Moment of Inertia of dysprosium-160

[Guessit]

Homework Statement

The nucleus dysprosium-160 (containing 160 nucleons) acts like a spinning object with quantized angular momentum, L² = l(l + 1) * h_bar², and for this nucleus it turns out that l must be an even integer (0, 2, 4...). When a Dy-160 nucleus drops from the l = 2 state to the l = 0 state, it emits an 87 keV photon (87 ✕ 10³ eV).

h_bar = reduced Planck's constant

Homework Equations

Kinetic Energy = L² / 2I , where I is the moment of inertia

The Attempt at a Solution

Change in KE = Change in L² / 2I = 5h_bar² / 2I
Substituting and solving for I gave me around 2*10^-54 which apparently isn't the answer.
Am I using the wrong formula?

edit: rookie mistake, Change in KE = 6 * h_bar... not 5.

 

[Simon Bridge]

Show your reasoning. Where does the energy come from? Where does it go?
How did you account for the energy of the photon, for instance?
Check other sources of mistakes - like the value of I and the units.