Determine the binding energy of an O-16 nucleus. The O-16 nucleus has a mass of 15.9905 amu. A proton has a mass of 1.00728 amu, a neutron has a mass of 1.008665 amu, and 1 amu is equivalent to 931 MeV of energy.

Question

BlackTom AI · Accepted Answer

Mass defect equals the difference between the total mass of separated nucleons and the actual nuclear mass; converting that mass defect to energy gives the binding energy.

1) Relevant concepts
- Mass defect Δm = (Z mp + N mn) − M_nucleus.
- Binding energy BE = Δm × (931 MeV/amu).
- For O-16: Z = 8 protons, N = 8 neutrons. Use given proton and neutron masses and the nuclear mass in amu.

2) Step-by-step reasoning
- Compute total mass of 8 protons and 8 neutrons.
  mp = 1.00728 amu, mn = 1.008665 amu.
  One proton + one neutron = 1.00728 + 1.008665 = 2.015945 amu.
  For 8 pairs (16 nucleons): total nucleon mass = 8 × 2.015945 = 16.12756 amu.
- Subtract the actual nucleus mass to find the mass defect:
  M_nucleus (O-16) = 15.9905 amu.
  Δm = 16.12756 − 15.9905 = 0.13706 amu.

3) Calculations (intermediate steps shown)
- Convert mass defect to energy:
  BE = Δm × 931 MeV/amu = 0.13706 × 931 MeV.
  Multiply: 0.13706 × 931 = 127.60286 MeV.
- Round to a reasonable number of significant figures: ≈ 127.6 MeV ≈ 128 MeV.

4) Why this is correct
The binding energy is precisely the energy equivalent of the mass lost when nucleons bind; the computed mass defect (0.13706 amu) times 931 MeV/amu gives the total nuclear binding energy. The result (≈127.6 MeV) matches the listed choice 128 MeV.

5) Why the other options are incorrect
- 8.84 MeV and 38.2 MeV are far too small for the total BE of a 16-nucleon nucleus.
- 138 MeV is larger than the computed 127.6 MeV—outside the calculation result.
- 78.1 MeV is also much smaller than the correct 127.6 MeV.
(Note: the binding energy per nucleon here is ≈127.6/16 ≈ 7.975 MeV, which is not 8.84 MeV.)

6) Conclusion
The calculated binding energy for O-16 is ≈127.6 MeV, which confirms the correct answer: 128 MeV.

Determine the binding energy of an O-16 nucleus. The O-16 nucleus has a mass of 15.9905 amu. A proton has a mass of 1.00728 amu, a neutron has a mass of 1.008665 amu, and 1 amu is equivalent to 931 MeV of energy.单项选择题

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