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Photon Energy

Learn what a photon is and how to determine the energy of a photon as you explore the dual nature of light as both a wave and a particle, known as wave-particle duality. Uncover the concept of quantum mechanics, where light deposits energy in discrete amounts called photons. Investigate Planck's constant and how it relates to the energy of a photon. Created by David SantoPietro.

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Video transcript

- We've been treating light as a wave, and we've been drawing it with this continuous wave pattern of oscillating electric and magnetic fields that are traveling in some direction. And why shouldn't we treat it as a wave? If you sent it through a small opening, this electromagnetic radiation would spread out, There'd be diffraction, and that's what waves do. Or, if you let it overlap with itself, if you had some wave in some region, and it lined up perfectly with some other electromagnetic wave, you'd get constructive interference. If it was out of phase, you'd get destructive interference. That's what waves do. Why shouldn't we call electromagnetic radiation a wave? And that's what everyone thought. But, in the late 1800s and early 1900s, physicists discovered something shocking. They discovered that light, and all electromagnetic radiation, can display particle-like behavior, too. And I don't just mean localized in some region of space. Waves can get localized. If you sent in some wave here that was a wave pulse, well, that wave pulse is pretty much localized. When it's traveling through here, it's going to kind of look like a particle. That's not really what we mean. We mean something more dramatic. We mean that light, what physicists discovered, is that light and light particles can only deposit certain amount of energy, only discrete amounts of energy. There's a certain chunk of energy that light can deposit, no less than that. So this is why it's called quantum mechanics. You've heard of a quantum leap. Quantum mechanics means a discrete jump, no less than that. And so what do we call these particles of light? We call them photons. How do we draw them? That's a little trickier. We know now light can behave like a wave and a particle, so we kind of split the difference sometimes. Sometimes you'll see it like this, where it's kind of like a wavy particle. So there's a photon, here's another photon. Basically, this is the problem. This is the main problem with wave particle duality, it's called. The fact that light, and everything else, for that matter, can behave in a way that shows wavelike characteristics, it can show particle-like characteristics, there's no classical analog of this. We can't envision in our minds anything that we've ever seen that can do this, that can both behave like a wave and a particle. So it's impossible, basically, to draw some sort of visual representation, but, you know, it's always good to draw something. So we draw our photons like this. And so, what I'm really saying here is, if you had a detector sitting over here that could measure the light energy that it receives from some source of light, what I'm saying is, if that detector was sensitive enough, you'd either get no light energy or one jump, or no light energy or, whoop, you absorbed another photon. You couldn't get in between. If the quantum jump was three units of energy ... I don't want to give you a specific unit yet, but, say, three units of energy you could absorb, if that was the amount of energy for that photon, if these photons were carrying three units of energy, you could either absorb no energy whatsoever or you could absorb all three. You can't absorb half of it. You can't absorb one unit of energy or two units of energy. You could either absorb the whole thing or nothing. That's why it's quantum mechanics. You get this discrete behavior of light depositing all its energy in a particle-like way, or nothing at all. How much energy? Well, we've got a formula for that. The amount of energy in one photon is determined by this formula. And the first thing in it is Planck's constant. H is the letter we use for Planck's constant, and times f. This is it. It's a simple formula. F is the frequency. What is Planck's constant? Well, Planck was basically the father of quantum mechanics. Planck was the first one to figure out what this constant was and to propose that light can only deposit its energy in discrete amounts. So Planck's constant is extremely small; it's 6.626 times 10 to the negative 34th joule times seconds. 10 to the negative 34th? There aren't many other numbers in physics that small. Times the frequency -- this is regular frequency. So frequency, number of oscillations per second, measured in hertz. So now we can try to figure out, why did physicists never discover this before? And the reason is, Planck's constant is so small that the energy of these photons are extremely small. The graininess of this discrete amount of energy that's getting deposited is so small that it just looks smooth. You can't tell that there's a smallest amount, or at least it's very hard to tell. So instead of just saying 'three units,' let's get specific. For violet light, what's the energy of one violet photon? Well, the frequency of violet light is 7.5 times 10 to the 14th hertz. So if you take that number times this Planck's constant, 6.626 times 10 to the negative 34th, you'll get that the energy of one violet photon is about five times 10 to the negative 19th joules. Five times ten to the negative 19th, that's extremely small. That's hard to see. That's hard to notice, that energy's coming in this discrete amount. It's like water. I mean, water from your sink. Water flowing out of your sink looks continuous. We know there's really discrete water molecules in there, and that you can only get one water molecule, no water molecules, 10 water molecules, discrete amounts of these water molecules, but there's so many of them and they're so small, it's hard to tell that it's not just completely continuous. The same is happening with this light. This energy's extremely small. Each violet photon has an extremely small amount of energy that it contributes. In fact, if you wanted to know how small it is, a baseball, a professional baseball player, throwing a ball fast, you know, it's about 100 joules of energy. If you wanted to know how many of these photons, how many of these violet photons would it take to equal the energy of one baseball thrown at major league speed? It would take about two million trillion of these photons to equal the energy in a baseball that's thrown. That's why we don't see this on a macroscopic scale. For all intents and purposes, for all we care, at a macroscopic level, light's basically continuous. It can deposit any energy whatsoever, because the scale's so small here. But if you look at it up close, light can only deposit discrete amounts. Now, I don't mean that light can only deposit small amounts. Light can deposit an enormous amount of energy, but it does so in chunks. So think about it this way ... Let's get rid of all this. Think about it this way: let's say you had a detector that's going to register how much energy it's absorbing, and we'll graph it. We'll graph what this detector's going to measure, the amount of energy per time that it measures. So we'll get the amount of energy per time. Now, you can absorb huge amounts of energy. And on the detector, on a macroscopic scale, it just might look like this. You know, you're getting more and more light energy. You're absorbing more and more energy, collecting more and more energy. But what I'm saying is that, microscopically, if you look at this, what's happening is, you've absorbed one photon here. You absorbed another one, absorbed another one, absorbed a bunch of them. You keep absorbing a bunch of these photons. You can build up a bunch of energy. That's fine. It's just if you looked at it close enough, you have this step pattern that's absorbing photons at a time, certain numbers of them. Maybe it absorbs three at one moment, four at another moment. But you can't absorb anything in between. It can't be completely continuous. It has to be a discrete all-or-nothing moment of absorption of energy that, on a macroscopic scale, looks smooth but on a microscopic scale is highlighted by the fact that light energy is coming in discrete chunks, described by this equation that gives you the energy of individual photons of light.