= Solution
Separate <center-of-mass motion> and replace $m$ by the <reduced mass> $\mu=mM/(m+M)$ in the relative-coordinate formulas. Then $r_n$ is the proton-electron separation, <Energy level>[energy levels] and the Rydberg constant scale by $\mu/m$, and transition wavelengths increase by $m/\mu$. The <electron>'s own <orbital radius> about the <center of mass> is $Mr_n/(M+m)$; the <proton> <radius> is $mr_n/(M+m)$. The relative <speed> retains $\alpha c/n$, while the <electron>'s individual <speed> acquires $M/(M+m)$. Replacing the <mass> in the <radius> alone but leaving energies unchanged would be inconsistent.
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