In a reference frame with the origin at the center of mass of an electron and the nucleus of an atom, the electron and nucleus have equal and opposite momenta of magnitude p.

(a) Show that the total kinetic energy of the electron and nucleus can be written K = p2/2mr, where mr = meM/(M + me) is called the reduced mass, me is the mass of the electron, and M is the mass of the nucleus. It can be shown that the motion of the nucleus can be accounted for by replacing the mass of the electron by the reduced mass. In general, the reduced mass for a two-body problem with masses m1 and m2 is given by

(b) Use Equation 37-14 with m replaced by mr to calculate the Rydberg constant for hydrogen (M = mp) and for a very massive nucleus (M = ∞).
(c) Find the percentage correction for the ground-state energy of the hydrogen atom due to the motion of theproton.

Transcribed Image Text:

mk²e4 4πch3 R = 37-14