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## Homework Statement

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.

## Homework Equations

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:

http://m.wolframalpha.com/input/?i=(hbar^2/(2*1.674929*10^-27kg))((3*pi^2((6*10^43)))/1m^3)^(2/3)

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

= 0.2547c

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?