Correction to the Rydberg Constant for Finite Nuclear Mass
Abstract
If the problem of the hydrogenlike 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 centerofmass 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, nonrelativistic physics. Also, an interesting conjecture about the energy levels of hydrogenlike atoms, under the assumptions of Bohr theory and classical physics, is obtained.
 Publication:

American Journal of Physics
 Pub Date:
 October 1965
 DOI:
 10.1119/1.1970992
 Bibcode:
 1965AmJPh..33..820C