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Difficulty: MediumNuclear Fission and Nuclear Fusion
In a nuclear fusion reaction, a deuterium nucleus (12H{^{2}_{1}\text{H}}) fuses with a tritium nucleus (13H{^{3}_{1}\text{H}}) according to the equation:
12H+13H→24He+01n+Q{^{2}_{1}\text{H}} + {^{3}_{1}\text{H}} \rightarrow {^{4}_{2}\text{He}} + {^{1}_{0}\text{n}} + Q

Given the atomic masses:
- Mass of 12H=2.0141 u{^{2}_{1}\text{H}} = 2.0141\text{ u}
- Mass of 13H=3.0160 u{^{3}_{1}\text{H}} = 3.0160\text{ u}
- Mass of 24He=4.0026 u{^{4}_{2}\text{He}} = 4.0026\text{ u}
- Mass of 01n=1.0087 u{^{1}_{0}\text{n}} = 1.0087\text{ u}
- 1 u=931.5 MeV1\text{ u} = 931.5\text{ MeV}

What is the total energy QQ released in this reaction?

  1. 17.51 MeV17.51\text{ MeV}Answer
  2. B
    957.12 MeV957.12\text{ MeV}
  3. C
    1.75 MeV1.75\text{ MeV}
  4. D
    4686.38 MeV4686.38\text{ MeV}

Answer

The total energy released in the reaction is 17.51 MeV17.51\text{ MeV}.
The correct answer of 17.51 MeV17.51\text{ MeV} is obtained by subtracting the combined mass of the helium-4 nucleus and neutron (5.0113 u5.0113\text{ u}) from the combined mass of the deuterium and tritium nuclei (5.0301 u5.0301\text{ u}) to yield a mass defect of 0.0188 u0.0188\text{ u}, which equates to 17.51 MeV17.51\text{ MeV} when multiplied by 931.5 MeV/u931.5\text{ MeV/u}.

Step-by-Step Solution

1
Calculate the total mass of the reactants before the fusion reaction.
Mass of reactants=2.0141 u+3.0160 u=5.0301 u\text{Mass of reactants} = 2.0141\text{ u} + 3.0160\text{ u} = 5.0301\text{ u}
To find the mass defect, we must first sum the masses of the initial nuclei.
2
Calculate the total mass of the reaction products.
Mass of products=4.0026 u+1.0087 u=5.0113 u\text{Mass of products} = 4.0026\text{ u} + 1.0087\text{ u} = 5.0113\text{ u}
The products include both the helium-4 nucleus and the emitted neutron.
3
Determine the mass defect (Δm\Delta m).
Δm=5.0301 u−5.0113 u=0.0188 u\Delta m = 5.0301\text{ u} - 5.0113\text{ u} = 0.0188\text{ u}
The mass defect represents the mass converted into energy during fusion.
4
Convert the mass defect into released energy QQ in MeV\text{MeV}.
Q=0.0188 u×931.5 MeV/u=17.5122 MeV≈17.51 MeVQ = 0.0188\text{ u} \times 931.5\text{ MeV/u} = 17.5122\text{ MeV} \approx 17.51\text{ MeV}
Using Einstein's mass-energy equivalence with 1 u=931.5 MeV1\text{ u} = 931.5\text{ MeV}.

Key Concept

Mass defect and energy release in nuclear fusion reactions
Estimated Time:1m 30s
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Topics

Nuclear Fission and Nuclear Fusion

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