Hello. Today, we're going to start talking about quantum mechanics, quantum mechanics and the structure of matter. So what do we need to know for thermodynamics. Well, there are basically three things we need to know. The first is how atoms and molecules store energy.. We know molecules can store energy by translation, by moving back and forth, up and down, in and out, three coordinate directions. That's kinetic energy. A molecule can also store energy by rotation. If it has a moment of inertia about any axis that it hasn't a moment of inertia. This is ethane C2H6. So it can rotate in several different directions, but only three independently. It can also vibrate. It can vibrate between the two carbons like this. But it can also have various bending motions and that sort of thing. Then finally, the electrons have motion around the molecule and I just represent that with the tips of my fingers. That's the first thing we need to know, how do they store energy? The second thing we need to know is what is the details of their structure? How do they store energy? In detail, we know from quantum mechanics that isolated particles exist in particular quantum states, and that those allowed quantum states can be described by quantum numbers and we need to know the properties of those states. Then the third thing we need to know is once we know a lot, how do the large numbers of particles behave in equilibrium, that's statistics. We've actually already done the statistics. You'll see that once we're done with quantum mechanics, then it will go pretty fast to figure out how large numbers of quantum mechanical particles as it were behave. But for now, we're going to talk about quantum mechanics. So to begin with, we do know that matter is made up of atoms and that atoms can combine to form molecules. We know that atoms are composed of a nucleus surrounded by electrons. We use the term structure to describe the allowed configuration of an atom or a molecule. From your high school chemistry, you'll recall that atoms have electrons around them, electrons exist in orbitals are shells as they're called. So for example what are the shells allowed shells for a particular atom, and if we put two molecules together, how far apart are they on average etc? If we have more than two atoms forming a molecule, what does their relative position with respect to each other and so on. We know that atoms and molecules generally exist in fixed states known as quantum states. Now there are many situations in which atoms and molecules are undergoing dynamic conditions that cause a change in quantum states, but if we leave them alone long enough, then they will tend to relax to one of the fixed quantum states or eigenstates of the system. So what is a quantum state? It's an allowed configuration that determines spatial and dynamic behavior of the nuclei and electrons. For example, only certain amounts of vibration are allowed. If I have a diatomic molecule, I can have different vibrational energy, kinetic and potential energy associated with vibration, but they come in discrete increments. In thermodynamics, we're mainly interested in the kinetic and potential energy of the particles, and of course what the accumulated kinetic and potential energy which we call internal energy of a macroscopic system. Typically, we describe the structure of atoms and molecules using, if we want to describe them graphically, we do so using energy level diagrams and here are two examples. The one on the left is for the hydrogen atom. For historic reasons in atomic structure, typically zero energy is considered to be when the outermost electron, it's the furthest away or as far enough away from the nucleus so that they are not interacting, that would be zero energy. However, as the electrons come closer, there is an actually an attractive force. So if you think of it as an ion, an electron coming back together, that's an exothermic reaction, releases energy. So as it drops down in the allowed quantum levels, we get more and more energy. So for instance for the hydrogen atom, the energy of the lowest state with comparison to the fully ionized state is minus 109678 inverse centimeters, and we'll talk about the units here. But units of inverse centimeter are commonly used to describe energies in the chemistry and physics world. The diagram on the right shows a potential energy diagram for a diatomic molecule. What we will learn is that because electrons are very light compared to nuclei, that the dynamic behavior of the electrons tends to relax to a steady-state condition much more rapidly than the motion of vibration or rotation. So we can characterize the effect of the electrons of all the electrostatic forces in terms of a potential energy, and it looks something like this solid line which I drew using the Morse potential. We'll get to what that is later. It's an analytic expression that looks like it ought to look. Not very accurate reality, but that's fine. We'll run into a lot of that. But it gives the general idea. So when molecules are far apart, there is no interaction. As you bring to, the nuclei are far apart. There's little interaction if they're far enough apart. But as you bring them together, then the electrons rearrange themselves in a way that results in a net attractive forces. These are called Van der Waals forces, and they tend to want to pull the nuclei together. As they get closer to closer together, that attractive force comes into competition with the repulsive force of the two nuclei which have the same charge. You will remember from freshman physics that likes oppose, opposites attract. So the nuclei are going to oppose each other. So there's a balance and the force between them and therefore in the potential energy and you'd get what this solid curves looks like. The minimum of that would be somewhere near an equilibrium distance between the two nuclei. The bottom dotted line shows what the potential energy for a harmonic oscillator, simple spring mass system looks like. We will in fact use that as an approximation to get an analytic solution for vibration. So what is quantum mechanics? It's the mathematics of atomic and molecular structure. Using that mathematics, we seek to determine allowed quantum states and their energies. In the next video, we'll explore. We'll start by exploring a bit of the history of quantum mechanics. So that's it for this video. Thanks and have a great day.
