 Okay, so our goal is to be able to understand quantum mechanics, to be able to predict energies of molecules or other chemical or physical systems, but to start with we'll review some things you already know about quantum mechanics from having taken some earlier chemistry courses. So to start with we can talk about the quantum mechanical properties of light and what you know about those. So one thing we know about light is we normally tend to think of light as a wave. It behaves like a wave, it behaves like other types of waves like water waves and sound waves and then it can reflect off of objects, it can diffract or bend in different mediums. It undergoes interference, two different light waves can constructively or destructively interfere with one another. Those are all things that we think of as behaving like waves. But turns out light is also made of particles, so it's not purely a wave, it's a wave that's made of particles and the individual particles of light are called photons. And one of the key things we know about photons is how to describe their energy. So these equations are likely familiar. Energy of light is either H times nu, Planck's constant times frequency, so both of these H's are Planck's constant which has a value of 6.626 times 10 to the minus 34 joules times seconds. I'll have occasion to write that down on the board in just a minute. So energy of light is either Planck's constant times the frequency of light or Planck's constant times the speed of light divided by the wavelength of the light. So perhaps the most common ways of thinking about these equations is just as a relationship between frequency and wavelength. Those are inversely proportional to one another. But the actual meaning of these equations is that the energy of one individual particle of light, one photon of light, is this value H times nu or Hc divided by lambda. So for example, if we have, let's say we have a photon of red light, probably if you look around where you are you won't have to look too far to find a red LED. Let's say the light coming out of that LED has a wavelength of 671 nanometers, which is a wavelength of light that would have the color red. If I ask you what is the energy of the photons of light with this wavelength, then we can plug into this expression. Energy is Hc over lambda just to work this example and see what the units are like. See what the numerical values are like. This constant as I mentioned is this value 6.626 times 10 to the minus 34th joule seconds. Speed of light is another constant 2.998 times 10 to the 8th meters per second. If I divide that by the wavelength 671 nanometers or 671 times 10 to the minus 9th meters. That's just a simple set of numbers to multiply and divide. When we do that, the energy works out to be some tiny number of joules. That's the thing to keep in mind about these equations for light. They don't just tell us the relative values of wavelengths and frequencies. The reason we use these particular values of Planck's constant is to tell us this is the energy of a single photon of light of this red color that has a wavelength 671 nanometers. When I say light is quantized, what I mean by that statement is that light comes in quanta, light comes in discrete little packets that I can't subdivide any further. So if I have one photon of light, it has this much energy. Let's call it 3 times 10 to the minus 19th joules. I can have that much energy from one photon or if I have two photons of light, I can have twice that much energy, but I can't have 4 times 10 to the minus 19th joules worth of red light. I can only have one photon or two photon or three photons or a large number of photons if I want, but it has to be an integer number of photons. It has to be a countable number of these particles, each of which has this much energy if they all have this wavelength. So light is quantized. We can break it down into photons, but we can't split up a photon into smaller pieces. So that's what we mean when we say something is quantized. That's going to turn out to be the key feature of quantum mechanics. The reason we call it quantum mechanics is because it describes how things are quantized. So for each of these features of quantum mechanics that I'll point out over the next few video lectures, I'll point out something that you already knew. Light is made up of photons and some equations, and I'll also discuss the evidence for how we know it is that nature behaves this way. How do we know that light is made up of photons as opposed to a continuous wave? And we've known this about light ever since we started studying the photoelectric effect over a century ago in 1905. And what the photoelectric effect is, it's also something you're familiar with the effects of even if you haven't heard those terms before. That's what opens the grocery store door from you when you move into an automated opening door at the grocery store or what keeps a garage door from closing on you if you pass your hand or a car in that invisible beam that triggers the door to go back up. Those all work on this photoelectric effect. And the name tells us photo meaning light and electric meaning electricity or electrons. So what the photoelectric effect is is if I shine light of a particular frequency or wavelength. So here's a light beam composed of a bunch of photons. So here's