Rotation of a deformed nucleus is predicted to produce nuclear excited states with energies given by E(J)=J(J+1)hbar/2I. The first two excited states of 238 U are Jpi = 2+(0.045MeV) and Kpi=4+(0.148MeV). Show these energies are consistent with rotational excitation stating any assumptions you make
The Attempt at a Solution
I is the moment of inertia of the nucleus. I=2/5 MR^2
For 238U I=2/5 * (92*938.272 +92*0.511 + 146*939.566) * [1.2 * (238)^1/3 ]^2
But I am getting a value of 4945058.626MeV fm^2 = 4.945...x10^-24 MeV
which is not giving me 0.045MeV for the 2+ state!??!?!!
any idea where I am going wrong?