In our last learning objective, I used the word photon and said we would talk more about them later. Well, in this learning objective we're going to look at the experimentation that led to the understanding of photons and the dual nature of light. Begin with Planck's work, in which he heated a solid until it glowed. And if you take a metal for example, and you heat it up, it is going to eventually glow, produce light. And he looked at that light and he examined it in various points of wavelength. So it's giving off a rainbow of light, he's observing one little section of that visible light spectrum. And he was measuring the energy being given off. He's making very careful measurements and he noted that the energy that was emitted was related to the wavelength he was monitoring. Classical physics could not account for this fact. In, the idea of classical physics in which energy is a continuum, if you measured an area with a certain wavelength, and you thought about light as a wave, you could get any, you should be able to get any amplitude of waves. So you could have a little bit of energy if the wave was taller. It would be more energy if the wave taller it would be more and we could have a whole spectrum of energy, but this was not the case. So Planck solved the problem. He was thinking about how this could be, and this is what he came up with. He said that the light, the molecules that were producing the light, could only absorb a certain amount or emit a very discreet amount of energy that he called a quanta. So we're back to our cat with our kittens. But in terms of energy, we know that a cat is only going to give a certain amount of kittens and it's always going to be based upon a certain quantity, with one kitten being the smallest amount. He was saying that, energy you could have a certain bundle of energy, or you can have twice that bundle of energy, or you can have three times that bundle of energy. But you couldn't have one and a half amounts of that bundled energy okay? So those little bundles of energy is what we call a quantum. And a quantum would be that smallest amount of energy that could be emitted, of energy that can be emitted when that body heats at a particular wavelength. He found that their relationship, in the, we have it not in terms of wavelength, but in terms of frequency. And we can solve for wavelength because we got a connection between wavelength and frequency and maybe we'll do that in a minute. But he found that at a certain frequency of light, that the energy would be related by Planck's Constants, okay. So, that is the energy of a single quanta of light, this little bundle. And this is Planck's Constant, so we named the constant after him, and the value is 6.63 times 10 the minus 34 joules times seconds. And actually, I could give that to you as a few more sig figs. 6.626 times 10 to the minus 34 joules times seconds. Of course, that's frequency. And the frequency is going to be in units of one over seconds. So we know c equals lambda mu. So we can solve this for the frequency c over lambda, and we could plug this in for that. So I don't ever have this one memorized, I'm always quickly solving for it, instead. But you could put in place of the frequency, you could put c over lambda. So hc over lambda would also give you the energy. Like I said, I'm never going to memorize that one, because I've got this one committed to memory. I've got this one committed to memory. And I could easily come up with the other one with a little bit of math. But if you like memorizing things, you can memorize that one. So we know what Planck observed. He observed that, when something is heated, it will glow. And if you monitor what comes off there at a certain frequency, you're going to get light coming off in these quantums, a quanta of in, no a quantum of energy or multiple of it, and it's always a multiple of e. Which is the Planck's constant times the frequency of light you're monitoring. But he did not know the why. He just knew what was observed, and he made this connection between energy and frequency. Along comes Einstein, and Einstein uses Planck's Quantum Theory to help explain something else that was observed at the time, and that was called the photoelect, electric effect. And he would took that information, and he was able to come up with the why of Planck's theory. So let's look at the Photoelectric Effect. So let's look at the components of this apparatus that leads to what's called the Photoelectric Effect. Forget about all the verbage that's around there for just a minute and let's describe what we have. We've got a battery which allows for the flow of electrons. We have the light coming in, okay? We have the light coming in and striking a metal surface. The light, when it strikes the surface could cause electrons to be ejected from the metal surface, and it's going to travel to this positive electrode. So this is a negative surface. Electron is going to flow, and then complete the circuit. And they can measure the information about those electrons. So if you strike the light onto the surface, and you can see it had blown up here, as light comes in it hits that metal surface, the electrons could be emitted. Now, based upon what they understood about light and waves. What they expected to happen is that any frequency of light would be able to eject out an electron as long as the light was intense enough. Now, I want you to think of the light as a big foot. Okay, so here we have a big foot. And I want you to think of the electron as a ball. So as long as the kick was hard enough, okay, it should be able to get that electron off of there. But this is not what they observed. What they observed was that there was some frequency below which you could not get the electron to come off. No matter how intense the light was. So you have, you know, light with various frequencies. There's some threshold frequency where it's not, it doesn't matter how bright, and how intense, no electrons will come off. So, you hit it with a real intense beam below a certain frequency, and no electrons come off. They found that as they, once they got to a place where you are getting electrons to come off, that what increasing the intensity did was increase the number of electrons that were coming off of that metal surface. And then they found that once it's coming off, what increasing the frequency would do, would increase the amount of energy those electrons were coming off with. They came off with more kinetic energy. So, if you increase the intensity, you're getting off more emitted electrons. So we'll have more arrows. That's an increase intensity. But if you increase the frequency, those electrons would come off with more kinetic