some h nu light of some particular frequency hitting a surface. Usually a metal surface, although it could be any surface. What happens is under some conditions that surface can kick out an electron. So if the energy of the light coming in is more than enough to pay for the energy binding that electron to the metal surface, that amount of energy is something we call the work function. Usually given the symbol phi. So if I send in a photon with more than this amount of energy, I can pay for the extraction of a photon. And that photon gets kicked out of the metal and flies away through vacuum or through air or through whatever medium is above the metal. So that process is called the photoelectric effect. In terms of equations, the kinetic energy of the photon, the energy with which that photon leaves is equal to however much energy I sent in, the energy of the photon minus the energy I had to pay to remove the photon from the metal surface, the work function. So if you study the photoelectric effect, if you say, okay, let's look at how the kinetic energies or how some other properties depend on the color of light I send in, what wavelength or what frequency. Let's say I change the frequency of the light coming in. And first, let's measure what's called the photocurrent, that I'll write as capital I. Essentially, that's just the number of electrons that get kicked out of the sample. So number of electrons, those electrons can be used as electricity. I can measure how many of them there are and that shows up as a current. So if I ask how many electrons get kicked out as I change the frequency, that graph looks like this. No, at low frequencies, no electrons get kicked out by the photoelectric effect. Once I reach some cutoff frequency, I'll call that new sub zero or new not. Then all of a sudden I start getting electrons kicked out, but that number doesn't change as I continue to increase the frequency. I can also ask, how does the kinetic energy of those electrons change as I increase the frequency? As I make this light change from red to yellow to green to blue to violet to ultraviolet by increasing the energy of the photon by changing its frequency. What happens to the energy of the electron that gets kicked out? This equation tells us h nu is the incoming energy, phi is the amount I have to pay to remove the electron. And as long as I have enough energy to remove an electron, then all the excess energy goes into the kinetic energy. So as long as I have more than enough energy to kick out a photon. So I can't kick out any photons if I don't have enough energy. But once I have enough energy to kick out a photon, all the excess energy just goes directly into kinetic energy of the electron that gets kicked out. So those two graphs make sense when we're thinking of this as individual photons coming in, having enough energy to pay for the work function or not, and all the excess energy going into kinetic energy. That makes sense when we think of light as being composed of photons. But before 1905, when we didn't know that light was made of particles, when we thought light was purely a wave, then these results didn't make sense. In fact, at the time, the natural way to think about, let's take the kinetic energy graph. So if you ask someone before 1905 if you know about the photoelectric effect, what they'd expect to happen. If you shine a wave, a continuous wave of light at a surface and ask about the energy of the electrons get kicked out of that surface, that's like asking if water waves approach a beach, what is the energy of the sand particles that get dislodged from the beach or something like that. And the natural way to think about what would have happened. Clearly, if I send in a particle with no energy, there's no excess energy to kick out any particles. But beyond that, the more energy I put into the surface, the more energy of the displaced particles. And there was no idea of this threshold because even if the individual waves themselves had relatively low frequency, we could always increase the amplitude of the waves. We could always just send more waves at the beach. We could always just send brighter light onto a surface. And surely that's going to dump more energy into the surface and therefore kick out electrons with higher energy. So this is what would have been predicted if light behaved like a wave. Because more frequency clearly just means more energy. This is not, I should make clear that this is not what actually happens. That's what might have been expected to happen. When people saw that this is actually what did happen when light was shined on a surface, it took some reevaluation. And eventually, we realized that actually, some lights made of individual particles and only when one quantum, one particle of the light has enough energy to pay to remove an electron, that's the threshold at which either do or don't get electrons kicked out. And if I do, all the excess energy begins to go into the kinetic energy of the electron. So as I said, that's the evidence for why it's one piece, one of many pieces of evidence for why we know light is actually made of photons. Turns out light is not the only thing that's quantized, it's composed of discrete individual amounts of energy. And so that's what we'll talk about next is other things that are quantized besides light.