Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below :
₁² X+ ₁² X= ₂⁴ Y
The binding energies per nucleon for 2/1 X and ₂⁴ Y are 1.1 MeV and 7.6 MeV respectively. The energy released in this process is _______________ MeV.

Solution

Physics sir · 4 steps

Turn each per-nucleon value into a total binding energy first, then subtract before from after.

1. Total binding energy. Binding energy per nucleon times the number of nucleons gives the total binding energy of a nucleus. Energy released is the total binding energy after minus the total before.
2. Before fusion. Each ²₁X has 2 nucleons, so its total is 2 × 1.1 = 2.2 MeV. There are two such nuclei, so the total before is 2 × 2.2 = 4.4 MeV.
3. After fusion. ⁴₂Y has 4 nucleons, so its total is 4 × 7.6 = 30.4 MeV.

   Q = 30.4 MeV - 4.4 MeV = 26 MeV

4. So. The product is more tightly bound, and the extra binding, 26 MeV, is released.

The common slip: 28.2. Counting the binding energy of only one ²₁X nucleus instead of both gives 30.4 - 2.2 = 28.2, not 26.

The idea to keep. Never subtract per-nucleon values directly. Multiply each by its nucleon count, add up every nucleus on each side, and the gain in total binding energy is the energy released.

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