In the next two Concept Development Studies, we're going to dig much more deeply into the structure of the atom then we have before. And this is going to require us to learn something about quantum mechanics and the way in which quantum mechanics describes the motion of electrons. Since quantum mechanics is pretty far from our intuition and has quite a bit of complexity, it's going to be important for us to build a good foundation for understanding this and that, that foundation should be based upon experimental observations. But to recap very briefly, remember our understanding of the structure of the atom up to this point is based upon this electron shell model. The idea is that we believe the electrons were arranged around the atom in shells and that the electrons in a particular shell are all about the same distance from the nucleus. That only a limited number of electrons can fit into each shell and each subsequent shell is farther away from the nucleus, call it larger, spatially larger, meaning that the electrons moving in that shell are more distant from the nucleus. But these models actually raise lots of interesting questions here. What does, what do these words mean if the electrons are in the same shell? The shell is not actually like a physical entity that we could literally put electrons into. What we're really saying is that the electrons in that shell are moving in similar ways, but we don't know anything about how they move. Furthermore, if the shell is not a physical quantity of some sort or another, that putting something into, what does it mean that electrons fit into a shell? What do those words actually imply? It just means that a certain number of electrons can only move in the same ways. But since we don't know how electrons move, we don't know how to interpret these words. So here are our questions. Why is it that electrons are restricted to move in these shells, and can't just move in any way that they want to? Why are the number of electrons that can fit into a shell limited for each of the shells? And overall, how do electrons move? How could we actually observe the way in which the electrons are moving about the nucleus, so that we can understand the answers to these questions? And understand a lot more detail about the structures, and therefore, the properties of atoms. This turns out to be a challenging question, because we can't really look at atoms. We can't really see them. We furthermore cannot see the motions of the electrons about the atoms. And in fact, we'll learn that the uncertainty principle tells us, that it's impossible for us to really observe electrons moving about the nucleus in an atom. So how are we going to pursue this? We're going to use a process called spectroscopy. There are lots of different forms of spectroscopy. The general idea here is that we shine light on material and we look and see what kind of light is absorbed by the atom or molecule or what kind of light is emitted by the atom or molecule. Well, if we're going to understand this, then we have to understand something about electromagnetic radiation. We need to understand something about light. And we're going to, here, borrow heavily from concepts of physics, in particular, noting that light is an oscillating electromagnetic wave. So it has an electric component and it has a magnetic component and both of these oscillate both in time and in space. So we'll recall that if it's traveling as a wave, then let's draw a picture of a wave. Here's best as I can do, freehand. You might want to try this yourself on your own pad of paper. And note that if that's a wave, then I'm likely to characterize that wave by the distance between the peaks, which I tried to keep constant as I drew this diagram. In fact, because this wave can be characterized by the distance between the peaks, we're going to give that a name. We're going to say that the distance between these two points here is a quantity we're going to call lambda, where lambda is going to be the wavelength of that particular wave. Aptly named, it appears to be the length of the wave at least as measured by the distance between the two points there. Notice the different waves can of course have different wavelengths. I'm going to draw a different wave here, which clearly has a much smaller wavelength and I'm trying to keep that wavelength constant. In this particular case, the wavelength is the distance between those two points, and therefore, is a much smaller number. This is a smaller wavelength wave than this one is. But of course, the wave is going to travel, so in fact, this wave is going to move forward and electromagnetic radiation moves forward at the speed of light, which is a constant, and we call that constant c. And if it's traveling, then it's going to travel past a particular point in space, and these peaks are going to travel past that point with a different frequency. When this wave travels, these peaks are going to pass this point more frequently than when this wave travels past this point. Consequently, we can also define something we'll call the frequency of the light, which is clearly related to the wavelength of the light. So the light is characterized by a frequency, nu, and a wavelength, lambda. And clearly, these two are related to each other, because the smaller the wavelength, the greater the frequency is going to be. And the mathematical relationship between the two is, that the wavelength of light is equal to the speed of the light divided by the frequency of the light. Notice a longer wavelength corresponds to a smaller frequency. A higher wavelength corresponds to a I'm sorry. A shorter