Nuclear fusion and energy in the Sun and stars
In fusion, light nuclei join into a heavier, more tightly bound nucleus. It needs millions of kelvin to beat electric repulsion, and it powers the Sun and stars.
Why fusion releases energy and needs heat
On the binding energy curve, light nuclei such as deuterium have a low binding energy per nucleon. When two of them join into helium, the nucleons are held much more tightly. The extra binding energy is released. But both nuclei are positively charged, so they repel each other. To fuse, they must come within about 10⁻¹⁵ m, the range of the nuclear force. Only very fast nuclei can get that close. Such speeds need temperatures of about 10⁷ K or more, so this is called thermonuclear fusion.
Worked example: fusing two deuterium nuclei
Two deuterium nuclei fuse into helium-4. The binding energy of a deuteron is 2.22 MeV and that of a helium-4 nucleus is 28.3 MeV. Find the energy released and the energy per nucleon, and compare with the fission of ²³⁵U (200 MeV).
- Binding energy before = 2 × 2.22 = 4.44 MeV.
- Binding energy after = 28.3 MeV.
- Energy released = 28.3 − 4.44 ≈ 23.9 MeV, about 24 MeV.
- Per nucleon: 24 ÷ 4 = 6 MeV.
- Fission: 200 ÷ 235 ≈ 0.85 MeV per nucleon. So fusion gives about 7 times more energy per nucleon.
About 24 MeV, or 6 MeV per nucleon: about 7 times the energy per nucleon of fission
Energy in the Sun and stars
Fission cannot power the Sun: it has very few heavy nuclei. It is mostly hydrogen and helium.
- 1The Sun's huge gravity squeezes its gases, raising the temperature at its centre to about 1.5 × 10⁷ K (15 million kelvin). Your NIOS lesson says 20 million kelvin; the accepted figure is about 15 million.
- 2At this temperature, hydrogen nuclei (protons) move fast enough to fuse.
- 3Through a series of steps, four protons join to form one helium nucleus.
- 4★Overall: 4 ¹₁H → ⁴₂He + 2 ⁰₊₁e + about 26.7 MeV. The ⁰₊₁e are positrons: particles like electrons but with a positive charge.
- 5Hans Bethe proposed this source of the energy of stars. The Sun has enough hydrogen to keep shining for billions of years more.
★ key step
Energy in the Sun: the proton-proton cycle
Overall, four hydrogen nuclei make one helium-4 nucleus and release about 26.7 MeV.
Fission and fusion
Fusion on Earth
Deuterium (heavy hydrogen) is plentiful in sea water. One gram of deuterium could give about 10⁵ kWh of energy by fusion. But no container can hold matter at millions of kelvin for long. Scientists use strong magnetic fields to keep the hot gas away from the walls. Controlled fusion power is still being developed, and India is a partner in the international ITER project.
Every bit of sunlight that ripens mangoes and grows our rice, wheat and sugarcane began as fusion energy in the Sun's core, where hydrogen turns into helium.
2 marks: “Define nuclear fusion and explain why it needs a very high temperature.” Fusion: light nuclei join into a heavier nucleus, releasing energy (²₁H + ²₁H → ⁴₂He + about 24 MeV). The nuclei repel each other; only at about 10⁷ K do they move fast enough to come within range of the nuclear force.
5 marks: “What is the source of energy of the Sun and stars? Explain how it is produced, with the overall reaction.” Thermonuclear fusion of hydrogen into helium. Gravity compresses the core to about 1.5 × 10⁷ K; protons fuse in steps (¹H + ¹H → ²H + positron; ²H + ¹H → ³He; ³He + ³He → ⁴He + 2 ¹H); overall 4 ¹₁H → ⁴₂He + 2 ⁰₊₁e + about 26.7 MeV. Fission is ruled out because the Sun has few heavy nuclei.
1 marks: “Why is fusion called a thermonuclear reaction?” It takes place only at very high temperatures, millions of kelvin.
Fission splits big, fusion joins small; both climb towards iron.