Chemistry Reference
In-Depth Information
Spin
In this chapter, starting from the Zeeman effect, we introduce elements of
Pauli's formal theory for one- and two-electron spin, with a generalization
to the Dirac formula for N-electron spin.
5.1 THE ZEEMAN EFFECT
The study of atomic spectra under high resolution reveals a new feature of
the electron: its spin. Even orbitally nondegenerate levels, like the 1s ground
state of the H atom, are split into a doublet under the action of a magnetic
field
B
,
1
the splitting being linear in the field strength (Zeeman effect).
To explain this effect, Pauli (1926) postulated for the electron
the existence of two spin states,
a
and
b
, satisfying the eigenvalue
equations
1
2
a;
1
2
b
S
z
a ¼
S
z
b ¼
ð
5
:
1
Þ
where
S ¼ i
S
x
þ j
S
y
þk
S
z
ð
5
:
2
Þ
1
For a magnetic field of 1 T, the splitting for a ground-state H atom is about 10
5
times smaller
than the separation of the first orbital levels.
