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Difficulty: MediumNuclear Fission and Nuclear Fusion

In a nuclear fission reaction, a Uranium-235 nucleus absorbs a neutron and splits into Tellurium-137 and Zirconium-97, releasing energy. If the total mass of the reactants is 236.053 u236.053\text{ u} and the total mass of the products is 235.853 u235.853\text{ u}, what is the energy released in MeV\text{MeV}? (Take 1 u=931 MeV1\text{ u} = 931\text{ MeV})

  1. A
    18.62 MeV18.62\text{ MeV}
  2. 186.20 MeV186.20\text{ MeV}Answer
  3. C
    0.000215 MeV0.000215\text{ MeV}
  4. D
    186.20 J186.20\text{ J}

Answer

The total energy released in the fission reaction is 186.20 MeV186.20\text{ MeV}.
The energy released during nuclear fission is calculated from the mass defect (Δm\Delta m). Subtracting product mass from reactant mass gives Δm=236.053 u−235.853 u=0.200 u\Delta m = 236.053\text{ u} - 235.853\text{ u} = 0.200\text{ u}. Multiplying this mass defect by the standard conversion factor (1 u=931 MeV1\text{ u} = 931\text{ MeV}) yields 0.200×931=186.20 MeV0.200 \times 931 = 186.20\text{ MeV}.

Step-by-Step Solution

1
Calculate the mass defect (Δm\Delta m)
Δm=236.053 u−235.853 u=0.200 u\Delta m = 236.053\text{ u} - 235.853\text{ u} = 0.200\text{ u}
Mass defect is the difference between the total mass of the reactants and the total mass of the fission products.
2
Convert the mass defect into energy in MeV\text{MeV}
E=0.200 u×931 MeV/u=186.20 MeVE = 0.200\text{ u} \times 931\text{ MeV/u} = 186.20\text{ MeV}
According to mass-energy equivalence, each atomic mass unit (u\text{u}) liberates 931 MeV931\text{ MeV} of energy.

Key Concept

Mass Defect and Energy Release in Nuclear Fission
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Topics

Nuclear Fission and Nuclear Fusion

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