The binding energy of a H-atom , considering an electron moving around a fixed nuclei is $B= \large\frac{-me^4}{8n^2\in_0 h^2}$If one decides to work in a frame of reference where the electron is at rest , the proton would be around it. By similar arguments, the binding energy would be , $B=\large\frac{-Me^4}{8n^2\in_0^2h^2}$ This last expression is not correct because ,

Question

$\begin{array}{1 1} \text{n would not be integral } \\ \text{Bohr-quantization applies only to electron} \\ \text{The frame in which the electron is at rest is not inertial } \\ \text{the motion of the proton would not be in circular orbits even approximately } \end{array}$