Calculate the velocity of the fastest neutron in a 96Mo nucleus and, based on this, explain whether or not we are safe to consider such nucleons in a non-relativistic way. Hint: first
calculate the Fermi energy.
Fermi energy from Fermi gas model: https://en.m.wikipedia.org/wiki/Fermi_gas
The Attempt at a Solution
Calculating the Fermi energy using Wolfram:
Fermi Energy = 30.3946 MeV
Fermi Momentum = √(2mE)
m: mass of neutron
E: Fermi energy
Fermi Momentum = √(2*939.565*30.3946) = 238.988 MeV/c
Velocity = Fermi Momentum / mass
= 238.988 MeV/c / 939.565Mev/c^2
So the fastest neutron in 96Mo is travelling at .2547 * speed of light. Provided my calculation is correct, I'm not sure whether we are safe to calculate them in a non-relativistic way though?