If a collection of molecules were all in the N = 0, L=0 ground state, how many lines would there be in the absorption spectrum?
This
question appears to be based on Figure 9.29, and I believe there is some confusion
here. The legend to the figure seems to
indicate that no transition is possible that does not satisfy the dipole
selection rules DL=±1 and DN=±1.
Certainly DL=0 is possible if the
electron wave function changes, making a transition that involves a change in
parity. Similarly, DN=0 is possible if the
molecule possesses a permanent dipole moment.
For
a homopolar diatomic molecule (such as H2, N2 or O2)
symmetry precludes a dipole moment.
Thus, no rigid rotor E1 microwave transition is possible unless there is
a change in the vibrational state to produce a dipole moment. Therefore such molecules are infrared
active, but not microwave active.
Perhaps Dr. Krane intended for this discussion to involve such a
molecule.
If
the molecule possesses a permanent dipole moment (as do all diatomic molecules
that do not have identical nuclei), rotational emission and absorption spectra
can be observed. The emission of
radiation is due to the rotation of the electric dipole, and the absorption of
radiation is due to the interaction of this dipole with the incident
radiation. These molecules are thus
microwave active, and can change their angular momentum state without an
accompanying infrared vibrational transition.
If
we assume that both Figure 9.29 and Question 11 are intended to involve a
homopolar diatomic molecule which can have no permanent dipole moment, then
both selection rules obtain. Hence
there will be only one absorption line in the spectrum, involving the transition
Level(N=0, L=0) Þ Level(N=1, L=1)