Page 132 - Bruno Linder Elementary Physical Chemistry

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

Elements of Molecular Spectroscopy 117

(1) For rotational transitions with no change in vibrational quantum
number, the molecule must have a dipole-moment.
(2) For a vibration transition, with or without accompanying rotational
transitions, the molecule must have a non-vanishing dipole moment
derivative. The dipole moment must not vanish upon vibration.

11.5. Pure Rotational Spectra
These spectra are observed in the far infrared and the microwave region.
In particular, the transition frequencies for absorption and emission are
respectively,

ν J+1←J =(E J+1 − E J )/hc (11.7a)
∗
=[(J +1)(J +2) − J(J +1)]B ∗ (11.7b)

=2(J +1)B ∗ (11.7c)

ν ∗ =(E J−1 − E J )/hc (11.8a)
J−1←J
=[(J − 1)(J) − J(J +1)]B ∗ (11.8b)
= −2JB ∗ (11.8c)

∗
Note: Spacing between adjacent absorption peaks equals 2B (i.e. it
is constant).

Exercise: The spacing between adjacent rotational lines in the far IR of HCl
is 20.5 cm −1 .Calculate

(1) the moment of inertia,
(2) the equilibrium separation of the two nuclei (or bond-length).

11.6. Vibration–Rotation Spectra
Vibrational energy levels are generally widely separated, implying that at
ordinary temperatures the molecules are in their ground state. It is then
reasonable to assume that there is only one vibration transition, namely
from v =0 to v =1.