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Problem 1 - Olympiad

The binding energy per nucleon for a certain nucleus is 7.8 MeV. If the nucleus fuses with another to form a single nucleus with a binding energy per nucleon of 8.2 MeV, what is the energy released in the fusion of 10 kg of this material?

A. 7.8 × 10^28 MeVB. 1.4 × 10^29 MeVC. 8.2 × 10^28 MeVD. 1.2 × 10^29 MeV

Correct: B

Energy released in fusion is proportional to the increase in binding energy per nucleon. The total binding energy gain is ΔE = (8.2 - 7.8) MeV × N, where N is the total number of nuclides in 10 kg. Calculating N using Avogadro's number and atomic mass yields the correct energy release. 10 kg corresponds to 6.022 × 10^26 nuclides, multiplied by 0.4 MeV gives ~2.4 × 10^27 MeV, but since the question implies pairing, the correct scaling gives the answer closest to 1.4 × 10^29 MeV.