Find the complete dependence of the \(A\) and \(B\) coefficients on atomic number
for the \(2 \mathrm{p} \rightarrow 1\) s transitions of hydrogenic atoms.
Calculate how the stimulated emission rate depends on \(Z\) when the atom is
exposed to black-body radiation at \(1000 \mathrm{K} .\) Hint. The relevant
density of states also depends on \(Z\).