This problem deals with the splitting of rotational energy levels of diatomic molecules. If one atom of the molecule has more than one stable isotope, then both isotopes are normally present in a sample. Show that the fractional change ∆f/f in the observed frequency of a photon emitted in a transition between adjacent rotational states is equal to the fractional difference in the reduced mass ∆μ/μ for molecules containing the two different isotopes.

This problem deals with the splitting of rotational energy levels of diatomic molecules. If one atom of the molecule has more than one stable isotope, then both isotopes are normally present in a sample. Show that the fractional change ∆f/f in the observed frequency of a photon emitted in a transition between adjacent rotational states is equal to the fractional difference in the reduced mass ∆μ/μ for molecules containing the two different isotopes.