If the problem of the hydrogen-like atom is done with the assumption that the nucleus is at rest, the resulting energy levels are proportional to the Rydberg constant for infinite mass. It is traditional to obtain the Rydberg constant for finite mass of the nucleus by a simple substitution of the reduced mass of the system for the electron mass in the expression for the Rydberg constant for infinite nuclear mass. Realization that such a substitution (which is drawn from classical mechanics) does not give a correct transformation to the center-of-mass coordinate system in the case of charged particles, leads one to significant corrections for the Rydberg constants of finite nuclear masses. The corrections are drawn from classical, non-relativistic physics. Also, an interesting conjecture about the energy levels of hydrogen-like atoms, under the assumptions of Bohr theory and classical physics, is obtained.