 Hello everyone, welcome back. In today's video, we are going to talk about a very important experiment in physics. An experiment that played a very vital role in the development of the basic ideas of quantum mechanics almost a century ago. That is the photoelectric effect experiment. I'm going to talk about four distinct things. First, we are going to talk about the photoelectric effect experiment and its setup. Second, we are going to talk about the experimental observations associated with photoelectric effect. Third, we are going to talk about the classical explanation of those observations or the failure of the classical explanations of those observations. And we're going to talk about Albert Einstein's idea of photoelectric effect, which won him the Nobel Prize in physics later on. So what is photoelectric effect? It's a very simple phenomena. It's a phenomena in which when incident radiation or light falls onto a metal surface, electrons are emitted. Whenever light of certain suitable frequency falls on a metal surface, electrons are ejected from the surface. This phenomena is known as photoelectric effect phenomena and the electrons that get ejected from the metal surface due to the action of some incident radiation, these electrons are known as photoelectrons. Now, I want to study this kind of a phenomena because there are so many different parameters involved. We have light. Light may have properties like frequency, wavelength, intensity. We have electrons which can have properties like kinetic energy, number of photoelectrons, etc., etc. We want to find the relationships between different kinds of quantities. For that, we have an experimental setup. This is a very basic experimental setup that we have that I want to use to just understand the observations involved. So first of all, we have this evacuated tube that has two electrodes, positive and negative, that is connected to a variable voltage supply. So we have a variable voltage supply created by the combination of a battery and a rheostat, which are connected to the positive and the negative terminals inside this evacuated tube. We have a wattmeter to measure the voltage difference between the electrodes and an ammeter to measure the current flowing through the circuit. So the positive terminal is the anode, negative terminal is the cathode. If we radiate the metal plate associated with the anode with some sort of an incident monochromatic radiation, then under suitable conditions, electrons are ejected from the metal surface of the anode. And if these electrons have sufficient energy, they go and reach the cathode and that constitutes a current in the ammeter. All right. Now, this is a very basic, simple setup that we have. If you study different books that they might have a little bit of a more complicated setup with possibilities of polarities of voltage being changed, et cetera, et cetera, I have kept a very basic setup because I simply want to understand the observations in a simple manner. So essentially, whenever you have incident monochromatic radiation falling on the metal surface, these electrons get ejected. They have some kinetic energy to overcome the potential barrier because you see this is negative polarity. They overcome this polarity difference and become part of the current in the circuit. Now electrons are negatively charged particles, right? Here, however, the polarity is positive on the left hand side and negative on the right hand side. So what is the direction of electric field? It's from left to right. Negatively charged particles travel usually in the opposite direction. They're supposed to travel in the backward direction. So if there are electrons traveling from left to right, they will experience some retardation, right? They will experience some deceleration in that particular journey. Only those electrons that have sufficient kinetic energy to overcome this negative potential difference will be able to reach the cathode. So let's suppose that these electrons have a kinetic energy, Ke. Now all the electrons will not have the same kinetic energy. So let's suppose we are only interested in the maximum kinetic energy possible for these photo electrons. So as these electrons go from left to right, many of the electrons will not be able to reach the cathode. Only some of the electrons which have very high kinetic energy will be able to reach the cathode. And whether or not it reaches the cathode also has to do with the potential difference between these two terminals, right? So for example, if the potential difference between these two terminals is very low, we will have a large number of electrons reaching the cathode thereby constituting a higher current. If we slowly increase the potential difference, then slowly, slowly more and more electrons will stop somewhere in the middle and a very less number of electrons will reach the cathode thereby constituting a smaller current. So increase in the potential difference between these two electrodes will decrease the current associated with the circuit because smaller number of electrons will now be able to go from left to right. A point is going to come in which if we take the potential difference between these electrons to a certain value known as the stopping potential, then the total amount of current in the system will come out to be zero. This is the particular point in which the maximum kinetic energy of the electrons is unable to overcome the potential barrier. Now what is the potential barrier? If we give some kind of a stopping potential, let's suppose V0, then because these electrons have electronic charge of E, so E V0 will represent the total amount of work that needs to be done for the electrons to go and overcome this barrier. So the maximum kinetic energy, the moment it becomes equal to E V0 or less than E V0, then entire current in the circuit becomes zero. Therefore this extinction potential or this potential at which the current in the circuit