Published by Patrick Mutisya · 14 days ago
Understand that stars, including the Sun, obtain their energy from nuclear reactions. In stable stars the dominant reaction is the fusion of hydrogen nuclei (protons) into helium nuclei.
The Sun appears to be a constant source of light and heat, but this energy originates from processes deep within its core. The core temperature is about \$1.5 \times 10^7\ \text{K}\$ and the pressure is more than \$2 \times 10^{11}\ \text{Pa}\$, conditions that allow nuclear fusion to occur.
The primary fusion pathway in the Sun is the proton‑proton (p‑p) chain, which can be summarised in three main steps:
\$\$
p + p \rightarrow \, ^2\!H + e^{+} + \nu_e
\$\$
\$\$
^2\!H + p \rightarrow \, ^3\!He + \gamma
\$\$
\$\$
^3\!He + ^3\!He \rightarrow \, ^4\!He + 2p
\$\$
Overall, four protons are converted into one helium‑4 nucleus, with the release of energy:
\$\$
4p \rightarrow \, ^4\!He + 2e^{+} + 2\nu_e + \gamma + 26.7\ \text{MeV}
\$\$
The mass difference between the four original protons and the resulting helium nucleus is converted to energy according to Einstein’s equation \$E = mc^2\$.
| Quantity | Value |
|---|---|
| Mass of 4 protons | \$4 \times 1.007825\ \text{u} = 4.03130\ \text{u}\$ |
| Mass of \$^4\!He\$ nucleus | \$4.002603\ \text{u}\$ |
| Mass defect \$\Delta m\$ | \$0.028697\ \text{u}\$ |
| Energy released \$E\$ | \$\Delta m c^2 \approx 26.7\ \text{MeV}\$ |
Not all stars fuse hydrogen at the same rate. The rate depends on mass, core temperature and composition. More massive stars have hotter cores and fuse hydrogen more rapidly, giving them shorter lifespans.