Nuclear fusion in stars

When two light nuclei fuse into a larger, more tightly bound nucleus, energy is released. Examples: ¹₁H + ¹₁H → ²₁H + e⁺ + ν + 0.42 MeV; ²₁H + ²₁H → ³₂He + n + 3.27 MeV; ²₁H + ²₁H → ³₁H + ¹₁H + 4.03 MeV (Eq. 13.13).

To fuse, the nuclei must come close enough for the short-range nuclear force to act, but both are positive and repel. They need enough energy to get over this Coulomb barrier, whose height depends on their charges and radii: about 400 keV for two protons, and more for more highly charged nuclei.

For the average proton in a gas to have that energy, (3/2)kT = 400 keV, which needs T ≈ 3 × 10⁹ K. Fusion driven by high temperature is called thermonuclear fusion, and it powers the interior of stars.

The sun's core is at 1.5 × 10⁷ K, well below that estimate, so the fusion there involves protons whose energies are far above average.

The sun burns hydrogen into helium through the proton–proton cycle: ¹H + ¹H → ²H + e⁺ + ν + 0.42 MeV; e⁺ + e⁻ → γ + γ + 1.02 MeV; ²H + ¹H → ³He + γ + 5.49 MeV; ³He + ³He → ⁴He + ¹H + ¹H + 12.86 MeV (Eq. 13.14).

The first three steps must happen twice for the fourth to occur. The net result is that four hydrogen atoms make one ⁴He atom and release 26.7 MeV (Eq. 13.15).

When the core's hydrogen has turned to helium, the core cools, the star contracts under gravity and heats up. At about 10⁸ K helium fuses into carbon, and so on to heavier elements, but not beyond those near the peak of the Ebn curve.

The sun is about 5 × 10⁹ years old and has hydrogen for about another 5 billion years. Then hydrogen burning stops, the core collapses and heats, and the outer envelope swells: the sun becomes a red giant.

Controlled fusion reactors aim to heat fuel to about 10⁸ K, where it is a plasma of positive ions and electrons. No container can withstand such heat, so the challenge is confining the plasma. Several countries, India among them, are developing ways to do it.

Chemical reactions also convert mass to energy, since chemical binding also lowers mass, but the mass changes are about a million times smaller than in nuclear reactions (Example 13.4).