becomes zero is known as stopping potential. Why is this stopping potential important by the way? It's important because it is a measure of the kinetic energy of the electrons. You see how else are we going to measure the kinetic energy of the electrons? We don't have a microscope that is looking at an individual electron and following its path and calculating its velocity, right? We want to know the energy of the electrons and this is just a technique to figure out the kinetic energy of the electrons. So essentially the stopping potential is a measure of the kinetic energy of the photo electrons emitted in this metal surface that is necessary to overcome the potential energy difference here. So whenever we reach this particular stopping potential, the entire current becomes zero. So below that stopping potential, the kinetic energy is basically greater than E V. So if you have some V which is less than V0, then the kinetic energy maximum will be greater than this and we will end up getting some sort of a current, right? So this is simply a mechanism to figure out the value of the kinetic energy of the photo electrons. The stopping potential is a parameter that gives us a measure of the energy of the photo electrons. Now let us discuss some of the experimental observations associated with this kind of an experimental setup. The first observation is that the photoelectric emission is an instantaneous process. Now of course this process is instantaneous up to the limits of experimental accuracy. So we can take some time frame of around 10 to the power minus 9 seconds. It means that if you look at the process of photoelectric emission, it is instantaneous. That means there is no time lag or almost no time lag between the arrival of the incident radiation and the emission of the photo electrons. So the moment incident radiation falls on the metal surface, electrons are ejected immediately if the photoelectric effect is happening in that situation. Now this is something very peculiar according to classical physics because according to classical physics, we have the wave theory of light in which light energy is spread out in a wavefront. And because light energy is spread out in a wavefront, therefore a metal surface can absorb the light energy in a continuous fashion. And because metal surfaces can absorb light energy in a continuous fashion, therefore there should be some time delay before enough amount of incident radiation energy has been absorbed by the metal surface so that the electron can now come out of the metal surface. Theoretically speaking, you can have hours, days or even weeks elapsed before the metal surface has accumulated enough energy for the photoelectron to come out. So for low intensity of radiation, some time delay has to be there before the electrons which absorb the incident radiation energy accumulate sufficient energy to come out of the metal surface. But that is not happening here. The experimental observation is that the moment incident radiation reaches the metal surface, photoelectrons are emitted instantaneously. There is no time delay and that is something that cannot be explained by classical physics. Now let's move on to observation number two. The second observation is that the kinetic energy of the electrons. The electrons have some kinetic energy right, which is related to the stopping potential as I just now mentioned. The kinetic energy of the photo electrons is independent of the intensity of the incident radiation. So let me draw a graph to show you the experimental observation. So if we measure the voltage difference between the terminals or the electrodes versus the current in the system, the graph that we end up getting looks something like this. What happens is that for zero potential energy difference, we end up getting the maximum current because that is the situation in which vast number of electrons can go from left to right. So let me say that this is a particular experiment for constant frequency. So let's say that here frequency is a constant. We are not changing frequency. It's a monochromatic radiation. So frequency is a constant. So in this situation for a given value of intensity, so let's say the intensity is small i1. So capital i corresponds to the current. Small i corresponds to the intensity of the incident radiation. So when intensity has some value, we end up getting some current. And as we increase the potential difference between the electrodes, automatically the current becomes zero because lesser and lesser electrons are able to overcome the potential energy difference between these two terminals to constitute the current. Now what happens if we increase the intensity of the incident radiation? The moment we increase the intensity of the incident radiation, so let's suppose I make it to i1 or rather I should say this should be small i and I make it to small i, then what happens is that immediately the current in the circuit increases. Now what is current? Current is essentially number of electrons passing through the ammeter per unit time. So greater current simply means greater number of photoelectrons that has reached the cathode. The moment we increase the intensity of the incident radiation, the current in the circuit has increased but it also corresponds to the same stopping potential. Stopping potential corresponds to the maximum kinetic energy of the electron. So even though I have increased the intensity of radiation and it has increased the number of photoelectrons, the individual energy of the photoelectrons is still the same as for the lower intensity. So I can keep on increasing the intensity. If I make it 3i, so for an intensity of 3i the current will again increase but the stopping potential corresponding to that is exactly the same as before. That means increasing the intensity of the incident radiation will increase the number of photoelectrons but not the individual energy of the photoelectrons. Now this is something