A certain molecule has a characteristic rotational energy of

A certain molecule has a characteristic rotational energy of 8.26x10^-4 eV. What is the energy of the decay photon towards the state with angular momentum quantum number l = 9?

Note: The selection rules of delta l = +/- 1 tell you to what state it can decay.

Please show work.

Solution

formula for characteristic rotational energy E= {h(cross)}²/ 2mr² = 8.26x10^-4 eV

for l=9 the formula becomes E₉= [{h(cross)}²/ 2mr² ]x l x (l+1)

= 8.26x10^-4 eVx 9x10 =74.34x10^-3 eV