wavelength corresponds to a greater frequency. All right, what do we need to know here? For our purposes in chemistry, what we really need to know is what the energy of the light is, because we're going to use the radiation to measure the energies of electrons and in the process learn something about the ways in which the electrons move. How are we going to do that? We're going to study something called the photoelectric effect. The photoelectric effect is a fascinating phenomena. I'm going to illustrate it very briefly here and give you more detail on another website that you can visit for yourself. Here is the idea. I'm going to take a piece of metal. And this'll just be my schematic drawing of the piece of metal. Okay, solid surface here. And I'm going to shine light on it. And since we just decided that light is moving as a wave, then I'm going to draw the light incident here as a wave inbound on the piece of metal. Under certain circumstances, when the properties of the light are appropriate when the intensity is appropriate or even more importantly, when the frequency is appropriate, electrons will actually be ejected from the surface of the light. Because these electrons are ejected by the light, we refer to them as photoelectrons. Hence, the photoelectric effect. The photo, of course, refers to the fact that the electrons are being ejected by the incident light here. What can we study here? Well, let's see. Where a couple of characteristics we could study, we know that light can be characterized by its frequency or equivalently, its intensity. I'm sorry, or equivalently its wavelength. And it can also be varied in terms of its brightness. So we could vary the frequency of the light and we could vary the intensity the intensity of the light. So the two variables that we can vary independently are here. They are frequency and they are light intensity. What can we measure as we vary those things? Well, we're going to measure something having to do with the photoelectrons. What could be measured, for example, could be the number of photoelectrons or equivalently and better stated, the electric current which is produced by the ejection of these electrons. We can also observe that these electrons depart with a certain speed. And we can also measure the kinetic energy of the departing electrons. So our two output variables here are the current and the kinetic energy. And correspondingly then, we ought to actually be able to produce four different sets of data here, because we're going to vary two inputs and we're going to measure two outputs. What is the data? Well, before I hit that data, I want to remind you that there is actually a very good website that you can go and visit. At the University of Colorado's Physics Education Group's website, the phet.colorado.edu. I've actually pulled up what that website looks like for you here. You can download this little Java application here. It's very simple. It'll just start running by itself. This is what the application actually looks like. What's being illustrated here, you'll notice is light shining on the surface of a metal and electrons being ejected. In the simulator here, you can vary the two independent variables that we just described, the intensity or the wavelength of light. And you can measure a variety of properties. One of the properties you can measure is the current, which is produced here. You can actually change the type of metal which is being incident here. And you can actually also measure the kinetic energy of these electrons. I'm going to leave that for you as an exercise to play with this particular demonstration, because it will actually produce for you the results that we're going to discuss here. In particular, these are the results that we observe. Again, we've got two independent variables, intensity and frequency. And as a consequence there should be four different graphs in which we have two independent variables and two dependent variables. What do these results actually tell you? So let's take a look at them. Here, this says, as I increase the intensity, I increase the current. I get more photoelectrons. But as I increase the intensity, the electrons are not speeding up. If I examine the current as a function of frequency, what I notice is I get no photoelectrons at all, until I hit a particular minimum threshold frequency here, and then I get a constant number of photo electrons. If I measure the kinetic energy of the electrons as a function of the frequency. Again, no electrons at all until I hit the threshold frequency, and then the kinetic energy increases with the frequency. Well, these results surprise us. Turns out actually, they were a 100 years ago when this was being examined by a number of physicists. And the person who actually figured this out was Einstein himself. So let's take a look at this. What are the really important characteristics here? The first has to do with the fact that we have this minimum frequency, which we're calling nu 0 . It's the threshold frequency. Until you hit that threshold frequency, you can't get any photoelectrons at all. That seems strange. It seems like even if I have, say low frequency light, I ought to be able to crank up the intensity of the light and get it bright enough, such that I could actually eject some electrons. So why can't we just crank up the intensity of the light here? Well, let's take a look and see what the data tells us if we do. Apparently, actually, we can only get photoelectrons still provided that we are above the threshold frequency. Furthermore, even though we probably associate the intensity of light with the energy, energy of