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Difficulty: MediumNuclear Fission and Nuclear Fusion
A nuclear fusion reaction between a helium-3 nucleus (23He{^{3}_{2}\text{He}}) and a deuterium nucleus (12H{^{2}_{1}\text{H}}) produces a helium-4 nucleus (24He{^{4}_{2}\text{He}}) and a proton (11p{^{1}_{1}\text{p}}) according to the equation:
23He+12H→24He+11p{^{3}_{2}\text{He}} + {^{2}_{1}\text{H}} \rightarrow {^{4}_{2}\text{He}} + {^{1}_{1}\text{p}}

Given the atomic masses:
- Mass of 23He=3.0160 u{^{3}_{2}\text{He}} = 3.0160\text{ u}
- Mass of 12H=2.0141 u{^{2}_{1}\text{H}} = 2.0141\text{ u}
- Mass of 24He=4.0026 u{^{4}_{2}\text{He}} = 4.0026\text{ u}
- Mass of 11p=1.0078 u{^{1}_{1}\text{p}} = 1.0078\text{ u}
- 1 u=931 MeV1\text{ u} = 931\text{ MeV}

What is the total energy released in this reaction?

  1. 18.34 MeV18.34\text{ MeV}Answer
  2. B
    0.0197 MeV0.0197\text{ MeV}
  3. C
    9.17 MeV9.17\text{ MeV}
  4. D
    36.68 MeV36.68\text{ MeV}

Answer

The total energy released in the nuclear fusion reaction is 18.34 MeV18.34\text{ MeV}.
The total energy released in a nuclear fusion reaction is proportional to the mass defect between reactants and products. The sum of reactant masses is 5.0301 u5.0301\text{ u} and product masses is 5.0104 u5.0104\text{ u}, giving a mass defect Δm=0.0197 u\Delta m = 0.0197\text{ u}. Multiplying this mass defect by the conversion factor 931 MeV/u931\text{ MeV/u} yields 18.34 MeV18.34\text{ MeV}.

Step-by-Step Solution

1
Calculate the total mass of the reactants before fusion.
Total reactant mass = 3.0160 u+2.0141 u=5.0301 u3.0160\text{ u} + 2.0141\text{ u} = 5.0301\text{ u}.
The initial mass is the sum of the helium-3 nucleus mass and deuterium nucleus mass.
2
Calculate the total mass of the reaction products.
Total product mass = 4.0026 u+1.0078 u=5.0104 u4.0026\text{ u} + 1.0078\text{ u} = 5.0104\text{ u}.
The final mass is the sum of the helium-4 nucleus mass and proton mass.
3
Determine the mass defect (loss of mass during fusion).
\Delta m = 5.0301\text{ u} - 5.0104\text{ u} = 0.0197\text{ u}.
The mass defect represents the missing mass that is converted into energy.
4
Convert the mass defect into energy released using Einstein's energy equivalent constant.
Energy = 0.0197\text{ u} \times 931\text{ MeV/u} = 18.3407\text{ MeV} \approx 18.34\text{ MeV}.
Multiplying the mass defect in atomic mass units by 931 MeV/u931\text{ MeV/u} yields the energy released.

Key Concept

Mass defect and energy release in nuclear fusion
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Topics

Nuclear Fission and Nuclear Fusion

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