Nuclear fusion · Grade 11
In Grade 11 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
- Fusion: light nuclei (e.g. hydrogen) join to make heavier ones; it needs extreme temperature and pressure.
- The Sun fuses hydrogen into helium in its core: it is not burning like a fire.
- Mass numbers and atomic numbers must balance on both sides of a nuclear equation.
- 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
What process releases energy in the Sun?
Answer: fusion of hydrogen nuclei into helium
Example 2
Why does fusion need extremely high temperatures?
Answer: Nuclei must move fast enough to overcome their electrostatic repulsion
Example 3
In this fusion, ²₁H + ³₁H → X + ¹₀n. What is the mass number (top number) of X?
Answer: 4
Example 4
In this fusion, ²₁H + ²₁H → X + ¹₀n. What is the atomic number (bottom number) of X?
Answer: 2
Example 5
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 6
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 7
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 8
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