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The electron that’s captured is an “inner” electron (1S) and bonding is via “outer” electron(s), so the effect on the decay is likely minimal. That Be sees an effect makes sense to me, since it only has the four electrons, so you would have the most possible effect on the 1S orbital depending on what bonds are formed.

The mathematical "engineer" (I prefer that to "father") of GR was Bernhard Riemann. And the mathematical "engineer" of QM is David Hilbert. By that I mean the people who introduced the "mathematical scaffolding" that later accomodated the physical theory. But I don't think either one of them would have come up with the respective physical theories without experimental or theoretical physics input. In fact, when the essential ideas of both theories were formulated, the physicists that did it couldn't imagine the mathematical tools were there already. That realisation, as always, came later. I think there's always a cycle that goes something like --example: electromagnetism--, 1) Induction: Observation of patterns, or "crude" observation: Lenz, Biot-Savart, etc. 2) Inference of a mathematical or pre-mathematical simple relations: Faraday. 3) The big picture in mathematical terms: Maxwell 4) Experimental confirmation of further predictions: Hertz Something like that. The history of the development of electromagnetism is a great example of how this works. But, of course, it's more complicated than just that. The different "branches" feed each other in a complicated way. Once we get the mathematically-closed form of the laws, the great generalisation, it's a matter of pushing and pushing the mathematical model until we find where it contradicts the experiments. It's also a matter of doing more and more refined experiments to check everything's OK. In the case of quantum mechanics: 1) Wien, Stefan, the spectroscopists (Lymann...), etc. 2) Planck, Bohr, Einstein 3) Heisenberg, Schrödinger, Dirac, etc. find out about a previously-existing mathematical scaffolding -> matrix algebra, Hilbert spaces, Poisson's formulation of mechanics... 4) Anderson finding positrons, which is a prediction of the relativistic version... Etc. Sometimes it goes the other way. We find a puzzling experimental discovery, and the theorists must rack their brains, within the mathematical scheme we already trust, in order to understand the unexpected result. If it doesn't, the mathematical scheme must be generalised minimally, ie, in such a way that the treasure of previous results is preserved. Example: discovery of the neutrino. So it's complicated. We may differ a little bit in what stage is what, but I think we agree in general terms.

Gamma photon(s) can be emitted by the nucleus, and X-rays and UV photon(s) can be emitted by electrons transitioning to the ground state of the daughter isotope. The 1s orbital is vacant, so further electrons will have to decay via photon emission to reach their final states.

Heisenberg? I think it was he that established the operator:observable formalism and the use of matrices. But the development of QM was very much a collective effort: more so than relativity.

And again, it depends on what precisely what we are talking about. Based on OP I would interpret it as general laws pertaining mostly to the Atlantic chattel slave trade, which as practice has ended. But if it is about slavery in general, including e.g. legal forms in the US as per the 13th amendment then it would be a very broad discussion.

Chart of the nuclides give decays for the known isotopes. There are a few software packages out there, and websites.

Now that we have gone through it for a while, what we have seen in practice is that online teaching is even less effective as in-Person. The latter kind of forces at least a minimum level of student engagement, whereas online it is just very difficult to achieve, even if you throw in all the gimmicks there are at them (polls, questions, exercises etc.). Folks just check out mentally much faster in front of a screen as opposed to have someone right in front of them (and scowling at them).

I must admit I haven't seen anything like this organised for a complete periodic table. I should have thought it would be quite difficult, as each individual radioisotope has a different decay mode, so you might need several different chains for each element if there is more than one radioisotope.

That is certainly true. Most students do not realize that a lecture is supposed to be a general guidance to the material, and is not the material itself.

I don't think you have to worry about igniting helium