that is very difficult to explain using classical theory because again what do we mean by intensity of the incident radiation? Intensity corresponds to energy of the incident radiation. So when we talk about energy of a wave, we are essentially talking about its amplitude. So if the amplitude of a wave is large, it has a greater amount of energy. So intensity of an incident radiation corresponds to a more energetic incident radiation. So if there is a more energetic incident radiation, then automatically it should correspond to greater energy of the photoelectrons, right? Greater energy of the incident radiation should correlate to greater energy of the photoelectrons but that is not what's happening here. What's happening here is that greater intensity corresponds to large number of photoelectrons but the individual energy of the photoelectrons remains exactly the same. So therefore classical physics fails to explain observation number two. Now let's move ahead to observation number three. So in the third observation which is probably the most important observation here is that below a certain cutoff frequency, below a certain threshold frequency, the phenomena of photoelectric effect does not happen. So if frequency of incident radiation is less than some cutoff, then we do not get photoelectric effect. Only when the incident radiation has a frequency greater than some cutoff or threshold frequency, only then we see photoelectric effect. This cutoff is known as threshold frequency and beyond this frequency, if we keep on increasing the frequency, then that simply leads to more energetic photoelectrons. That means the kinetic energy of the photoelectrons which can be measured by the stopping potential has a direct linear proportionality with frequency. Greater the frequency of the incident radiation, greater is a kinetic energy of the photoelectrons. That means blue light would lead to faster photoelectrons compared to red light. Now let me draw a couple of more graphs to illustrate this particular point. All right, so here I have two graphs. First I have the current versus the voltage between the electrodes and I have three distinct frequencies of incident radiation. So as you can see, you get a similar kind of a variation for any given frequency because the moment you have a particular light, you increase the potential difference between the electrodes, the current decreases, goes to zero at the stopping potential. The moment I compare the graphs for three distinct frequencies, I end up getting three distinct stopping potentials. That means these three distinct frequencies correspond to photoelectrons that have three distinct kinetic energies. So for every single frequency, we end up getting a different kinetic energy of a photoelectron. Now because intensity is a constant, therefore current initially is a constant, that means the number of photoelectrons in all the three cases of constant intensity of incident radiation is constant. That means for a given intensity, we can change the frequency, the number of photoelectrons will remain the same but the kinetic energy associated with the photoelectrons will be different and increasing frequency corresponds to increasing kinetic energy or increasing stopping potential for those radiations. Now we can also compare the stopping potential with frequency. So as you can see below a particular cutoff or below a particular threshold frequency which I am going to call as a nu naught. So below nu naught there is no photoelectric phenomena but beyond nu naught you end up getting photoelectric phenomena also and the stopping potential also increases linearly. Now what is stopping potential? It is a measure of the kinetic energy of the photoelectron. So that means the kinetic energy of the photoelectrons increases linearly with the frequency of incident radiation. Now this is something that is completely different from what we would expect in classical physics. In classical physics, the kinetic energy of the photoelectrons should come from the energy of the incident radiation and the energy of the incident radiation has to do with intensity of the incident radiation. It has nothing to do with frequency. In classical wave theory, the frequency does not correspond to energy of a wave. It is the amplitude that corresponds to energy of a wave. The amplitude square gives us an idea about the energy of a wave. So how is it possible that frequency variation can lead to change in the energy of the photoelectrons themselves? That is something that classical physics fails to explain. So we can see that there are three very simple observations related to the photoelectric phenomena that classical wave theory is unable to explain based on its idea of light being a wave front which is continuously being absorbed by a metal surface and the energy transfer happens in a continuous fashion and the energy transfer is related to the intensity of the radiation. All these things do not explain the three phenomena or three observations associated with photoelectric phenomena. So now we come to the last portion of the video which is the Einstein's resolution to this particular problem. So what did Einstein say about all these three different points? You see before Einstein, we had Max Planck who gave an explanation to the black body radiation spectrum. I have made a couple of lecture videos on that particular topic. So if you are interested in that topic, you can go through those particular lectures. But what essentially Max Planck said about the black body radiation spectrum is what Einstein borrowed for this particular photoelectric effect and let me just give you a very simple sort of explanation of that assumption. So if you have a black body surface, so let's suppose that you have a black body surface. The black body surface in a cavity is capable of emitting electromagnetic waves or electromagnetic oscillations of different frequencies. Now what Max Planck said was that the