Nuclear fusion · Year 13
In Year 13 you learn: energy released by fusion: E = mc².
In fusion, two light nuclei, such as isotopes of hydrogen, join to make a heavier nucleus, releasing energy. Nuclei are positive and repel each other, so fusion only happens at the huge temperatures and pressures inside stars. Fusion of hydrogen into helium powers the Sun.
Key facts
- E = mc² (c = 3.0 × 10⁸ m/s); 1 u of mass ≡ 931.5 MeV; 1 MeV = 1.6 × 10⁻¹³ J.
- Fusing light nuclei releases more energy per kilogram of fuel than fission does.
Worked examples
Example 1
In a fusion reaction the mass decreases by 0.0189 u. How much energy is released, in MeV and in J?
Answer: 17.6 MeV; 2.8 × 10⁻¹² J
Example 2
In the reaction four ¹H → ⁴He (overall, in the Sun), the mass lost is 0.02866 u. How much energy is released, in MeV, to 3 significant figures? (1 u = 931.5 MeV)
Answer: 26.7 MeV
Example 3
In the reaction ²H + ³H → ⁴He + ¹n (deuterium–tritium fusion), the mass lost is 0.01888 u. How much energy is released, in MeV, to 3 significant figures? (1 u = 931.5 MeV)
Answer: 17.6 MeV
Example 4
In the reaction ²H + ²H → ³He + ¹n, the mass lost is 0.0035 u. How much energy is released, in MeV, to 3 significant figures? (1 u = 931.5 MeV)
Answer: 3.26 MeV