Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 9E / a / Solution

Chemical equilibrium in $n+{\nu }_e\leftrightarrow p+e^{-}$ givesThe negligible lepton chemical potentials therefore imply ${\mu }_n\simeq {\mu }_p$. Nonrelativistic Maxwell--Boltzmann number densities satisfyNeutrons and protons have equal spin degeneracy and nearly equal masses, so their prefactor ratio is approximately one. Hence