Question

Consider an ideal degenerate gas of electrons, protons and neutrons and the equilibrum established by the two reactions, namely beta decay and inverse beta decay:

n ? p + e ? + ¯?e and e ? + p ? n + ?e (1)

(a) In the case where all particles are highly degenerate and ultra-relativistic, show that the number densities of the particles are in the ratio: ne : np : nn = 1 : 1 : 8.

(b) If the mass density is ? = 2 × 1017 kg m?3 , all Fermions in the gas are highly degenerate. For the electrons, protons, and neutrons, evaluate each case whether they are non-relativistic or ultra-relativistic. To make the calculation simpler, you may use the approximate values of nn : np = 200 : 1.

(c) At the density assumed in part (b), estimate the number densities of electrons, protons, and neutrons. Show clearly what your assumptions are.

Answer 1