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The binding energy per nucleon of ¹⁶₈O is 7.97 MeV and that of ¹⁷₈O is 7.75 MeV. The energy required to remove one neutron from ¹⁷₈O is ______ MeV.

Asked in GUJCET 2014 · Mass defect and binding energy

• (1) 3.52
• (2) 3.62
• (3) 4.23
• (4) 7.86

Step-by-step solution

Why the other options are wrong

• (1) 3.52=16×(7.97-7.75) — the difference of the two binding energies per nucleon, multiplied by 16. The two total binding energies have to be formed first, 17×7.75 and 16×7.97, and only then subtracted.
• (2) No single slip produces 3.62. Sanity check: 17×7.75=131.75 MeV and 16×7.97=127.52 MeV, so the difference is fixed at 4.23 MeV.
• (4) 7.86 is the average of the two binding energies per nucleon, (7.97+7.75)/2. An average of two binding energies is not an energy difference and cannot answer this question.

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