Einsteins photoelectric equation & work function

when you shine light on any metallic surface and when photoelectric effect happens we find that electrons come with different different energies some electrons are coming out very fast with very high kinetic energy while some electrons come out very slow with very low kinetic energy and the goal of this video is to explore why that happens now to answer this question we need to understand a very important thing the most crucial thing to understand is the idea of work function so let's take an example imagine this is gold and i looked up online it turns out the work function which is often represented by the symbol phi the work function of gold happens to be somewhere around five electron volt though so the question is what is the meaning of this statement well first of all what is this electron volt it's a unit of energy let me write that this is a unit in fact it's a tiny unit of energy just like how when we're dealing with very tiny masses like mass of an atom we are using we don't use kilograms right because it's very small so we use a different unit like atomic mass unit right similarly when we're dealing with energies of electrons or photons because those energies are very tiny we don't use joules we came up with a new unit a very small unit which we call electron volt and of course we'll talk more about exactly what it is its connection with joules all of that will do in the future videos but again coming back to the question what does it mean to say that work function of gold is 5 electron volts well the gold gold metal has electrons inside of it right now if you want to pull that electron out then it doesn't happen for free you have to spend some energy because this electron is attracted by the different positive nuclei right and so you have to spend some energy so this number tells you the minimum energy needed to pull an electron out of gold so let me write that this represents minimum energy minimum energy needed to pull an electron from gold all right so let me draw a few electrons over here and now our stage is set and now let's say we shine some light on this so let's say we shine i don't know some light i'm going to use some color don't take that color very seriously it's not the exact color of light but let's say i like i shine some light and because light is particles let me draw photons this is a photon let's say i shine light uh whose photon has an energy of seven seven electron volt fine so i shine light whose photons have seven electron volts of energy i know the minimum energy needed to pull this electron is five electron volt the important part is the minimum over here my question to you is what energies do you think with what energy do you think the electrons will come out what will be their kinetic energy when they come out of this metal i want you to pause the video and think a little bit about it what do you think what would your answer be all right i would think look i know to remove this electron out of the metal it takes five electron volts of energy so when it absorbs seven electron volt it has more than energy needed so it will use up 5 to escape and then the left over 2 comes out as kinetic energy because energy is conserved so that's what that's my answer that's what i usually think so this electron must be coming out with two electron volts of kinetic energy and that's certainly possible but there are many other things possible as well let me give you another example of what can happen let's say this electron pretty much the same story let's say this electron also requires five electron volts of energy to escape it absorbs it uses five to escape it only needs five to escape so the remaining two comes out as kinetic energy but let's say while it is moving up it collides with some of the electrons and loses energy then out of two it would have lost some some energy and so this electron will not come out with two maybe it only comes out with i don't know maybe 1.5 electron volts of energy that's completely possible maybe even this one absorbs seven electron volts and when it is coming out maybe it collides with so many electrons maybe so it got so unlucky that let's say it lost all its kinetic energy and so maybe it doesn't come out at all that's also possible and there's another case possible maybe this electron is more tightly bound to the gold nucleus and therefore maybe this one needs six electron volts to escape you might say wait a second you said you know gold requires five electron volts and that's what i want you to remember it's the minimum energy some electrons will need more than that see the way to read this is at least five is needed to pull an electron all but some electrons would require more than that so maybe this one requires six to pull out and when it absorbs it uses six and only one is remaining and maybe it got lucky it did not collide so then it will come out with kinetic energy of one electron volt and so on and so forth do you think and any electron in this situation for gold when you shine seven electron volts of light do you think any electron can come with more energy than two electron volts can someone have more than two i want you to pause and think a little bit about it do you think that's possible no it's not possible because i know for sure that any electron i take i at least you have to at least spend five from this to escape you can spend more but you at least need to spend five so if i at least spend five the maximum available energy for kinetic energy is two it can be less also but you cannot have more than two and therefore i know that in this situation this is the maximum kinetic energy available so given this value when given the energy of the photon i know i now can tell that the kinetic energies of the electrons that are coming out will be a range it will be between 0 because 0 is totally possible and i know the maximum value is to electron volt and now we see in photoelectric effect why electrons don't just come out with a single energy there's a whole spectrum of it the main reason being because electrons can be more or less tightly bound requiring more or less energy to escape and electrons can also collide its way in you know on its way out and can lose energy now just to check our understanding let's do one more quick quick problem let's say we take the metal cesium it turns out that the work function of cesium is somewhere around two electron volt and let's say we shine the same light which has the same photon strength seven electron volt can you pause and think about what would be the kinetic energy range over here in this case all right i always think about the electron that is the most loosely bound the luckiest one which is not going to collide what would happen to that electron well when that electron absorbs the energy seven electron volts it will take two to escape two is the minimum that's the minimum you can't avoid that it's gonna take two to escape and so the remaining energy would be kinetic energy which would be five but i know that other electrons may not be so lucky and so we can have anything between zero and five so immediately i now know that the kinetic energy in this case is going to be between 0 and 5 electron volt and so the final question i have for you is since this is the maximum kinetic energy this represents maximum kinetic energy the final question i have for you is what is the connection between the maximum kinetic energy the work function and the energy of the photon can you can you based on whatever you just learned can you come up with uh an expression that connects them all right we see that the maximum kinetic energy always happens to be the energy of the photon minus the work function can you see that that's how we got that so let me write that down the maximum kinetic energy of an electron in photoelectric effect happens to be the energy of the photon minus the work function work function and this is the famous einstein's photo electric equation which won him the nobel prize and you may be wondering hey we also came up with this equation yeah but we knew about photons and all of that he had to come up with all of this himself but what i love is that it's not very complex equation or something it's a simple elegant looking equation which is able to explain amazing things that couldn't be explained you know back in the 1900s but the important thing to stress on is i was always confused why this equation had k max in it why was it kinetic energy maximum um but hopefully now you understand that well because electrons can come out with energy less than this they can lose energy to collision or they can be more tightly bound so because of that all electrons will not come out with this energy and that's why this equation has a k max in it