This is the final report on my modern physics class from last term, covering the last week of classes, which generally deal with nuclear and particle physics. This was actually three-and-a-bit classes, because I lost one class to a nasty cold a few weeks earlier, and used part of the lab period to make up for it.
Class 28 was actually taught by a colleague of mine (thanks, Rebecca!), because Kate and I were in Boston for her father’s wake. She taught off my notes, though, so I’ll still report it as if I did the class.
This class opens with a brief return of the historical treatment of the early weeks of the course, talking about Rutherford’s discovery of the nucleus– Marsden and Geiger, and “It was as amazing as if you fired a fifteen-inch shella t a piece of tissue paper and it came back and hit you.” The book goes through the derivation of Rutherford scattering in great detail, but there’s not much done with it after all that math, so I just state the results.
Rutherford scattering is used to introduce the idea of learning about subatomic structure by slamming things into other things, and then I talk about what we know of the structure of the nucleus. I talk about how there must be some very short-range force that acts between nuclei, in order to keep the nucleus from just flying apart into a billion pieces, and sketch the form of the potential.
I run through what can be inferred about the strong nuclear force from this, and then state that this comes about because the strong force really acts between quarks. I discuss color charge briefly, and make an analogy to the dipolar force between atoms that we talked about with molecules.
Class 29 picks up from there, and introduces all the Standard Model particles– six quarks, six leptons, and the four fundamental interactions. I talk very briefly about all the botany that goes on with naming different particle types.
Then we move back up to nuclei, and talk about the stability of nuclei. I show a chart of the nuclides, and point out the two main features, namely that the number of protons and neutrons is roughly equal in light elements, but there are always more neutrons in heavy elements. This can be explained (following the Six Ideas model) by thinking of two sets of bound states in each nucleus, one for protons and another for neutrons, and filling those states according to Pauli exclusion.
For light elements, the proton and neutron states are at roughly the same energy, so the lowest energy configuration will have roughly equal numbers of the two. A large excess of one or the other produces a system whose energy can be lowered by converting protons to neutrons (or vice versa) through the weak force, so the nucleus will undergo beta decay until roughly equal numbers are obtained.
In heavy nuclei, with lots of protons, the repulsion between protons shifts their energy states up relative to the neutron states, meaning that equal numbers of protons and neutrons leads to many protons being above the energy of the last neutron state. This system can lower its energy by beta decay, leading to more neutrons than protons.
It’s a nice, qualitative explanation of how nuclear stability works, that captures both of the main features in a very natural way. It’s also one of the few things from this section that leads to homework and exam questions, as I’m free to make up absurd unstable isotopes, and ask students to explain why and how they decay.
Class 29a, part of the lab period, rounds out nuclear physics by explaining the statistical treatment of radioactive decay. I describe alpha, beta, and gamma emission, and then show how you get exponential decay from the assumption of a constant decay probability. This leads into half-lives and radioactive dating, and all that fun stuff.
Class 30 is basically Chapter 9 of the book-in-production, the Bunnies Made of Cheese chapter, framed as an explanation of the absurdly good precision of the g-factor of the electron. I talk about the exchange model of interactions, how energy-time uncertainty helps explain the range of forces, and draw a few Feynman diagrams. Then I talk about virtual particles, and the extra diagrams added by those. I explain that the theoretical calculation of the g-factor involves the summing of nearly 1000 Feynamn disgrams, up to something like eight virtual particles, and that it agree perfectly with experiment (to the point where the most recent experiments have stopped comparing to theoretical predictions, but use the experimental number and the theoretical coefficients to obtain a measurement of the fine-structure constant alpha.
It’s entirely qualitative– I don’t tell them how to calculate anything from a Feynman diagram– but it’s great fun. This is consistently the class with the most questions, mostly of the form “Wait– what? Are you kidding?” And I think it ties the whole thing together very nicely– the agreement between QED and experiment is one of the real triumphs of modern physics, and a fitting end to the course.