All Problems Scattering of Particles. Rutherford-Bohr Atom
Problem 6.46
Taking into account the motion of the nucleus of a hydrogen atom, find the expressions for the electron's binding energy in the ground state and for the Rydberg constant. How much (in per cent) do the binding energy and the Rydberg constant, obtained without taking into account the motion of the nucleus, differ from the more accurate corresponding values of these quantities?
\(6.46 . E_{b}=\mu e^{4} / 2 \hbar^{2}, R=\mu e^{4} / 2 \hbar^{3},\) where \(\mu\) is the reduced mass of the system. If the motion of the nucleus is not taken into account, these values (in the case of a hydrogen atom) are greater by \(m / M \approx\) \(\approx 0.055 \%,\) where \(m\) and \(M\) are the masses of an electron and a proton.