the light. The kinetic energy of the electron ejected is independent of that intensity. These results seem rather strange. Why does an increase in the light intensity, which makes more energy in the light, why doesn't that produce a sufficient amount of energy to kick the electrons out? And furthermore, why doesn't an increase in the light intensity make the kinetic energy of the electrons even greater? Why don't they come out at a more rapid speed? The answer to these questions, actually provided by Einstein, is really a fascinating one, which is to suggest that the photoelectric effect tells us that the energy of light is actually quantized into little packets that we're going to call photons. To analyze this a bit, let's think about an analogy. Let's imagine that what we wanted to do, for whatever reason, was break a window pane. We have a piece of glass. We're trying to break that window pane. Imagine first that we were trying to break it with a stream of water. So we're going to take a garden hose, aim the stream of water at the glass, and probably it's not going to break. We respond by not changing anything else other than cranking up the intensity of the garden hose. Probably, it still doesn't break. It won't break at all until the intensity of the water coming out of the garden hose is sufficiently high perhaps, it will require a fire, a firehose. If I had a firehose with a really good nozzle on it, I could get sufficient intensity that I could actually smash the glass. The photoelectric effects is not like that. We cannot actually increase the intensity and get something to happen which wouldn't happen with lower intensity. What is it more like? Let's instead say, as I would probably, we want to do, I'm going to try to break the glass pane by throwing things at it. Let's imagine that I pick up a set of ping pong balls, and throw them at the glass. Probably, they're not going to break. Let's say I respond to that increasing the intensity with which I throw the ping pong balls, meaning I'll throw more ping pong balls per second. No impact. It doesn't make any difference how many ping pong balls I throw at the window, the window won't break. But I can respond rather differently. I could instead throw a baseball at the window pane. And then, it'll smash with a single baseball. So, low intensity baseballs can accomplish what high intensity ping pong balls cannot. And it's not at all like the fluid that we might expect if we were trying to aim water at it. What this tells us is in a similar way, if I have low intensity, high frequency photons, I can kick out electrons. Where with high intensity, low frequency photons, I cannot. That tells me that light is much more like ping pong balls or baseballs than it is like a garden hose. And that the energy that is impacting the surface to remove the electrons is being provided in little packets with individual impacts with the surface in the same way that ping pong balls make individual impacts with the surface. And so, do baseballs. How much energy is there in each one of these packets? We can actually answer that question by going back and looking at the data that tells us, let's see, the data that I wanted to look at is this graph. If I increase the frequency of the light above the threshold frequency, the kinetic energy increases in proportion to that. That tells me that the energy of each photon must be increasing with the frequency so that the kinetic energy the electrons ejected can increase with the frequency. And so, the energy in an individual photon is h nu, where h is just a proportionality constant. And nu is the frequency of the light. Now, each photon can eject a single electron, provided that the energy of that one photon is sufficiently high to ionize that electron from the metal. It won't make any difference how many frequency photons I have. Each one of those photons would have insufficient energy to pull an electron out. Consequently, a high-frequency photon, one, can accomplish what a great many low-frequency photons cannot. What happens when we crank up the intensity? Cranking up the intensity just increases the number of photons. And, therefore, should increase the number of photoelectrons. Let's look at the data again then and make sure that this explains the results. Notice, increasing the intensity increases the number of photons. That should increase the number of electrons. And it does. But increasing the intensity does not change the energy of the photons; therefore, the energy of each individual impact of a photon with the surface of the metal does not add more energy; therefore, the kinetic energy of the ejected electrons is constant. What about changing the frequency. If the frequency is too low, each individual impact is, doesn't have sufficient energy to eject the electrons, so no electrons are ejected. Once we have energy sufficient to eject photoelectrons, we eject them, but the number doesn't depend upon the energy of those photos. It depends upon the number of those photons. And lastly, of course, if I increase the frequency of the photons, the kinetic energy increases, because each individual impact is energetic. For our purposes, the most important thing that we can conclude here are these two primary results here. That the energy is quantized into packets and that each packet has photon h nu. Now, this discussion seems to have very little to do with chemistry and only to do with light. But now, we're going to use the radiation and our understanding of the energy of the radiation to try to understand the energies of individual electrons and atoms. And we'll pick that up in the next lecture.