A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is _________ MeV.

Solution

Physics sir · 3 steps

Same 242 nucleons before and after, so the gain is just 242 times the jump in binding energy per nucleon.

1. Before fission. Total binding energy is nucleons times binding energy per nucleon. The parent has 242 × 7.6 = 1839.2 MeV.
2. After fission. Each fragment has 121 × 8.1 = 980.1 MeV. Two fragments together hold 2 × 980.1 = 1960.2 MeV.

   Δ E = 1960.2 - 1839.2 = 242 × (8.1 - 7.6) = 121 MeV

3. So. The total gain in binding energy is 121 MeV.

The common slip: 60.5. Counting only one fragment, 121 × 0.5, gives 60.5. Both fragments gain binding energy, so use all 242 nucleons.

The idea to keep. When nucleons are conserved in a split, the gain in binding energy is (total nucleons) times (change in binding energy per nucleon). Always count both fragments.

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