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The binding energy per nucleon for deuteron ²₁H nucleus is 1.1 MeV and that for ⁴₂He nucleus is 7 MeV. If two deuteron nuclei fuse to form ⁴₂He nucleus, how many energy will produced?

Asked in RS Academy GUJCET booklet · Energy released in fission and fusion

• (1) 11.8 MeV
• (2) 23.6 MeV
• (3) 26.9 MeV
• (4) 32.4 MeV

Step-by-step solution

Why the other options are wrong

• (1) 11.8=2×(7-1.1) — the difference of the two binding energies per nucleon multiplied by the number of deuterons instead of by the four nucleons that actually change their binding.
• (3) 26.9=28-1.1 — one deuteron's binding energy per nucleon subtracted once, instead of the whole binding energy of both deuterons, 2×2×1.1=4.4 MeV.
• (4) 32.4=28+4.4 — the two total binding energies added instead of subtracted. Energy comes out only because the helium nucleus is more tightly bound than the deuterons, so it is the difference that is released.

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