emission of energy in the form of these standing waves or these electromagnetic waves happens not in a continuous fashion, but in a discrete manner. That means the energy radiated by the black body walls happens in discrete values of 0, h nu, 2h nu and on and on and on and h nu. Where h is the Planck's constant, nu is the frequency. This is a very unique resolution to the problem of the black body radiation spectrum because Max Planck merely tried to change or modify the calculations so as to fit the experimental data. And the way to avoid the ultraviolet catastrophe in black body radiation was to assume that the manner in which the walls are emitting energy in the form of radiation is happening not in a continuous fashion, but in discrete values of 0, h nu, 2h nu and h nu etc. Now Max Planck did this in an act of desperation to explain the black body radiation spectrum and he did not really think much into what it means in terms of the physical reality of what light is. It is Albert Einstein who realized that this had greater implications in terms of our understanding of what light is. You see before Max Planck, before Albert Einstein, we had the classical theory of radiation in which light is composed of wave fronts, waves, electromagnetic oscillations traveling through space. But Einstein said that this brilliant hypothesis by Max Planck is not something that is unique to the phenomena of black body radiation only, but is true about the nature of light itself. That means light propagates through space in discrete amounts of energy that we call as photons or packets of energy or quantized values of energy. So this picture of radiation in which I have drawn these waves is not the picture that is required to explain this phenomena. In fact, we have to get rid of this picture completely. So if I completely forget this picture of what light is supposed to be and look into Einstein's explanation, then what Einstein simply said was that this idea that light energy consists in discrete values can be taken forward, not just for emission or absorption, but in general to how light behaves or propagates in terms of packets of energy. So if we assume that these packets of energy are these localized packets, so let's suppose every light consists of these small packets of concentrated energy which is localized in a small volume in space and every single packet corresponds to an energy given by the Planck's postulate. What was the Planck's postulate? So let me write Einstein's quantum mechanical explanation. I should say quantum explanation because till that point in time quantum mechanics did not really emerge as a subject. So I should say quantum theory or whatever. Einstein used the explanation of Planck's postulate which said that light is consisting of these packets of energy, these localized packets of discrete energy, these quantized values of energy, these photons. So we call these packets of energy as photons and every single photon has an energy of h nu. So h nu is essentially equal to the energy of one packet of energy or one photon. So the incident radiation consists of all these photons which come and reach the metal surface and the moment they reach the metal surface they end up creating photoelectric phenomena. How does that explain these observations? First of all because the incident radiation is now consisting of these packets of energy or photons and individual photon interacts with an individual electron and because this energy is not spread out it is absorbed one at a time therefore there should not be any time delay in the process of photoelectric emission. You see in classical theory because wave is supposed to be a continuous spreading of wavefront and the energy is absorbed continuously there should be time delay but now the light is consisting of these small granular particles or photons and every single photon interacts with an electron. So the moment the photon which interacts with an electron if the photon has sufficient energy for the electron to come out the electron absorbs that energy and comes out of the surface. So therefore this process is an instantaneous process and therefore explains the first experimental observation. Second the intensity of radiation has nothing to do with the energy of the photon because the energy of the photon has to do with the frequency and because we are using monochromatic radiation therefore the radiation consists of a large number of photons and every single photon contains this much energy. If this energy is sufficient for the electron to come out of the metal surface the moment the electron absorbs the photon it comes out of the metal surface. So the kinetic energy therefore is constant it is independent of the incident radiation. So what happens when we have a higher intensity of incident radiation? Higher intensity of incident radiation simply means a larger number of photons. You see so if we have a greater intensity of incident radiation that simply corresponds to a large number of these photons. So the intensity of the incident radiation is n times h nu, h nu is the energy of one photon and is the number of photons constituted in that particular incident radiation and because the number of photons is larger for greater intensity of incident radiation therefore the number of photo electrons also increases which corresponds to greater current. You see higher the intensity of the incident radiation greater is the overall energy but not of individual energy of a photon but instead you have larger number of photons and larger number of photons corresponds to larger number of photo electrons constituting a larger current. You see how simple that explanation now becomes. Let us move on to the next observation. The next observation is that for frequency below a threshold you do not see photoelectric effect which is kind of obvious because the interaction between the electron and the photon happens one on one basis. So if a photon has energy h