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The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

1. 30.2 MeV
2. 23.6 MeV
3. 2.2 MeV
4. 28.0 MeV

Correct answer: 23.6 MeV

Solution

The energy released in fusion is calculated by finding the difference in total binding energy before and after the reaction. For deuterium, the total binding energy is 2 × 1.1 MeV = 2.2 MeV. For helium, the total binding energy is 4 × 7.0 MeV = 28.0 MeV. The energy released is 28.0 MeV - 2.2 MeV = 23.6 MeV.

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