Hydrogen spectroscopy + what’s actually measured

1:08:34hydrogen atom. >> Okay. >> This is our favorite atom. Every physicist's favorite atom. If you don't understand the hydrogen atom, there's no hope in understanding anything else. [laughter] And um it's something that we do on our first first uh semester quantum mechanics you do the Schroinger equation and you solve the hydrogen atom because because it is the only um atom that you can like perfectly solve for. >> Okay. >> The idea with quantum mechanics is the following, right? We can never observe the electron. This is something that Heisenberg said when he actually came up with quantum mechanics 100 years ago in 1925. We can never observe the electron moving around a hydrogen atom. But we what we can observe is electrons jumping

1:09:17from one energy state to another energy state because that's when light comes out. >> When we make hydrogen atoms glow, certain colors are emitted by that hydrogen atom. Different atoms emit different colors. And by observing those colors of light, we [clears throat] can discern >> the structure of the atom inside. >> That's always the game when it comes to quantum optics. Mhm. >> Okay. >> Mhm. >> Now, these shells are not just like simple bore shells. They're actually very complicated. >> The hydrogen wave function >> looks like very cool clouds. >> Yes.

1:09:57>> Of electrons around the central proton. >> This looks like some sick app icons right here. >> Yeah. But that's actually what the electrons are doing around a hydrogen atom. If you were to put them in certain orbitals, in certain states of angular momentum and energy, they would occupy those clouds. Those are the probability clouds that the electrons occupy. Okay. Got it? >> And so what what we want to do when we want to probe something like what is the size of the proton? >> Yes. is we want to probe what the colors of light are and how those colors of light shift when the proton is yay big versus yay big.

1:10:37>> Right. Okay. >> Because if the proton is some size or some other size, what that is going to do is change the electron orbitals. >> Yep. >> Which will then change the light that comes out when electrons transition from one orbital to the other. >> Yes. Yes. [snorts] >> Is that perfectly clear? >> Yeah. So at different sizes of the proton >> m >> uh the way in which we can uh look at the the way in which we understand the probabilities of where the electron will be which is this electron cloud concept is going to be fundamentally different. >> Yes. >> And we use uh like the the color spectra like the energy and how it appears on the as a means by which to identify what

1:11:17those cloud configurations will look like. >> Yes. If the proton is a certain side, the cloud will look a tiny bit different, which means that the >> um which means that the the light that comes out when the electron transitions from one cloud, one energy state to another is going to be slightly different frequency. And if we can measure that very precisely, then we can tell >> back calculate what the size of the proton is. >> I I I see what you're saying. And so, okay. Yes. Makes sense. Okay. So what what what we're getting at is is we're not measuring the proton. >> Yeah. You're not taking a ruler, >> right? And looking like, hey, here's the it's you know three angstrom. What we're

1:11:58saying is there is there is an emission >> uh which is this electron changing energy states. >> That emission if we measure that emission with a level of precision, we can derive the size of the proton from that quote. I'm using emission as a loose. Yes. >> Term here. >> Exactly. And if we look at photo number eight right? >> Yes. >> The electrons are in these different clouds. >> Yes. >> There's there's different orbitals. For those in chemistry, you guys will remember something called 1s, 1 s2, 2 s2, 2p6, 3s2, 3p6. It's like a rap game that we used to memorize about all the electron configurations of each of the

1:12:39elements on the periodic table. Um, each of these orbitals are shapes of the electron clouds. The 1s and the 2s are spherical. >> Okay, there's no net angular momentum. >> But like the two ps, those are when electrons are loed in particular axes. Like there's the x axis, the y ais, and the z-axis, right? And that's that second energy level. The first energy level, there's just the sphere. The second energy level, the electron can be in the sphere, or it can be in these like dung bell shapes along the three axes right? >> Yes. >> Now notice the 1s and the 2s, those are spheres. Yes, >> those will actually interact with the proton if there's a proton in the middle

1:13:20of that sphere. >> Okay, the 2s and the 2p most of the time the electron is hanging out on the outside. It's not hanging out near the nucleus of the atom, >> which in this context is where the XYZ intersects >> the center, right? Yes. And so by looking at transitions between these different energies, we can figure out what is the contribution of the proton that's in the center and what is not. >> Because we're looking at basically the difference. >> Yes. >> Yes. >> Because the difference in these energies tells us what the frequency of the light that will come out. Higher frequency means higher energy difference. Okay. >> But to give you a a sense of the scale of what we're talking about, right? >> [laughter] >> Because because we're let's not let's

1:14:02not lose sight of the fact that we're talking about a hydrogen atom and on top of that we're talking about a proton at the center of the hydrogen atom.