energy. So, they would be moving faster. Greater speeds as they came off. Those are the two big things that they observed. So how do we make sense of all that? Well the way we make sense of that is that light is now thought of not just as waves, but as particles. And we call those particles photons. Now how in the world does that explain the photoelectric effect? Well if each photon has a single, is a, is the little bundle of energy, and each photon has this much energy, Planck's Constant times the frequency. If it's frequency is high enough, then it will have enough energy to knock off one electron. Knocking off an electron it has to overcome what we call the binding energy. The energy is bound to that metal surface. So if the photon is the foot and that foot has enough energy to kick off the electron, then that electron will leave the metal surface. The more intense light is just more photons. It's not an, we don't think about it in terms of amplitude. If you increase the intensity, the brightness of the light, basically what you do is you have more feet kicking at the little electrons. So, increasing the intensity, more photons. Each kick could kick off an electron, so more electrons leave. Okay, so we have light coming in. If it's a low frequency light, as it comes in and strikes that metal surface. If it's low intensity nothing will happen, because that little piece of light, which we think of as our foot kicking a ball off of the surface, which is our electron. If it doesn't have much energy, that one little photon, it can’t kick an electron off. But if the frequency gets high enough, it can kick off the electron. At some point, it’s going to have just enough to overcome the binding energy of that electron and kick it off. If it’s kicking it with more energy than is need to get it off. Then all the extra energy it has is the kinetic energy of the electron. So this is the energy of the kick, so we've got the photon coming in and kicking the electron. Some of the energy of that kick removes the electron, the rest of the energy of the kick gives the electron kinetic energy. So if you hit with a higher and higher frequency, this kick would be harder and harder. There is no change in how much energy it takes to kick the electron off, but we've got more and more kinetic energy with that electron. Now what happens if we increase the intensity at a certain frequency, well we're not going to get more electrons off because each photon can only do one electron. And so if we increase the intensity, we're just hitting it. Oops, don't want to do it in blue. We're hitting it with more photons, and therefore you're ejecting more electrons. If we change the frequency, and let's make it, a higher frequency so I'm hitting it with a higher frequency, that's going to be closer together waves. Then that electron is going to come off with even more kinetic energy. And that explains what's observed with the photoelectric effect. So now we have the notion that light, light has a dual nature. It behaves as waves. We can monitor the frequency. We can monitor the wave length. We can see the defracting pattern of the light as it goes through slits. But it also has a particle nature. We see this with the photons, and we see this with a connection between electrons and photons. So depending upon the experiment, you're going to see light behaving one way or the other. You can't see it behaving both simultaneously, but you can observe it one way and you can observe it the other way. We're going to see later that matter also has this dual nature when you're getting down to the particle level of protons, neutrons, and especially as we look at it in terms of electrons. So now we can add calculations to what we know. So far we have these two equations. This is because of the wave nature, and this is because of a particle nature of light. These two equations have the function of getting s if we know anyone of these 3, 1, 2, 3. If we know anyone of those three, we can get the other two. And that's their job. A lot of students like to have things memorized, so you could memorize this equation, which'll get you between wavelength and energy. But like I said, you don't have to memorize that third one, because those two equations are all you need to get between those three. So now that you have two equations, let's see if you can use those two equations. You're going to, here in just a minute after my explanation, pause it and try to solve for the frequency and the energy of this photon. And remember the equation for energy is for a single photon of light. So we're going to calculate the energy and frequency associated with x rays, we're in the x ray region. And the wavelength is 0.154 nanometers. Pause, see which one you choose, and then resume. Well did you choose number 1? If you did, that's the correct answer. Now a lot of the people were going to pick number 2. If you picked number 2, then you made the common mistake of not watching your units. Watch you units, you have to get the nanometers to meters before you can use your equations. If you want to skip ahead you can if you got it right, but if you did not get it right and you want to watch me through, walk through this work, then we'll do so. First thing I'm going to determine is frequency. C equals lambda nu. C over wavelength equals nu. C is 3 times 10 to the 8th meters per second, so our wavelength needs to be in meters. Now I can, after you do this for a little while you realize that if I just multiply by 10 to the minus 9 I would have it in meters instead of nanometers. And so my meters are cancelling, and I have 1.95 times 10 to the 8th. One over seconds is my frequency. Now I can get energy. Energy equals h times nu. So energy is 6.626 times 10 to the minus 34 joules times seconds, and I'll multiply that by the frequency I got above. And this will give me an energy of 1.12. No, not that, try again. This will give me an energy of 1.29 times 10, to the minus 15 joules. Now that's a tiny amount of energy, very small. But it's just a single photon. And when you see light, there are many, many, many of these photons. When it warms up, the light from the sun warms up the Earth, there are mm-hm, way more than we can count, photons hitting, striking the surface. So each photon just has a tiny amount of energy. But there's a lot of photons out there. So this ends our learning objective number three. We've looked at the connection between way,. We had looked at the connection between wavelength in frequency in our previous learning objective. Now we're seeing the dual nature of light. And understanding that each little particle of light that we call a photon, has an energy equal to h times nu or h times frequency.
