M2L4d_cq.txt

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Let me formulate a question, because I will need that
later on.
So if you have a hydrogen-like atom,
and the electron is in a state with principal quantum number
n.
And let's assume there is no angular momentum.
And so, what I'm writing down for you,
is the probability for the electron to be at the nucleus.
This will be very important later on,
when we discuss hyperfine structure,
because hyperfine structure is responsible-- for hyper fine
structure-- what is responsible is the fact that the electron
can overlap with the nucleus.
So this factor will appear in our discussion
of hyperfine structure.
And what I want to ask you is, how does this quantity depend
on the principle quantum number n, and on z.
And I want to give you four choices.

Of course, for dimensionalist reasons,
everything is 1 over the Bohr radius cubed,
because it's a density.
But you cannot use dimensional analysis to guess how do things
scale with z and with n.
So here are your four choices.
Does it scale with z, z squared, z cubed?
Does it scale with n squared, n cubed, n to the six?