Chemistry Reference
In-Depth Information
(a)
D
kT (narrow multiplets)
We have
m
eff
b
e
¼½
4J
ð
J
þ
1
Þ
1
=
2
ð
10
:
100
Þ
This is the case of the ions of the metals of the first transition
group, and of the triplet ground state of O
2
.IfL and S are
quantized independently (like in Fe
2
þ
), then
m
eff
1
=
2
b
e
¼½
4S
ð
S
þ
1
Þþ
L
ð
L
þ
1
Þ
ð
10
:
101
Þ
D
kT (wide multiplets)
Now, almost all particles are in the state of lowest energy J:
(b)
m
eff
b
e
¼
g
e
½
J
ð
J
þ
1
Þ
S
ð
S
þ
1
Þ
L
ð
L
þ
1
Þ
2J
ð
J
þ
1
Þ
3
2
þ
=
1
2
;
g
e
¼
ð
10
:
102
Þ
the case of the rare-earth ions.
(c)
D
kT (at room temperature, T
¼
293 K)
This is the most difficult case (for example, NO, Sm
3
þ
and
Eu
3
þ
), and it has been treated in detail by Van Vleck (1932).
We now discuss briefly a few interesting cases of paramagnetism in
atoms, molecules and ions. In comparingwith experiment, it is convenient
to put
eh
2mc
¼
N
A
erg
gauss mol
585
10
3
N
B
¼
N
A
b
e
¼
5
:
ð
10
:
103
Þ
1mol of Bohr magnetons, and an effective magnetic moment
m
eff
defined through
2
2
e
3kT
J
ð
J
þ
1
Þ¼
x
m
¼
N
A
g
e
b
g
e
N
B
3RT
J
ð
J
þ
1
Þ¼
ð
N
B
m
eff
Þ
ð
10
:
104
Þ
3RT
