A neutral atom has A = 56, Z = 26 and atomic mass M(atom) = 55.9371 u. Take mₚ = 1.0073 u, mₙ = 1.0087 u, mₑ = 0.00055 u and 1 u c² = 930 MeV. Its total nuclear binding energy is approximately:
Options

Question

A neutral atom has A = 56, Z = 26 and atomic mass M(atom) = 55.9371 u. Take mₚ = 1.0073 u, mₙ = 1.0087 u, mₑ = 0.00055 u and 1 u c² = 930 MeV. Its total nuclear binding energy is approximately:

G1 Physics · Accepted Answer

A neutral atom with Z = 26 contains 26 electrons. Total electron mass: 26mₑ = 26(0.00055) = 0.0143 u. Therefore, M(nucleus) = M(atom) − 26mₑ = 55.9371 − 0.0143 = 55.9228 u. Number of neutrons: Nₙ = A−Z = 56−26 = 30. Mass of separated nucleons: M(free) = 26mₚ + 30mₙ = 26(1.0073) + 30(1.0087) = 26.1898 + 30.2610 = 56.4508 u. Mass defect: Δm = 56.4508 − 55.9228 = 0.5280 u. Binding energy: BE = Δm c² = 0.5280×930 = 491.04 MeV ≈ 491 MeV. Correct option: B.