nu if it is sufficient to cause photoelectric emission then it will happen but if the frequency is less that means the energy of the photon is not sufficient so photoelectric effect does not happen at all because individual photons do not have sufficient energy for the electrons to come out but now if we increase the frequency then the individual photons will have greater energy so the electron can absorb that energy and come out of the metal surface and it happens in a linear fashion why because if you look at the phenomena of conservation of energy then the photon energy one photon which interacts with the electron essentially goes into what? It goes into the electron for the electron to overcome the metal surface threshold because the electrons are part of the metal surface they cannot just come out randomly there is some amount of energy it requires for the electron to come out of the surface right otherwise we would see electrons pouring out of metal surface all the time no so it requires some amount of energy to come out of the metal surface first so that is known as work function or some sort of a threshold function so first of all it needs to overcome the work function of the metal surface and if there is an excess amount of energy beyond the work function that goes into the kinetic energy of the electron so that goes into the kinetic energy of electron so this translates into a very beautiful equation the photon energy for every single photoelectric effect interaction between a photon and electron is equal to h nu contributes to overcoming the work function of the metal surface and the rest goes into the kinetic energy of the electron so this gives us a very simple equation of k e max is equal to h nu minus w which is the Einstein's photoelectric effect equation now we can go a step further what if the amount of the photon energy is exactly equal to the metals work function if the amount of let's suppose the work function is exactly equal to the let's suppose photon energy that corresponds to the threshold frequency right when we reach the threshold frequency then the photon has just enough energy for the electron to be ejected but it doesn't really have much kinetic energy all right so all the energy gets absorbed in just the electron coming out of the metal surface so that corresponds to threshold frequency right so if I put k e max is equal to zero h nu is equal to w but that nu corresponds to threshold frequency so if I substitute h nu naught into w here this simply gives me a new equation which is what k e max is equal to h nu minus h nu naught this is the very famous photoelectric effect equation given by Albert Einstein and this explains this particular graph that the moment we increase the frequency there is a linear relationship with kinetic energy of the electron in fact I can substitute e v naught here in kinetic energy max and I get a little bit of a different result so if I substitute e v naught I should get v naught is equal to h upon e nu minus h upon e nu naught you see this h upon e comes from left hand side h upon e nu naught so what is this equation this is the straight line relationship here v naught versus nu so if we trace this line below it will create a negative intercept which is equal to minus h upon e nu naught and because h upon e is a constant v has a direct proportionality with frequency the slope of this line will give you an idea about h upon e so if you know the electronic charge if you perform this experiment in some sort of a lab then by the slope of this line you can measure h upon e and finally you can measure the value of the plan constant in fact this is a very popular experiment in laboratories in some colleges where you can use the photoelectric effect phenomena to draw this graph and by applying the electronic charge value you can calculate the plan's constant from here so you see how Einstein was successfully able to explain these three phenomena and provide a very simple very simple equation which is known as the Einstein's photoelectric effect equation to explain the photoelectric effect experiment or phenomena but it happened at a cost and the cost was to completely get rid of the previous wave theory of light you see when Einstein wrote this paper in 1905 many scientists did not like this paper because it went completely against the previously held belief of what light is light was supposed to be a wave a wave front which transfers energy in a continuous fashion with matter that is what we know from classical electrodynamic theory. Einstein proposed that light was instead composed of packets of photons having some energy and interacting individually with an electron just like one particle electrons a particle interacts with another electron so even though the simple equation explains these three phenomena or these three observations it happens at the cost of a radical shift in how we look at what light is in classical theory light is a wave front a wave in this new theory that we are developing right now in front of our own light consists of these packets these localized photons having energy that is directly proportional to its frequency that interacts with particles like electrons just like another particle interacts with a particle and because of this genius of Albert Einstein he actually got the noble prize in physics for this particular experiment you see Einstein did not get the noble prize for relativity or GTR he got the noble prize for photoelectric effect that is how significant photoelectric effect is in the development of these ideas so I hope you have understood what photoelectric effect is and I have been able to explain to you the classical explanations the quantum ideas behind this particular phenomena and we will take these ideas forward in our next video where we discuss discuss another very important phenomena known as the Compton effect till then I am Divya Jyothidas that is all for today thank you very much have a nice day