A hypothetical nucleus has 32 nucleons. The total mass of its separated protons and neutrons exceeds the nuclear mass by 0.262 u. Use 1 u c² = 931.5 MeV and 1 MeV = 1.602 × 10⁻¹³ J. (a) Calculate total binding energy in MeV and joules. (b) Find binding energy per nucleon. (c) Explain whether assembling this nucleus releases energy and whether these data alone determine its radioactive half-life.

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Accepted Answer

Total 244.1 MeV = 3.91e-11 J; per nucleon 7.627 MeV; assembly releases energy, but half-life cannot be inferred. The mass defect is positive because the bound system has less rest mass than the separated nucleons. Its binding energy is Δmc² = 0.262 × 931.5 = 244.1 MeV, using the supplied mass–energy conversion. Convert this energy to joules: E = 244.1 × 1.602 × 10⁻¹³ = 3.91e-11 J. The conversion factor applies to MeV, so no additional factor of one million is required. Divide by the nucleon count to compare binding on a per-particle basis: E/A = 244.1/32 = 7.627 MeV per nucleon. Dividing by proton number alone would answer a different question. Assembly into this bound state releases the binding energy; separating it completely requires that energy to be supplied. Binding energy per nucleon is useful in energetic comparisons, but it alone does not determine which decay channels are allowed, their probabilities or a radioactive half-life.

Mass defect and nuclear binding 7

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