Page 199 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

190 The hydrogen atom

~
ν ¥
Figure 6.7 A typical series of spectral lines for a hydrogen-like atom shown in terms of
the wave number ~ í.

A typical series of spectral lines is shown schematically in Figure 6.7. The
line at the lowest value of the wave number ~ í corresponds to the transition
n 1 ! (n 2 ˆ n 1 ‡ 1), the next line to n 1 ! (n 2 ˆ n 1 ‡ 2), and so forth. These
spectral lines are situated closer and closer together as n 2 increases and
converge to the series limit, corresponding to n 2 ˆ1. According to equation
(6.83), the series limit is given by
~ í ˆ R=n 2 (6:85)
1
Beyond the series limit is a continuous spectrum corresponding to transitions
from the energy level n 1 to the continuous range of positive energies for the
atom.
2
The reduced mass of the hydrogen isotope H, known as deuterium, slightly
1
differs from that of ordinary hydrogen H. Accordingly, the Rydberg constants
for hydrogen and for deuterium differ slightly as well. Since naturally occurring
hydrogen contains about 0.02% deuterium, each observed spectral line in
hydrogen is actually a doublet of closely spaced lines, the one for deuterium
much weaker in intensity than the other. This effect of nuclear mass on spectral
lines was used by Urey (1932) to prove the existence of deuterium.

Pseudo-Zeeman effect
The in¯uence of an external magnetic ®eld on the spectrum of an atom is
known as the Zeeman effect. The magnetic ®eld interacts with the magnetic
moments within the atom and causes the atomic spectral lines to split into a
number of closely spaced lines. In addition to a magnetic moment due to its
orbital motion, an electron also possesses a magnetic moment due to an
intrinsic angular momentum called spin. The concept of spin is discussed in
Chapter 7. In the discussion here, we consider only the interaction of the
external magnetic ®eld with the magnetic moment due to the electronic orbital
motion and neglect the effects of electron spin. Thus, the following analysis