The binding energy of an H-atom,

The binding energy of an H-atom, considering an electron moving around a fixed nucleus (proton), is

$B=\frac{m e^{4}}{8 n^{2} \epsilon_{0}^{2} h^{2}} \quad(m=$ electron mass $)$. If one decides to work in a frame of reference where the

electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be

$B=\frac{M e^{4}}{8 n^{2} \epsilon_{0}^{2} h^{2}} \quad(\mathrm{M}=$ proton mass $)$ This last expression is not correct because

(a) n would not be integral

(b) Bohr-quantisation applies only to electron

(c) the frame in which the electron is at rest is not inertial

(d) the motion of the proton would not be in circular orbits, even approximately