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Question:

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:

23.6MeV

28.0MeV

30.2MeV

2.2MeV

Solution:

¹H² + ¹H² → ²He⁴ + ΔE
The binding energy per nucleon of a deuteron = 1.1 MeV
∴Total binding energy = 2 × 1.1 = 2.2 MeV
The binding energy per nucleon of a helium nuclei = 7 MeV
∴Total binding energy = 4 × 7 = 28 MeV
∴Hence, energy released ΔE = (28 - 2.2) = 25.8 MeV