[BLANK_AUDIO]. Hi there. In a previous video we had shown how Max Planck had proposed that energy is not continuous, but it is composed of small packets or indivisible packets, called quanta. And he had come about this from studying trying to explain the black body radiation curves, there were none at the time. And we remember that he proposed that energy is absorbed or emitted from a body in discrete packets. So a lot of the energy would be con, continuous in nature. It has got a a granular quantity if you like. Now. Another experiment that was difficult to explain at that time on the basis of the wave-like nature of energy was called the, the Photoelectric Effect. Now, the Photoelectric Effect in very simple terms, can be described as, as follows. So, if you had a, if you have a, some form of metal here, so here's your metal. And then you have some type of incoming electromagnetic radiation. And what was known that if the conditions are right then, you have, we'll have electrons will be emitted. From this from this metal and without getting into the, the detail of how these are, are measured, you can have some form of detection mechanism. So it had a detector over here and again, without going into details, what you can do is you can measure the kinetic energy of these emitted electrons. [BLANK_AUDIO]. So, it was proposed at that time, before the advent of, of, of quantum theories. People thought that electromagnetic radiation had some wave like nature, so you can imagine a wave coming in like that to electromagnetic radiation. And it, if you consider energy as a wave, then what you would expect if you study how the kinetic energy of the electrons that are, are knocked off, how they vary. You would expect these, the energy of the electrons to vary directly with the intensity of the en of the wave form of the energy. Now, under conditions in which the electrons were emitted. If you plotted that. If you plotted the the kinetic energy of the emitted electrons, and you plotted that as a function of the the intensity of the incoming radiation, what you found was, you found a line like that. There was no variation in the kinetic energy of the electrons as a function of the intensity of the radiation. What was found however, was that if you plotted the kinetic energy of the emitted electrons as a function of the frequency, which we'll call nu, of the incoming radiation. What you found was that as you increase nu there was a certain value here before which there was no emitted electrons. And after that then, the kinetic energy of the emitted electrons varied linearly with the, the frequency of the, of the radiation. Now, this really cannot be explained satisfactorily in terms of a wave-like nature for the incoming energy. But what Einstein proposed was that this is evidence that in this case the energy is behaving not like a wave but like a particle. What he further proposed was that these particles correspond to what Planck was referring to as the, the quantums of energy. So, he said that E is equal to h nu. And these are, are the quanta. A particle like nature of energy. And that these are behaving, the energy now in the Photoelectric Effect we were watching appear, is behaving just like the classical particle. So if we take out the the wave-like nature here, for our victim radiation. So if we draw this again. So here we have our incoming radiation and what Einstein was saying was instead of behaving like the wave, you should think of it as a stream of particles. And these particles correspond to this h nu. So now you can understand this like a classic classic particle so you have a classic on the snooker table, so you have a, an inclement particle. It hits the electron. If it's got enough momentum to, to knock the electron out, the electron will, will, will move from its position. And if it's got more than enough energy to knock that position, electron out. Then the extra energy will be transformed into the movement energy or the kinetic energy of, of the electrons. So this really, if you think about it explains this curve down here quite nicely. So here you have kinetic energy, and what we said before was that you have some threshold frequency. Which must, which must the energy must have before any electrons are emitted, and this corresponds exactly to the value of the energy needed to knock the electron out from its position. Again, going back to the snooker table analogy the the, the, the snooker ball is held on the table. And you will require a minimal momentum to just knock it from that position, so that will correspond to there. And then if you hit it with greater energy than needed here, then that extra energy will be transferred into the kinetic energy of the the billet ball or in this case of the electron. So what we call this threshold frequency here, we give it a it's usually given a special name and it's called nu sub, sub 0. So this again, is called the threshold frequency. And the corresponding threshold energy will be given by h nu 0. And that's often symbolized by the Greek capital letter, letter Phi. So what we can write therefore, is we have our inputted photon energy. So let's I'll put that in yellow, so we're inputting photon energy, which is h nu. So what we can say that, that's going to be equal to the threshold value of the energy. And then if there's any extra energy from knocking the electron out that will be transformed into the kinetic energy of the emitted electron. So we therefore confront, rearrange that equation for our purposes. And we can say that Ek, the kinetic energy of the electron, is equal to h nu. That's the incident energy minus the threshold, threshold energy. So we can also rearrange that a little bit more. So we also should know from general chemistry that will be noting this as h nu, we mentioned that already. But nu, the frequency is equal to the speed of light divided by the wavelength. And I'm sure you also heard Einstein's relativistic equation. For rating mass and energy that E is equal to mc squared. So, combining these two, we have that hc over lambda is equal to mc squared. So if we cross the c out there, so we find that h over lambda is equal to mc. Now this is the mass times the velocity of the radiation, so this really is a momentum, momentum term. And that brings home to you the idea that energy [COUGH] can be regarded, as a particle in nature. With, and these, and the photons, if you like, have a certain momentum, and it's this momentum property of the photon that explains the Photoelectric Effect. So this was a, a, a real significant finding because what we all, what we've known for some time, what physicists have known for some time was that energy has a wave-like nature. You have phenomena like diffraction patterns etc. And these can only be interpreted in terms of a wave-like nature. But in certain cases we see is, in the Photoelectric Effect as, as a really good example, it behaved like a particle. So this transformed if you like the whole interpretation of what we understand as energy so energy can behave as a particle. Or it can behave like, hit like a wave. [BLANK_AUDIO]