A certain molecule has a characteristic rotational energy of

A certain molecule has a characteristic rotational energy of 4.16 e-4 eV. What is the energy of the decay photon towards the state with angular momentum quantum number I = 9? The selection rules of delta I = +/- 1 tell you to what state it can decay.

Solution

rotational energy of molecule Er = L^2 /2I
when L = 0 , Er = 0
when L = 1 , charecteristic energy

         Er = 1 /2I = 4.16x 10-4 eV

when L = 9, the energy is,
               Er = 9^2 /2I = 81/2I = 81* 4.16x 10-4 eV = 336.96x 10-4 eV
the required enrgy:

        dE = 336.96x 10-4 eV - 4.16x 10-4 eV

             = 3.328e-2 eV