Physics 441/541: Homework Questions Due March 8th

The first step of the proton-proton chain:
1 H + 1H = 2H + positron + neutrino
and the intermediate step of the CNO cycle:
13N = 13C + positron + neutrino
both involve beta decays and hence require the mediation of the weak interaction. Yet the latter reaction occurs every 870 seconds while the one involving hydrogen takes 14 billion years! (per particle). Why?

It is sometimes stated that it is fortunate that the first step of the proton-proton chain involves the weak interaction, and is extraordinarily rare, because otherwise the Sun would explode like a bomb. This is not true. What would happen to the Sun if the first step of the proton-proton chain were easier to accomplish than the weak interaction allows?

problem 12.3

problem 12.5