# 6.3 The de Broglie Relation, the Heisenberg Uncertainty Principle, and Orbitals

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##### Video Transcript

Cool. So it was kind of a crazy discovery to find out that light was not just a wave. We always thought it was a wave classically and now we found out it's not just a wave, it's a particle. More properly, it has both wave-like and particle-like characteristics. It's not a wave, it's not a particle, but it's got characteristics of both. So matter, we always thought was particles and light we always thought was waves. So somebody came along, Mr. De Broglie in fact, and came along and said "You know what if light is not just a wave but also has particle-like characteristics, maybe matter also has wave-like characteristics." He was right! This is one of my favorite stories. He was a grad student getting his PhD and usually you write a thesis that's like 100 pages long or more. It's a real pain in the butt. His was like a page or two. Turns it in. Committee looks at it and they like sent him out of the room. They were like "You guys know what he's talking about?" "No." "You know what he's talking about?" "No." And so they just kind of dismiss him. They don't know what to tell him yet; they're like "We'll get back to you." They send off his paper to Einstein and they ask him "What do you think?" and Einstein gets back and he's like "He's a genius! Give him his PhD and send him to me." So, but I like it because he was smarter than his professors. Good times. So it turns out that particles do have wave-like behavior. So and here's the relation. So notice the bigger the mass, what does that do to the wavelength? According to this relation right here. What's the relation between wavelength and mass? It's actually inversely related. If I double the mass that actually cuts the wavelength in half. So can you see my wavelength right now? No you can't because I'm too fat! I have too much mass. So it turns out mass and velocity and your wavelengths are inversely proportional to both. And it's only when you see like very small things, like electrons, can we actually measure their wavelength. But like you and I? Never going to happen. Our wavelengths are like, you know even when I'm moving at a moderate pace, ten to like minus 40 something meters, you're never going to see it. But for an electron with a much, much, much, smaller mass we can totally measure the wavelengths. De Broglie was right. Cool. I don't know if you're gonna have to do a calculation with this. I doubt it. What you should know is the relations here. As wavelength, let's do it the other way around. As mass goes up, wavelengths goes down. As velocity goes up, wavelengths goes down. So your wavelength is inversely proportional to both mass and velocity. But Natali, what also, what funky constants also show up in this relationship? Planks proportionality constant is showing up yet again, rearing its ugly head. All right. Heisenberg uncertainty principle. It's a little bit of a funky thing. You need to know a couple things about this. Mathematically we'd state it like this. I don't care that you know what the constant is. But this stands for the uncertainty in an object's position. Usually we're talking about electrons here. And this is the uncertainty in the object's momentum. Those are two very important words when talking about this. So this is position and momentum. So if it turns out if you take the uncertainty in one and the uncertainty in the other and you multiply them together, it always has to come out bigger or equal to a certain constant. So it means you always have to have some certain amount of uncertainty. So let's say you minimize the uncertainty in the position, what's that going to do the uncertainty over here if it's still got to come out bigger than this constant? It's going to maximize it. And so it turns out the better you know the position the less you'd know the momentum. The better you know the momentum the less you know the position. This is kind of weird. Momentum is related to like, mass and velocity, so kind of dealing with like where an object's going, if we're going to limit the velocity part. Where ass the position is kind of where of an object is. And so it turns out if we try and look at where an electron is in an atom, the more we know where it is the less we know where it's going. The more I know where it's going the less I know where it is. It's a weird conundrum and it's totally true. Good times, right? So this guy was genius. He was also head of Germany's H-bomb project glad he didn't succeed. And there are people who think he did it on purpose, not succeeding anyways. Cool. Shapes and orbitals. S, P's and D's. What's an S orbital look like? Not a circle, it's three-dimensional. It's a sphere. And again is it a solid sphere or a hollow shell? No, no, it's a solid sphere. The S orbital is not just this hollow basketball shell. It's like a bowling ball from the nucleus all the way out to a certain distance, that's where we've got kind of a 95% probability of finding that electron. Cool. So P orbitals those are those dumbbell shapes. And again these are three-dimensional, which I can't really draw. So one lies on the y-axis, one lies on the x axis, and one lies on the z axis. They have different, different, orientation. And then your D orbitals. Most of your D orbitals look like a four-leaf clover. And they differ based on their orientations and stuff as well. Well again it's going to look like a four-leaf clover, or it could look like this funky shape as well. So if you notice that they're all on your handout. Four of the d-orbitals look like this. They only differ in their orientations. What axis they're on and stuff like that. But the fifth one just looks funky. You should recognize S is spherical, P is dumbbell shaped, and D is one of these two shapes. Just recognize their shapes. Life is good.

## The de Broglie Equation

The de Broglie equation shows the dependence of the wavelength of a particle of matter on its mass and velocity.

The de Broglie equation shows that this wavelength is inversely proportional to both the mass and velocity of the particle (h is Planck's constant, 6.626x10^{-34}J^{.}s). This explains why this wavelength is so small as to not be observable for large objects. But for a particle as small as an electron (m = 9.11x10^{-31}kg) the wavelength can be observed and lines up with that predicted by the de Broglie equation.

To obtain a wavelength in meters, be sure to use the mass in kg and the velocity in m/s (all SI units).

## The Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle quantifies the limits to which a particle's (usually an electron) position and momentum can simultaneously be known.

The product of the uncertainties in the position and momentum will be a minimum of h/4ℼ. This means the greater the precision to which the position is known, the greater the uncertainty in the momentum and vice-versa. This is by no means intuitive and is just another example that the quantum world is distinctly different than the macro world we experience every day.