Determine the binding energy per nucleon of ¹⁹⁷₇₉ Au , given that its atomic mass is 196.96 u .

Step-by-step solution

Mass of a hydrogen atom, m_H = 1.007825 u Mass of a neutron, m_n = 1.008665 u Number of protons in ¹⁹⁷₇₉ Au , Z = 79 Number of neutrons, N = A - Z = 197 - 79 = 118 Mass defect, m = Z m_H + N m_n - M m = 79 1.007825 + 118 1.008665 - 196.96 m = 79.618175 + 119.02247 - 196.96 m = 198.640645 - 196.96 = 1.680645 u Total binding energy, E_b = m 931.5 MeV E_b = 1.680645 931.5 1565.52 MeV Binding energy per nucleon, E_ bn = E_b A E_ bn = 1565.52 197 7.94 MeV