Big Bang nucleosynthesis

Remarks

The main steps are as follows. While weak interactions are fast, the neutron-to-proton ratio follows the Boltzmann distribution $n/p = e^{-Q / k T}$, with $Q \approx 1.293$ MeV the neutron-proton mass difference. The weak rates freeze out near $k T \approx 0.8$ MeV, leaving $n/p \approx 1/6$, which neutron decay lowers to about $1/7$. Deuterium is destroyed by the many photons until $k T$ drops to about $0.1$ MeV; then nearly all neutrons are bound into ${}^4\mathrm{He}$.

Example: if all neutrons end in ${}^4\mathrm{He}$ and $n/p = 1/7$, the helium mass fraction is $$Y_p = \frac{2 (n/p)}{1 + n/p} = \frac{2/7}{8/7} = 0.25.$$ Check: each helium nucleus has two neutrons and two protons, so the helium mass is about twice the neutron mass, in units of the nucleon mass.

Non-example: the formation of carbon and heavier elements does not belong to Big Bang nucleosynthesis. There are no stable nuclei of mass $5$ or $8$, and the density falls too fast, so heavier elements are made later in stars.