Fermi Energy of Nucleus (Derivation)

What is Fermi Energy of a nucleus?
In the Fermi Gas Model of the nucleus, it is assumed that the particles inside the nucleus (protons and neutrons) are present in a general potential field which can be approximated to that of a 3D square/ rectangular potential well. Since protons and neutrons are fermions, they will organize themselves in discrete energy levels. These energy levels are the result of the Schrodinger Equation solution for the case of a 3D rectangular potential.
Fermi Energy is the difference between the highest occupied energy level and the lowest occupied energy level in the ground state configuration of a nucleus.
In this video, I derive the Fermi Energy for a nucleus.

As you will see, the Fermi Energy of protons is different from that of neutrons.

*********Correction***********
Near the end of the video, I mistakenly wrote the power of one expression as 1/3 while it should have been 2/3.. Rest of the calculations are correct
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