Given: mass of a deuteron (^{2}H) = 2.014102 u, mass of a proton = 1.007276 u, mass of a neutron = 1.008665 u. Compute the binding energy per nucleon of the deuteron nucleus. (1 u = 931.5 MeV/).
Answer
≈0.86 MeV
The correct answer is ≈0.86 MeV — Divide the total binding energy by the number of nucleons (2) to get binding energy per nucleon: 1.713 MeV ÷ 2 = 0.8565 MeV ≈ 0.86 MeV.
Step-by-step solution
- Calculate the total mass of a free proton and a free neutron: 1.007276 u + 1.008665 u = 2.015941 u.
- Find the mass defect by subtracting the actual deuteron mass from the sum of separate nucleon masses: Δm = 2.015941 u – 2.014102 u = 0.001839 u.
- Convert the mass defect to energy using 1 u = 931.5 MeV/: E = 0.001839 × 931.5 MeV = 1.713 MeV (total binding energy).
- Divide the total binding energy by the number of nucleons (2) to get binding energy per nucleon: 1.713 MeV ÷ 2 = 0.8565 MeV ≈ 0.86 MeV.
Common mistake: Using atomic masses that include electron mass, leading to a slightly larger defect.
Concept tested: Binding energy per nucleon
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