Another typical example is that of the particles in a nucleus of an atom. The radius of the nucleus is roughly:
where A is the number of nucleons.
The number density of nucleons in a nucleus is therefore:
This density must be divided by two, because the Fermi energy only applies to fermions of the same type. The presence of neutrons does not affect the Fermi energy of the protons in the nucleus, and vice versa.
The Fermi energy of a nucleus is approximately:
where m is the proton mass.
The radius of the nucleus admits deviations around the value mentioned above, so a typical value for the Fermi energy is usually given as 38 MeV.