See attachment for full problem and symbols.
Calculate the Fermi energies Eg (in units of eV) and the corresponding Fermi temperatures TF for:
a. Liquid 3He (density 0.0823 g cm^-3)
b. Electrons in aluminium (valence 3, density 2.7 g cm^-3)
c. Neutrons in the nucleus of 16O. The radius r of a nucleus scales roughly as r = 1.2 A ^1/3 x 10^-15m where A is the atomic mass number.
The pdf file contains the explanations and I also upload the Matlab script I used for calculations in case you may have use for ...
This in-depth solution calculates the Fermi energies and temperatures of the elements using the Fermi energy of an ideal gas spin formula on different situations. All steps are shown with explanations in the pdf file and a Matlab script is provided.