Question 3: White dwarf stars [10 points]. (a) Derive the expression for the Fermi energy EF of an ideal gas of N non-relativistic particles of mass m and spin 1/2, confined to a sphere of radius R, in terms of N, R, m, and ħ. (Assume that the single-particle energies are the same as for a particle in a cubic box of volume V = L³, with V equal to that of the sphere of radius R). (b) Find the total energy of the gas at zero temperature, Uo. (c) Consider a white dwarf star composed of ionized hydrogen atoms. Assume that the mass of the star is equal to that of the Sun M 2 × 1030 kg, while the radius is R = 8 × 106 m. Find the = Fermi temperature of the electron gas TF, and of the proton gas TF,p· (d) If the temperature of the white dwarf is 107 K, discuss whether the electron gas is in the quantum regime or not. What about the proton gas?