15.3 Rotational modes of diatomic molecules
,...
2
,
1
,
0
,
)
1
(
2
2
=
+
=
l
l
l
L
h
The rotation is modeled as the motion of a quantum mechanical
rigid rotator. The moment of inertia of the molecule rotating
around the axis:
I=m
r
r
0
2
,
where m
r
=m
1
m
2
/(m
1
+m
2
) is the reduced mass,
r
0
is the equilibrium distance between the nuclei.
Quantum mechanics states that the allowed values of the
angular momentum L meet
The rotation energy is given by
ε
= (½)I
ω
2
.
ω
is the angular
velocity. Since L=I
ω
,
ε
=L
2
/2I.
So that the quantized energy
levels are:
r
0
ω
.
2
/
)
1
(
2
I
l
l
r
l
h
+
=
ε
(15.13)

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