 ###### Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

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# Photoelectric Effect

Jonathan Osbourne ###### Jonathan Osbourne

PhD., University of Maryland
Published author

Jonathan is a published author and recently completed a book on physics and applied mathematics.

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The photoelectric effect is a tool that we use to determine how much energy electrons have. The photoelectric effect was explained by Albert Einstein in 1905 and states that when light shines on metal in a vacuum, it emits electrons. We are able to determine how much energy electrons have by using the formula Kmax = h(f - f).

So let's talk about the photoelectric effect. The photoelectric effect is a very very very important effect that was discovered by Heinrich Hertz in 1887, who is incidentally the first guy that made electromagnetic waves and was able to demonstrate their existence. It was during this study of electromagnetic waves that he saw that if you send ultraviolet light onto metals, you'll get sparks coming off. Now he didn't really know what it was but he was the first one to see that effect.

Now, later on, it was explained by Albert Einstein in 1905. He actually won the Nobel Prize in physics for that explanation later on. This explanation actually cemented the place that photons in the development of quantum mechanics because the photoelectric effect was one of the first direct observations of photons that can't even be pointed to. Alright. So what is the photoelectric effect?

Well essentially what we're going to do is we're going to take a freshly cut piece of metal and put it in a vacuum. And then we're going to shine light on it. Now, sometimes this light will cause electrons to jump off of the metal, alright? Now, classically, we would expect, I mean, light's a wave right? So if you pump up the intensity then you ought to get more electrons, right? So, regardless of what the metal is, I mean if I shine a 300 watt laser on it, I ought to get some electrons jumping off. So that's what I expect. The observation is that that's not what happens. Alright? The observation is that if I have some frequencies, yes, increasing the intensity will increase the number of electrons. But if I try to go below a certain frequency, I don't get any electrons at all. Doesn't matter what the intensity is. Doesn't matter and it's a sharp cut off. Get electrons, no electrons. Alright? So this was not understood at all. Now the experimental set up is important to understand. What we're doing is we've got a vacuum chamber in here, we've got a circuit that we're driving by a battery.

Now, this is all vacuum. Nobody can get across without an impedance to do so. The electrons however, would desperately like to be on this side because that's the positive side. Remember the long side is the positive side of the battery so the electrons really do want to jump across. So what we do is we then shine our light. Now if an electron is liberated, it's going to jump across definitely because it wants to be on that positive side. But the electrons are in the metal. They have to be liberated from the metal first. So classically we expect several things. We expect you increase the intensity, you're going to increase the electrons. We also expect you increase the amount of time, because it's a wave so the electrons should be absorbing the energy as time goes on and you increase the amount of time, you should increase the amount of energy. That's not observed.

So, how do we understand what's observed? Well, it turns out we need a little bit more in order to really do this. So what we're going to do is we're going to ask how much energy do the electrons get when we shine this light on them. And the way we're going to do that is we're going to re- reverse the battery. So now the electrons really don't want to make that jump and in fact they can't make that jump unless their energy is higher than the amount of energy it requires to jump from that side to that side. Alright? So we again shine the light and we turn up the voltage until there's no more current. So until there's no more electrons that have enough energy to make that jump. So this vs is called the maximum reverse voltage, it's called the stopping voltage. It's the voltage that you need in order to stop the current so that it won't come anymore. The maximum kinetic energy is the amount of energy that it takes for the electron to make that jump. So it's equal to the charge of the electron times the stopping voltage.

Now, the weird thing about all this was that the stopping voltage was found to depend only on the frequency, not on the intensity. So again, classically I expect if I bump up the intensity then I'm going to give the electrons more kinetic energy because there's more energy coming in but that's not what happens. I do get a bigger current but I don't change my stopping voltage. So that's a bit of an issue. So when we make a graph, this is what we find. We have the maximum kinetic energy versus the frequency, flat up until you get to this threshold frequency. That's because there is no current at all. The electrons can't jump at all so what's the stopping voltage, zero because [IB] I don't need a voltage, it's done. But then as soon as I hit this threshold frequency, I increase the frequency and look. It comes up linearly. That's extremely important. So what that means is that I can write a functional form for that relationship. Kmax equals h which is a constant that I can measure in experiment, times f-f not So what equals f not is zero. But then when f is greater than f not it goes up linearly. now multiplying this out, what we've got is hf minus and then hf not which we call the work function. This is associated with the threshold frequency and it only depends on the metal. That's it. so sodium has a certain f not and any piece of sodium I use same f not, you know, if I use lithium, now it's a different f not alright? So it depends only on the metal.

Now, the way that we understand this and this was the beauty of the explanation that Einstein gave us, is that this kinetic energy is equal to something minus this work function that depends only on the metal. So we say, huh. This something must be the energy carried by the light. So that's the energy that the electron absorbed. This work function must be the amount of energy that's required to leave the metal. So how much work is needed to pull that electron out of all the bonds that it's got with the nuclei, with the metal nuclei and get it out of that metal so that it can jump across this vacuum? so that was the explanation. We've got energy giving minus work function required and the way that we look at this, is that this energy given, depends only on the frequency. So that means it doesn't matter how much light we're sending. The only amount of energy that the electron can absorb is hf. That's it. So if I increase the intensity, then that's great if hf is enough to get it to jump out of the surface, but if it's not enough, doesn't matter. Still zero curent.

And that's the photoelectric effect.