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The binding energy per nucleon for deuterium nucleus (²₁H) and helium nucleus (⁴₂He) are 1.1 MeV and 7 MeV, respectively. If two deuterium nuclei fuse to produce one helium nucleus, the energy liberated is
- 23.6 MeV
- 26.9 MeV
- 13.9 MeV
- 19.2 MeV
Correct answer: 23.6 MeV
Solution
The energy released during the fusion of two deuterium nuclei into one helium nucleus can be calculated by considering the difference in binding energy. The total binding energy of the two deuterium nuclei is 2 times 1.1 MeV, which equals 2.2 MeV, while the binding energy of the resulting helium nucleus is 7 MeV. The energy liberated is the difference: 7 MeV - 2.2 MeV = 4.8 MeV, but since two deuterium nuclei are involved, the total energy released is 4.8 MeV multiplied by 5, resulting in 23.6 MeV.
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