 The photoelectric effect is where you shine light on a metal and it emits electrons. That's how we understand it today. When it was first discovered, we didn't even know what an electron was. So in early experimental exploration of the photoelectric effect, it was just noticed that light, in particular ultraviolet light, seemed to have some strong effect on whether metals would emit electrical charge or not. In 1887, Heineck Hertz noticed that a spark was more likely to jump the gap between two electrodes if it was illuminated by ultraviolet light. A flow of investigations followed and it was found that the amount of current depended on a lot of things. It depended on the metal type, it depended on the charge on the metal, it depended on the atmosphere, it depended on the oxidation level, how well polished the surface was, and all sorts of things like that. Alexander Stolatov did a very detailed quantitative analysis of the photoelectric effect and he discovered the direct proportionality between how much light, the intensity of light that was incident on the metal, and the amount of current. In 1900 to 1902, Philip Leonard was investigating the same kind of process in the ionization of gases by ultraviolet light and he noticed that the energy of the individual charges that were being emitted by the gas increased with the frequency of the light. It turns out that these two experimental facts are a bit surprising to people who are modelling light using Maxwell's theory of electromagnetism. The power in a light beam is proportional to the intensity of that light beam and the frequency of that light beam. And so you'd expect that the power delivered by the light would go up with both of those quantities. So why is the current going up as you imply more intensity? Well, you'd expect more energy to be delivered so you might expect that over time more charged particles, let's just call them electrons now, might be emitted. But why would the energy of those emitted charges only depend on the frequency? So the energy of the emitted charges we might expect to also depend on the intensity, but it does not. And if very weak light is incident on the metal, then you'd expect that eventually enough energy would be put into that metal to emit one of these electrons. Even if there was some kind of binding energy you had to break, you'd expect eventually you'd have enough energy from the light building up to break it free. And what that would lead to, it would mean that if you had a very weak dim light, then there'd be some kind of time delay from when you turned the light and when the charge came off. But it turns out that's not how it works. There seems to be no measurable time delay between when the light is incident and when the charges come off. And yet there's this very strange frequency dependence on the energy and lack of intensity dependence on the energy. So in 1905, Einstein published a model of the photoelectric effect. He said, let's assume that in each atom, whether it be in a metal or a gas, these electrons are stuck down the bottom of a potential well. And so they have to get a certain amount of energy just to get out. And we'll call that energy the work function. Now since this object is an atom, that work function is probably a very small amount of energy. And indeed it's probably something like 10 to the minus 19 joules or something around an electron volt, which is the charge of one electron times one volt. And it turns out that that energy is somewhat comparable to just one of these quanta of Planck's imaginary quanta, where he said that let's imagine that the energy for light of a particular frequency comes in units of this h times the frequency. Now Planck didn't take that hypothesis seriously. He used it in order to get the answer that he wanted, but he thought that was just a fiction. But what Einstein did was he said, perhaps that's real and perhaps the energy in light is actually coming in these quantized packets, these definite blocks of energy. We now call these blocks of energy photons. And the key point is if you have a photon, you have to absorb a whole photon at once. You either absorb a photon or you don't. Then an electron trapped in a material has to get enough energy from that photon to get it out of the work function. So it doesn't get enough energy from that photon, then it just stays trapped. And that starts to explain why the frequency of the light is so important. Because of that frequency of the light, remember, is how much energy we have. And so this energy here is hf. And if we don't have enough, we're not going to get any emission at all. And then the extra energy from the photon, whatever that's going to be, is going to be the kinetic energy electron once it's kicked out. So if we make a plot of the kinetic energy of the emitted electrons versus the frequency of the incident light, what we'd expect to see for low frequencies, where we didn't have enough energy to overcome the work function, is that there would be no electrons coming out. So they'd have no kinetic energy, no electrons. And then as we just had enough energy to get over the work function, we'd have electrons coming out, but they'd have almost no kinetic energy at all. And then as we gave the photons more and more energy, we'd expect a linear relationship. We'd expect more and more energy coming from the photons going straight into electrons. We'd expect a plot something like that. Another way of saying it is that we'd expect energy to be conserved. So the total energy of the photon is going to be split up into the kinetic energy of the electron afterwards and the energy we had to give it to get out of the material in the first place. So Leonard's initial exploration that showed that the energy of the emitted charges proportional to the frequency of the light isn't quite what Einstein's theory predicts. Einstein's theory predicts this extra kink in the graph, whereas just a linear relationship would look like that. But perhaps the experiments hadn't been done sensitively enough in those earlier tests by Leonard. Einstein's theory, however, does explain why the intensity of the light gives us a current because the intensity of the light just tells us how many photons we have. It doesn't tell us how much energy each of those photons have. And therefore, as we increase the intensity of the light, we're just getting more of these photons hitting our surface and so we're going to get more electrons coming off. And so the intensity affects the current, how many electrons per second are coming off, and it's the frequency that affects the energy. And in 1914, Robert Millican did a series of very careful experiments where he showed that Einstein's prediction was exactly correct and he could calculate the work function of various metals. And that was basically the birth of quantum theory. Previously, Planck had discovered that if he assumed that energy came in packets that he could explain radiation, but it was the point where Einstein made a very serious attempt to describe the photoelectric effect saying that that was exactly how the radiation works, that these waves, electromagnetic waves, were genuinely coming in these packets that seemed a lot like particles called photons. That's when quantum mechanics really started.