The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton) is $\mathrm{B}=-\frac{{\mathrm{me}}^4}{8{\mathrm{n}}^2{\mathrm{\epsilon }}_0^2{\mathrm{h}}^2}$ (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 $\mathrm{B}=-\frac{{\mathrm{Me}}^4}{8{\mathrm{n}}^2{\mathrm{\epsilon }}_0^2{\mathrm{h}}^2}$ (M=proton mass), This last expression is not correct because