Explain why the core temperature of a star must reach approximately 10⁷ K before hydrogen fusion can occur.

IB DP Physics Standard Level (2023 syllabus) — E.5 Fusion and stars · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Stars generate energy through nuclear fusion reactions in their cores. Before fusion can begin, specific physical conditions must be met.

Model answer (4 marks)

Protons are positively charged and therefore repel each other via the Coulomb force. For two protons to fuse they must approach within a distance where the strong nuclear force can act, which requires them to overcome the electrostatic potential energy barrier. The kinetic energy of the protons is proportional to the temperature of the core, so a very high temperature is necessary to give a sufficient number of protons enough kinetic energy to either classically overcome the barrier or, more realistically, to quantum‑tunnel through it. A core temperature of about 10⁷ K provides the required kinetic energy distribution so that a measurable fraction of protons can fuse, making hydrogen fusion possible.

Examiner tips

  • Mention Coulomb repulsion and the need for kinetic energy to overcome it.
  • Explain the link between temperature and kinetic energy.
  • Include the role of quantum tunnelling.
  • State the approximate temperature (~10⁷ K).

Common mistakes

  • Confusing the temperature with the energy of a single proton; students often give the wrong unit or magnitude.
  • Omitting the concept of quantum tunnelling and relying only on classical over‑the‑barrier fusion.
  • Using the wrong temperature value (e.g., 10⁶ K or 10⁸ K).

Mark scheme (4 marks)

  1. Protons are positively charged and so repel each other (Coulomb/electrostatic repulsion).
  2. Protons must have sufficient kinetic energy to overcome this electrostatic potential energy barrier and come close enough for the strong nuclear force to act.
  3. Kinetic energy of particles is proportional to (absolute) temperature, so a very high temperature is needed to provide this kinetic energy.
  4. A temperature of ~10⁷ K is required so that a sufficient proportion of protons have enough energy to undergo quantum tunnelling through the barrier / to overcome the Coulomb barrier.

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