 So, we know that light is quantized, light is made up of individual particles and we have to have an integer number of those, one, two, three, or some integer number of photons make up a light beam. Turns out not just the energy of light is quantized, meaning we can have the energy of one photon or two photons or three photons, but we can't have the energy of one and a half photons. We can't have a non-integer number of photons, so we have certain allowed energies of light that are allowed. So we say the energy of a light beam is quantized. Turns out not just light, but the energies of other things are quantized as well. And that's also something we at least have a little bit of experience with from general chemistry or earlier chemistry classes. So when we write an energy level diagram, so let's say in particular for something like the hydrogen atom, the electrons in a hydrogen atom can occupy certain states and those states have certain energies. We know we can call those things like S and P and D orbitals, but for now if I just say the energy of that electron can have this value E1 or this value E2 or this value E3 or various other values, essentially what I've done is say the energy levels of that hydrogen atom are quantized. I can have this value or I can have this value or this value. I can't have any values in between the values that I've drawn. There's no way to make the hydrogen atom have this amount of energy. It can only have these discrete individual quantized amounts of energy that I've drawn on this diagram. So that's something that we know about hydrogen atoms and in fact every molecule, every atom, every chemical system has quantized energy levels. And as usual, we didn't suspect this weird quantum behavior was true even if it seems fairly commonplace now. It wasn't always so. And the evidence that we have that first told us that energy levels were quantized was understanding how light is either emitted or absorbed by atoms and molecules. So something called an atomic emission spectrum. If I bring up a picture here of the atomic emission spectrum for hydrogen. So let's go ahead and bring up a picture. This diagram for hydrogen tells us the frequencies of light as a function of the frequency here, the frequency of light given off by hydrogen. And we see that only certain frequencies of light are emitted. So this reddish color of light can be emitted by hydrogen atom if I excited up to some higher energy level. It can drop down to a lower energy and emit a photon of this reddish color or this bluish color or these violet colors. But only these colors. I never see hydrogen emit the orange or yellow or green frequencies of light that would be here. So only certain discrete or quantized photons are emitted by hydrogen and that's because when a hydrogen is in this state it can only fall let's say to this state or to this state. It can't fall anywhere in between because there's no level there to accept it. So for example, this reddish photon is emitted when hydrogen falls from its third state down to its second state. There's other each one of these different photons corresponds to a different individual transition between discrete quantized states of the hydrogen atom. And that's true not just for hydrogen. If I pull up another picture of what that looks like for helium. This is the emission spectrum for a helium atom and notice that the colors of light given off by a helium atom are a not the same as they are for hydrogen because the energy levels are different for hydrogen than they are for helium. And also they're still discrete and quantized only this color of light or this color of light or this color of light and so on can be given off by helium not anything in this range where we don't see emission. So it's not just the energy of light that's quantized but also the energy levels of matter meaning atoms meaning molecules that are made of atoms. Those energy levels themselves are quantized as well. And also interestingly it turns out it's not only energies that are quantized but other properties of matter can be quantized as well and that's the next thing we're going to talk about.