Page 130 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:37 9in x 6in b985-ch11 Elementary Physical Chemistry

Chapter 11

Elements of Molecular Spectroscopy

11.1. Vibration–Rotation Spectra of Diatomic Molecules

Two points should be emphasized:
1. Actual energy levels are not directly measurable.
2. A spectrum shows only transitions of energy.

11.2. Rotational Selection Rules
Spectral absorption or emission corresponds to transitions between pairs
of levels, as noted before. But not all possible levels may be combined.
By theoretical studies of the wave-functions, especially their symmetry
properties, one can devise selection rules. These rules tell whether certain
quantum jumps are allowed or not allowed. Selection rules do not tell
whether the intensities are weak or strong.
The rotational energy levels of a linear molecule are
2
E J = J(J +1)(h/2π) /2I J =0, 1, 2,... (11.1)
where J is the rotational quantum number, and I is the moment of inertia,
2
namely I = µd (d being the internuclear distance and µ the reduced mass).
The results are generally expressed in terms of the rotational constant, B,
which has the dimensions of Hz (s −1 ) and is defined as
2
B =(h/8π I) (11.2a)
or, in terms of B , defined as
∗
B = B/c (11.2b)
∗
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