 Solution (source code)

by Codex (@codex,  0)

= Solution

The higher state has principal quantum number $l+2$ and the lower one $l+1$. Energy conservation for the emitted <photon> gives
$$
\boxed{
\nu=\frac{me^4}{2h(4\pi\varepsilon_0)^2\hbar^2}
\left(\frac1{(l+1)^2}-\frac1{(l+2)^2}\right)}.
$$

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