The atomic mass of ²⁰⁹₈₃Bi is 208.980388 u. Using the mass value 1.007825 u for each hydrogen-atom contribution, neutron mass 1.008665 u and 1 u = 931 MeV·c⁻², what is the binding energy per nucleon of ²⁰⁹₈₃Bi?
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Question

The atomic mass of ²⁰⁹₈₃Bi is 208.980388 u. Using the mass value 1.007825 u for each hydrogen-atom contribution, neutron mass 1.008665 u and 1 u = 931 MeV·c⁻², what is the binding energy per nucleon of ²⁰⁹₈₃Bi?

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G1 Physics · Accepted Answer

For ²⁰⁹₈₃Bi, Z = 83, A = 209, N = A-Z = 126. Using atomic masses, the source calculation uses Δm = 83m(H)+126mₙ-M(atom). Substitute: Δm = 83(1.007825) +126(1.008665) -208.980388. This gives Δm = 1.760877 u. Total binding energy: BE = Δm×931 MeV = 1.760877×931 ≈ 1639.38 MeV. Binding energy per nucleon: BE ÷ A = 1639.38 ÷ 209 ≈ 7.844 MeV. Therefore the closest value is 7.84 MeV. Correct option: B.