one looks good so i 'll click right over here and check my answer . how do we count the mice ? let 's see , one , two , this is n't the third mouse ! this is the second mouse ! this is crazy , this is n't right . all right , this one over here . one , two , three , four , five , six , seven , this is right . up here they skipped the number two , this should be the second mouse , not the third mouse ! all right . let 's keep going . type the missing numbers . it says count the ladybugs . type the missing numbers in the boxes . all right , this is ladybug number one . two , then let me type three , then let me type four . it 's a lot of fun . count the flowers . type the missing numbers in the boxes . this is flower number one , flower number two . just gon na type that right in there . check it , lem me do one more . how do we count the flowers ? so , we saw one like this a few questions ago . one , two , three , four , five , six , seven , eight , nine , 10 . that one looks good . this one , just like the last time , they skipped , actually they skipped the same ones . this would n't be the right way to do it . so , we select this one right here , and then we 're done .
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it 's a lot of fun . count the flowers . type the missing numbers in the boxes .
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so to count in order you have to count number by number not by spaces ?
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