Page 329 - Instant notes

I3
ROTATIONAL SPECTROSCOPY

Key Notes
The allowed energy levels of a rigid linear rotor are E J =BJ(J+1)
where J is the rotational quantum number, and B is the rotational
constant, which is inversely proportional to the moment of
inertia. The energy levels of a symmetric top molecule (one axis
of rotational symmetry) are described by two quantum numbers,
J and K, and two rotational constants B and A.
A molecule only gives rise to a rotational spectrum if it possesses
a permanent electric dipole. The specific selection rule allows
transitions of ∆J=±1 and ∆k=0. The allowed transitions in the
rotational spectrum of a polar linear and symmetric top molecule
have energy 2B(J+1) and generally fall within the microwave
region of the electromagnetic spectrum.
A rotational spectrum has a characteristic intensity distribution
that passes through a maximum because the population of
rotational levels from which the spectral transitions originate is
proportional to the Boltzmann factor (declines with rotational
quantum number, J) and the degeneracy of the rotational level
(increases with J). The rotational level with maximum population
is

The polarizability of the molecule must be anisotropic to give rise
to a rotational Raman spectrum. The specific selection rule for
linear molecules allows transitions of ∆J=±2. The anti-Stokes and
Stokes rotational transitions occur at energies ±2B(2J+3) from
the energy of the incident excitation radiation.

Related topics The wave nature of matter (G4) Practical aspects of
spectroscopy (I2)
General features of
spectroscopy (I1)