White dwarf stars are essentially plasmas of free electrons and free protons (hydrogen atoms that have been stripped of their electrons). Their densities are typically 5 × 109 kg/m3 (i.e., 106 times the average density of Earth). Their further collapse is prevented by the fact that the electrons are highly degenerate, that is, all the low-lying states are filled and no two identical electrons can be forced into the same state.
(a) Estimate the temperature of this system. (Assume nonrelativistic electrons and that p2 f /2m = (3/2)kT.)
(b) Now suppose that the gravity is so strong that the electrons are forced to combine with the protons, forming neutrons (with the release of a neutrino). If the temperature remains the same, what would be the density of this degenerate neutron star?