Answer
28.6 eV.
Work Step by Step
Find the photon’s momentum.
$$p_{\gamma}=\frac{E_{\gamma}}{c}$$
Momentum is conserved.
The recoiling nucleus has equal and opposite momentum.
Calculate the recoil energy from the momentum. Assume that the energy is small enough to not be relativistic – at the end, we’ll see that is true because the energy is much less than the rest energy of the nucleus.
$$KE_K=\frac{ E^2_{\gamma}}{2m_Kc^2 }$$
$$KE_K=\frac{ (1.46MeV)^2}{2(39.963998u) \left( \frac{931.49MeV/c^2}{u}\right)c^2 }$$
$$=2.86\times 10^{-5}MeV=28.6\;eV$$
It is indeed a nonrelativistic problem.
