Page 203 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

7

Spin

7.1 Electron spin
In our development of quantum mechanics to this point, the behavior of a
particle, usually an electron, is governed by a wave function that is dependent
only on the cartesian coordinates x, y, z or, equivalently, on the spherical
coordinates r, è, j. There are, however, experimental observations that cannot
be explained by a wave function which depends on cartesian coordinates alone.
In a quantum-mechanical treatment of an alkali metal atom, the lone valence
electron may be considered as moving in the combined ®eld of the nucleus and
the core electrons. In contrast to the hydrogen-like atom, the energy levels of
this valence electron are found to depend on both the principal and the
azimuthal quantum numbers. The experimental spectral line pattern corre-
sponding to transitions between these energy levels, although more complex
than the pattern for the hydrogen-like atom, is readily explained. However, in a
highly resolved spectrum, an additional complexity is observed; most of the
spectral lines are actually composed of two lines with nearly identical wave
numbers. In an alkaline-earth metal atom, which has two valence electrons,
many of the lines in a highly resolved spectrum are split into three closely
spaced lines. The spectral lines for the hydrogen atom, as discussed in Section
6.5, are again observed to be composed of several very closely spaced lines,
with equation (6.83) giving the average wave number of each grouping. The
splitting of the spectral lines in the alkali and alkaline-earth metal atoms and in
hydrogen cannot be explained in terms of the quantum-mechanical postulates
that are presented in Section 3.7, i.e., they cannot be explained in terms of a
wave function that is dependent only on cartesian coordinates.
G. E. Uhlenbeck and S. Goudsmit (1925) explained the splitting of atomic
spectral lines by postulating that the electron possesses an intrinsic angular
momentum, which is called spin. The component of the spin angular momen-

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