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Photoelectric effect explanation using quantum theory

Let's explore how the quantum theory of light explains the below experimental results of photoelectric effects. 1. The kinetic energy of the photoelectrons are independent of intensity but depend on frequency. 2. Below a minimum frequency called the threshold frequency, no photoelectric effect takes place, even if the light has very high intensity. 3. Photoelectric effect is almost instantaneous. Created by Mahesh Shenoy.

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Video transcript

even if you shine blindingly bright visible light on the zinc metal surface you get no photoelectric effect and even if you shine extremely dim but ultraviolet light you get photoelectric effect why because it turns out that the visible light has just too low frequency it's too low to cause photoelectric effect and the ultraviolet light has high enough frequency for zinc to cause photoelectric effect and so the goal of this video is to see how quantum nature of light helps us understand this weird nature of photoelectric effect as to why the brightness or the intensity doesn't matter but it's the frequency that matters so let's begin so let's consider the wave model and the quantum model separately let's start with the wave model imagine this is our zinc metal and here's an electron trapped inside the metal now for it to escape it needs to gain some energy for simplicity let's say it requires three units of energy now according to the wave model light is a wave and when you shine light so wave when you shine light uh the the electron starts absorbing the energy from this wave and so the electrons energy will start increasing from whatever it is right now you'll get plus one plus two and finally once it increases beyond three it has now enough energy it escapes from that metal it's happy goes photoelectric effect and according to this model it doesn't matter what the frequency is any frequency light you shine the electron must gain enough energy eventually and should just escape and in fact according to this model if you shine brighter light the electron gains so much more energy and it should be able to escape much more easily and therefore you should get more photoelectric effect over here and that's why according to wave model it doesn't make sense why does the frequency matter and not the intensity but now let's see what the quantum model says the quantum model says hey light is not made of waves it's made of photons and we've explored this right according to the quantum model light is made of particles what we call photons now what happens when an electron absorbs this photon same electron again even this one needs three units of energy let's take some numbers let's say the energy of this photon is five units it has five units of energy it's a packet that contains five units of energy now when this electron absorbs this photon it absorbs that phi units instantly what this means is that the energy of the electron instantly jumps plus phi and try to understand what that means it doesn't go plus one plus two plus three plus four and then plus five it instantly goes plus five it's kind of like your car going from zero to hundred kilometers per hour directly without going through plus ten plus uh ten kilometers per hour 20 kilometers per hour 30 kilometers can you imagine that direct jump you can't imagine that you might think that's so weird but that's what quantum mechanics is all about that's what quantum is all about you can't get one or two units of energy you either get all the five at once or you don't get anything at all that's the weirdest coolest thing about quantum mechanics anyways once it absorbs that energy now because it has gotten plus five instantly it has more than energy needed to escape it escapes it immediately escapes and you get photoelectric effect but now what if what if the photon that we are incidenting does not have five units of energy it has say only two units of energy let me draw a smaller photon to represent that okay let's say it only has two units of energy what would happen now now again the electron would absorb that energy but it's not enough to escape and so it still stays uh stayed trapped inside the metal and so the electron does get excited because it has absorbed the photon of energy but almost instantly it de-excites it comes back to wherever it was before and it you know it releases that energy maybe in the form of you know heat or maybe collisions and so it comes back to where it was and so now what happens if it if it absorbs another photon same thing it excites then de-excites now these electrons will always absorb one photon at a time the chances of it absorbing two photons at the same time is almost very negligible and therefore you can see even if i shine millions of photons on this it will not cause any photoelectric effect it's kind of like trying to knock this boat out of the ocean by using ping pong balls if you use a ping pong ball one ping pong ball nothing is going to happen so even if you shoot multiple ping pong balls millions of ping-pong balls one after the other nothing is going to happen to this boat the number of ping-pong balls don't matter what matters is that a single ball imagine you have a single large cannonball one cannonball is all that it takes to shoot this boat and knock it off and that's how you should think about it the number of photons don't matter it's a single a single photon should have enough energy to knock it off only then photoelectric effect will happen and what does the energy of a photon depend on you've seen the energy of any photon depends on from flank planck's equation the planck's constant h times the frequency of light so more frequency of light more energy of photon so now can you pause the video and come back and explain why we don't see any photoelectric effect here but we do see it over here pause and can think about it all right so what might be happening over here well because the frequency of the light is too low that means the energy of the photon over here must also be too low and so i'm going to draw one you know tiny black dot to represent very low energy photon and it does not have enough energy to knock the electron off and that's why you get no photoelectric effect but it's so bright why doesn't that matter because brightness if high intensity means you have a lot of these photons so let me draw lots of them okay my pen slipped over here so we have a lot of photons falling on a lot of electrons but none of them have enough energy to knock him off so you get no photoelectric effect like lots of ping-pong balls coming and hitting this boat is not gonna happen what's happening here you have high frequency light and therefore the photon over here i'm going to draw a big photon over here the photons have enough energy to knock the electrons off and so but it's so dim so yeah it's very dim and therefore there might be very few photons over here very few but whenever these photons get absorbed by the electrons you get photoelectric effect so you see what's happening even if you have a lot of energy over here it's kind of like diluted into very tiny photons none of them are able to do anything and even if you have very weak energy over here it's very concentrated into large photon packets each one of them is able to knock off the electrons that's why photoelectric effect depends on the frequency whether it's going to happen or not depends on the frequency and not the intensity okay but let's not stop here let's see if we can explain all the results we saw photoelectric experiment one of the experts one of the things that we saw is even if you had to increase the intensity of this light you make it more energetic the electrons do not come out with more energy we saw that the kinetic energy does not increase instead we get more photoelectrons oh sorry we get more electrons coming out can you explain why this is happening okay when you increase the intensity you do not change the energy of individual photons the energy of the individual photon stays the same and therefore when an electron absorbs that photon nothing has changed and so the electron comes out with pretty much the same energy as before and therefore the electrons energy does not change but when you increase the intensity you do increase the number of photons so the number of photons increase and therefore now more electrons are going to get those photons and therefore you expect more electrons to come out per second so now it makes sense okay the second thing we saw is if you increase the frequency of the light then the kinetic energy increases electrons now come out with more energy can you explain that using the quantum model yes because if you increase the frequency the energy of the photons start increasing electrons gain more energy when they absorb that photon and so they come out with more energy so that makes sense the final thing we saw over here was photoelectric effect is instantaneous even if you shine extremely dim light as long as it's above threshold frequency you get photoelectric effect instantly no time delay now according to wave theory this did not make sense because if you're shining very very low intensity light then the electron will take more time to gather that all of those energy and so it will take more time for the electrons to come out so according to the wave model there should have been a delay but now according to the quantum model does it make sense yes as long as the photons have enough energy the interaction is almost instantaneous so the electron almost instantly gets all that energy remember it doesn't gain energy slowly and steadily it instantly gains all of that energy and then it instantly comes out and so because the interaction between the electron and photons are instantaneous almost instantaneous you get an almost instantaneous effect and so hardly any time delay so this is how the quantum model beautifully explains all the weird results of photoelectric effect it's no longer weird now right