In a nuclear fission process, a high mass nuclide (A ≈ 236) with binding energy 7.6 MeV / Nucleon dissociated into middle mass nuclides (A ≈ 118), having binding energy of 8.6 MeV / Nucleon. The energy released in the process would be ______ MeV.

Solution

Physics sir · 3 steps

Energy comes out as the binding energy goes up, so compare total binding energy before and after the split.

1. Before fission. The heavy nucleus has 236 nucleons at 7.6 MeV each. Its total binding energy is 236 × 7.6 = 1793.6 MeV.
2. After fission. It splits into two nuclei of 118 nucleons each, so all 236 nucleons are still there, now at 8.6 MeV each. The total binding energy is 2 × 118 × 8.6 = 2029.6 MeV.

   Q = 236 × (8.6 - 7.6) MeV = 2029.6 - 1793.6 = 236 MeV

3. So. The nucleons end up more tightly bound by 1 MeV each, and this extra binding is released as energy. The energy released is 236 MeV.

The common slip: 118. Multiplying the 1 MeV gain by only one fragment's 118 nucleons gives 118, not 236. Both fragments gain this energy, so you need all 236 nucleons.

The idea to keep. Energy released in fission or fusion equals the final total binding energy minus the initial one. Multiply each binding energy per nucleon by the number of nucleons it applies to.

Answer from the NTA final answer key. Solution by PrepWiser.