Consider a Fermi gas of N electrons each of rest mass m in a sphere of radius R. condition sin certain white dwarfs are such that the great majority of electrons have extreme relativistic kinetic energies ε ≈ pc, where p is the momentum. The de Broglie relation remains λ = 2πh/p. Problem 2 gives the ground state kinetic energy of the N electrons on the assumption that ε = pc for all electrons. Treat the sphere as a cube of equal volume.
(a) Use the standard virial theorem argument to predict the value of N. Assume that the whole star is ionized hydrogen, but neglect the kinetic energy of the protons compared to that of the electrons.
(b) Estimate the value of N. A careful treatment by Chandrasekhar leads not to a single value of N, but to a limit above which a stable white dwarf cannot exist;