Know that stars are powered by nuclear reactions that release energy and that in stable stars the nuclear reactions involve the fusion of hydrogen into helium

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – The Sun as a Star

6.2.1 The Sun as a Star

Learning Objective

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.

Why the Sun shines

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.

Key nuclear reaction: Hydrogen fusion (the proton‑proton chain)

The primary fusion pathway in the Sun is the proton‑proton (p‑p) chain, which can be summarised in three main steps:

  1. Two protons combine to form a deuterium nucleus, releasing a positron and a neutrino:

    \$\$

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

    \$\$

  2. Deuterium fuses with another proton to produce a helium‑3 nucleus and a gamma photon:

    \$\$

    ^2\!H + p \rightarrow \, ^3\!He + \gamma

    \$\$

  3. Two helium‑3 nuclei combine to give a helium‑4 nucleus and two protons:

    \$\$

    ^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}

\$\$

Energy released

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\$.

QuantityValue
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}\$

Why the Sun is stable

  • Hydrostatic equilibrium: outward pressure from the energy released balances the inward pull of gravity.
  • Rate of fusion is self‑regulating: a slight increase in core temperature raises the pressure, expanding the core and reducing the temperature, which slows the reaction rate.
  • Long‑term fuel supply: the Sun contains about \$10^{57}\$ protons; at the current fusion rate it can shine for roughly \$10^{10}\$ years.

Comparison with other stars

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.

Suggested diagram: Cross‑section of the Sun showing the core, radiative zone, convective zone, and photosphere, with arrows indicating the direction of energy transport.

Key points to remember

  • The Sun is a typical main‑sequence star powered by nuclear fusion.
  • In stable stars the dominant reaction is the conversion of hydrogen into helium via the proton‑proton chain.
  • Mass is converted to energy; \$1\ \text{kg}\$ of mass would release \$9 \times 10^{16}\ \text{J}\$.
  • Hydrostatic equilibrium keeps the Sun stable over billions of years.