Thermonuclear Fusion in the Sun and Other Stars — Question 1

Question 1

Adding proton-proton-chain steps reveals the net stellar reaction

Use two copies each of $p+p\to d+e^++\nu_e$ and $d+p\to{}^3\mathrm{He}+\gamma$, followed by ${}^3\mathrm{He}+{}^3\mathrm{He}\to{}^4\mathrm{He}+2p$.

1. Cancel intermediate nuclei to obtain the net nuclear reaction, and check charge and lepton number.

2. Include annihilation of both positrons with ambient electrons and write the resulting net matter transformation.

Question 1 - Solution

Adding proton-proton-chain steps reveals the net stellar reaction

(a) Method and calculation

$$6p\to{}^4\mathrm{He}+2p+2e^++2\nu_e+\text{photons}.$$$$\boxed{4p\to{}^4\mathrm{He}+2e^++2\nu_e+\text{energy}};\quad Q:\ 4=2+2,\ L:\ 0=-2+2.$$

(b) Interpretation and further calculation

$$2e^++2e^-\to\text{annihilation photons}.$$$$\boxed{4p+2e^-\to{}^4\mathrm{He}+2\nu_e+\text{energy}};\quad L:\ 2=2.$$

Physical check

Four protons are consumed per completed chain, although six participate in the written intermediate steps. Photons and neutrinos carry energy away from the reaction sites.