A neutral atom X has A = 16 and Z = 8. Its atomic mass is M(atom) = 16.0324 u. Take mₚ = 1.0073 u, mₙ = 1.0087 u, mₑ = 0.00055 u and 1 u c² = 930 MeV. If the binding energy of its nucleus is N MeV, find N.

Question

G1 Physics · Accepted Answer

Because the atom is neutral, the number of electrons is Z = 8. Total electron mass: 8mₑ = 8(0.00055) = 0.0044 u. Therefore the nuclear mass is M(nucleus) = M(atom) − 8mₑ = 16.0324 − 0.0044 = 16.0280 u. Number of neutrons: Nₙ = A−Z = 16−8 = 8. Mass of separated nucleons: M(free) = 8mₚ + 8mₙ = 8(1.0073) + 8(1.0087) = 8.0584 + 8.0696 = 16.1280 u. Mass defect: Δm = M(free) − M(nucleus) = 16.1280 − 16.0280 = 0.1000 u. Binding energy: BE = Δm c² = 0.1000×930 = 93 MeV. Hence N = 93.