Question

What is the source of energy of the Sun?

Hint:

Fusion releases \(\sim 10^{7}\) times more energy per nucleon than chemical reactions—hence stars shine for billions of years.

Answer 1

Proton–Proton Chain Fusion in the Sun

Step 1: Conditions in the Core. The \( \sim 200{,}000 \, \text{km} \)-wide solar core has \( T \approx 1.5 \times 10^{7} \, \mathrm{K} \) and density \( \approx 150 \, \mathrm{g\,cm^{-3}} \), enabling quantum tunnelling so that protons can overcome Coulomb repulsion.

Step 2: Fusion Pathway. In the proton–proton (p–p) chain:

\[ p + p \rightarrow {}^{2}\!H + e^{+} + \nu_e \]

\[ {}^{2}\!H + p \rightarrow {}^{3}\!He + \gamma \]

\[ {}^{3}\!He + {}^{3}\!He \rightarrow {}^{4}\!He + 2p \]

Net reaction:

\[ 4p \rightarrow {}^{4}\!He + 2e^{+} + 2\nu_e + \text{energy} \; (\approx 26.7 \, \text{MeV}) \]

The mass defect \( \Delta m \) converts to energy via \[ E = \Delta m c^{2}. \]

Step 3: Energy Transport. Gamma photons produced in the core undergo a random walk outward, being repeatedly absorbed and re-emitted. By the time they reach the photosphere, they emerge as the solar spectrum with an effective temperature \( T \approx 5778 \, \mathrm{K} \). Neutrinos escape almost instantly, confirming ongoing fusion in the core.