 Hello, I'm Professor Stephen Nescherben. I want to tell you a little bit about wave particle duality, which is a fundamental idea of quantum mechanics. That is to say that electrons have a dual property. They are particle-like and they are also wave-like. So what could that possibly mean? And let me go back to the Ruthford model of an atom. So you can design and carry out experiments that measure where an electron is. And those experiments generally come up with the result that they find an electron somewhere at some particular place. Now, it probably won't stay there afterward for very long, and there's other quantum mechanical theories like the uncertainty principle that play in there. However, the point is that when we do that measurement, we know that the electron was at some particular place at some particular moment from which we conclude, oh, well, electrons must be particles. On the other hand, there are also experiments that show that if you take a bunch of measurements of where an electron is, some patterns begin to emerge. So an example of a pattern is shown below. We have called this sort of thing an orbital. And the way we interpret that is that when an electron is in that orbital we're more likely to find that electron in the middle of those lobes, like there, there, there, or there. But it wouldn't be found in between those lobes. Our conclusion? Well, electrons, yeah, they're still particles, but they're also waves. So that notion is called the wave particle duality. So to understand that duality, we need to answer a couple of questions. One is exactly how is this a wave? Because it doesn't look like a wave at the moment to me. And what do those colors mean? So to answer both questions, we're gonna just dive into an analogy, which is the analogy of waves on a string. So here's, we are imagining that there's a string and it's tied to a wall over here and we're kind of shaking it a little bit off in that direction. So I'm gonna go to Wikipedia, actually. And so here's a gif and it shows that somebody's just shaking that string and we're getting all kinds of crazy stuff. You can see that this wave, it's called a transient wave because it doesn't keep the same shape over time. It's just evolving and changing all the time. Now, there's a special category of waves on a string, which most, if you're a string player, you might know about this. And they're called standing waves and they are special because although their amplitudes change over time, their shapes do not. And let me kind of explain a little bit about what I mean by that. So here's a standing wave and the idea is this might be a guitar or violin or something and it's pinned down here, pinned down here. And you can see that this string is swinging down and then it swings up, okay. And so what we wanna get out of this is that the shape of it stays kind of the same. It's this one sort of big loop, but now the amplitude is positive and now the amplitude is negative. It just goes up and down like that. Here's another standing wave. It's also a standing wave because its shape stays the same. Cause look, where it's up here and down there, then it changes. So again, its amplitude is the only thing that's changing and the same thing is happening with the rest of these. Another thing to note that's of interest to, known to most string players I would say is that this is like a harmonic on a guitar string. They're all harmonics and they vibrate at different frequencies, which means that you get different notes when you manage to pluck a string that way. Okay, so what we're gonna do is do some color coding because it'll be obvious in a moment. So the amplitude can be positive or negative up or down relative to the baseline, that string. And everywhere the string goes up, I'm just gonna color code it with a red line. So this is the same line going the same baseline of the string left to right here. It's just here, I've color coded it so that when the string has got positive amplitude, it's red and where the string has negative amplitude, it's blue. Now, we also know that since this is a standing wave, that also changes over time. Although I do wanna point out that these points called nodes, they are not actually changing over time. But you can see that the amplitude's positive, negative, positive, negative for that part of it and so on. So if I just waited for a little bit of time on this standing wave, when it's positive here, a little bit later it would be negative. So I would wanna code that as blue for this part of it, red, blue, red. Okay, so the main point is that the amplitude of a wave can be positive or negative up or down relative to the baseline if it's a string. And we're just color coding it as red or blue to indicate whether that segment of the string has got positive amplitude or negative amplitude. So if we now go back to our orbital idea, here's the deal, orbitals are waves in three dimensional space, not in the one dimensional space of a string. So we can't show an up or down unless we can draw and visualize things in four dimensions, which I can't do. However, we can still color code the amplitudes. So in other words, I go to some point in space and I say, okay, the amplitude of the wave is positive because I can see it's red and the amplitude of the wave must be negative there and positive and negative. This happens to be a d orbital of titanium. And if I waited a little bit, probably that positive amplitude over here in this region of space would become a negative amplitude. So that's why it's blue and so on. So, and I have another example. Here's a 3S orbital of the element sodium. In this case, I don't have the opposite sign for you, but here you can see since on the outside of this orbital, the wave amplitude is negative because it's blue, but you can kind of see that in the middle of it, it's red. And so that must be positive amplitude right in the center of this and negative amplitude in the outside. Now, a little bit later, probably the blue and red colors will switch, meaning that the wave amplitude would be positive on the outside, negative on the inside. So to summarize, orbitals are standing waves in a three dimensional space that tell you where you're likely to find an electron. And we color code the wave amplitudes with red and blue to indicate positive and negative wave amplitudes because the orbitals are standing waves. Their amplitudes switch back and forth from positive and negative over time and therefore go from red to blue to red. But their shapes remain the same, just as in the same way that the string did. I just a little caveat. The wave amplitude has nothing to do with an electron's charge, which is always minus one and it has nothing to do with its spin, which is either plus or minus one half quantum number. However, the wave amplitude has everything to do with how atoms form bonds, which is why it's useful for us to spend some time understanding it.