For a mole of photons, multiply the result by Avogadro's number. Identify the wavelength or frequency of the beam of light.

You normally state wavelength in nanometers nm and convert it to meters for energy calculation purposes. Note that it is easy to convert between frequency and wavelength using the equation, the speed of light, c, equals the frequency times the wavelength. Thus, nm is equal to 5. Substitute this value into the equation for the energy of photon.

The energy of a photon is equal to the product of the speed of light, or 3.

Therefore, using the example problem the energy of a photon would be equal to 3. Why shouldn't we call electromagnetic radiation a wave? And that's what everyone thought. But, in the late s and early s, 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.

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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.

### Photon Energies and the Electromagnetic Spectrum

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.

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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.

## Photon Energy (video) | Photons | Khan Academy

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.

## Quantum Physics

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. 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.