The spectrum of hydrogen with a nucleus of ﬁnite mass. The analysis in Section I-7 of the text assumes that the nucleus remains ﬁxed as the electron orbits about it. This corresponds to assuming that the proton mass is effectively inﬁnite. More correctly. we should picture the proton and electron as orbiting about their common center of mass. The effects of this can be incorporated in the analysis of Section I-7. but a simpler approach is to use the quantization of angular momentum (Section I-l2) and assume that the permitted circular orbits are those for which the total angular momentum of proton and electron together about the center of mass is nh/2pi (Eq. I-29).
(a) Show that the corrected value of the Rydberg constant Rh is
Rh = [Mp/(Mp + Me)]Rx
where R, is the value for an inﬁnite-mass nucleus.
(bl What is the difference in wavelength for the n = 2 —-> n = 1
"Lyman alpha" transition (A == l2l6 A) calculated using Rx and Rh.respectively?
The hydrogen with a nucleus of finite mass is examined. Angular momentum quantization are provided.