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

the characteristic rotational energy

E={ h(cross)} ² /2mr²

here m is reduced mass and r is the separation between two.

given E=4.16x 10^-4 eV

for l=9

so E₉=[{ h(cross)} ² /2mr²] x l(l+1)= Ex 9x10 =4.16x 10^-4 x90=37.44x10^-3eV

itcan decay to +1 state.