Krane- Chapter 9, Question 11

 

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)