# Light Quanta

**Light quanta**, called photons, are the smallest discrete amounts of light. For light quanta, we use the formula *the energy of a photon = planck's constant x frequency*. Because this is the smallest discrete amount of energy, there can only be whole number quantities of photons. As shown by the Compton effect, light can behave like waves or particles.

Alright. Let's talk about light quanta. So the idea is that at the end of the 19th century, we had two major results; blackbody radiation spectrum and the photoelectric effect.

Now, according to Planck, in 1900 and little bit later, Einstein in 1905, both of these guys indicate the existence of photons which are light quanta. Now specifically what these two things indicate is that energy can only be contained in an electromagnetic wave in discreet amounts. So if I have an electromagnetic wave that has frequency f, then I can only have energies that are multiples of h times f, where h is Planck's constant which can be determined from experiment to be 6.626 times 10 to the -34 joule seconds. So the way that we interpret is that the energy that's present in electromagnetic waves is in these discreet packets called light quanta or photons. So we can only have one photon, or two photons or three photons, we can't have two and a half photons. And this is very separate from the way that it was classically because classically you could have any amount of energy you want in your electromagnetic field. It just depends on what's the amplitude of that electric field and the magnetic field. But here, what we found and again this is straight from experiment is that it can only be present in these discreet amounts, hf. Alright.

Now when we go further into experiment and into theory of photons, we find that photons actually behave like particles, So they have a discreet amount of energy and they also have a momentum associated with them. So rather than behaving like waves when looked at on this microscopic scale, light actually behaves like particles, kind of. Alright.

So, light with the wavelength of 550 nanometers has a frequency that's give by c over lambda. c is the speed of light in the vacuum which is 3 times 10 to the 8 in SI units. Writing down our wavelength again in SI units, we have 5.5 times 10 to the -7 because it's 550times 10 to the -9. So then we'll do numbers first, 3 over 5, 5.5 which is 0.5454 times and then the tens 7+8 is 15. Alright. So our frequency is fi- 5.454 times 10 to the 14 hertz. So what's the quanti's energy? Well, e=hf. So we multiply by Planck's constant and we get the discreet amount of energy, 3.614 times 10 to the -19 joules. Alright. So what this means is that electromagnetic radiation with a wavelength of 550 nanometers cannot carry 4 times 10 to the -19 joules, it can't, it's impossible. It can can have 3.614 times to the -19 joules, 77.228 times 10 to the -19 joules etcetera. One photon, two photons, three photons and so on and so forth. You can't go in between. You cannot have light with this wavelength that has energy that's inbetween these two numbers. Alright.

Now, a little bit furthermore, photons are going to carry energy and momentum just like particles and in fact they'll behave just like particles. They collide like particles. So even though there are some wave properties in light, the energy of a photon is absorbed all at once. Now that's very very very different from the way the energy classically is thought of as being absorbed from a wave. The wave comes and gives part of its energy and it keeps on coming and delivering more and more and more energy but as far as light quanta are concerned, the energy is absorbed all at once. Alright.

Of course if you've got light with a long wavelength or you got a lot of light coming, you've got lots and lots and lots of photons coming and so that's why we don't notice this in our everyday lives because there are so many coming that, yes, we're absorbing all the energy at once but we're doing it again and again and again and again and again and it seems like a wave. So the standard rule of thumb goes like this. When the wavelength is much much much larger than the scale at which you're probing, the experimental evidence or the phenomenon or whatever, then you're going to see wave behavior in your electromagnetic wave. Alright? So when the wavelength is really big, wave.

On the other hand when the wavelength is much much much smaller than the scale on which you're probing the physical spectrum, then you're going to get this particle behavior. Everything is going to behave like photons. And the easy way for you to think about that, is that when you have a really really really large wavelength, it means that the energies of the photons are very very very very very small. So that means that in order to get an appreciable amount of energy in your electromagnetic wave, you've got to have a ton of photons. And so they're coming so fast that you don't, you can't tell that they're discreet. So it seems to you just like classical. It's the right wave. But if you've got a really really really small wavelength, then you've got a big frequency and each of the photons carries a lot of energy. And that means that an appreciable amount of energy can be obtained from only a couple of photons. And that means that their particle nature becomes more apparent.

And that's light quanta.

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