Determine the binding energy per nucleon of ^ 197 _ 79 Au , given...

Mass of a hydrogen atom, $m_H = 1.007825 \text{ u}$

Mass of a neutron, $m_n = 1.008665 \text{ u}$

Number of protons in ^{197}_{79}\text{Au}$,$Z = 79$<br><br>Number of neutrons,$N = A - Z = 197 - 79 = 118$<br><br>Mass defect,$\Delta m = Z m_H + N m_n - M$<br><br>$\Delta m = 79 \times 1.007825 + 118 \times 1.008665 - 196.96$<br><br>$\Delta m = 79.618175 + 119.02247 - 196.96$<br><br>$\Delta m = 198.640645 - 196.96 = 1.680645 \text{ u}$<br><br>Total binding energy,$E_b = \Delta m \times 931.5 \text{ MeV}$<br><br>$E_b = 1.680645 \times 931.5 \approx 1565.52 \text{ MeV}$<br><br>Binding energy per nucleon,$E_{bn} = \dfrac{E_b}{A}$<br><br>$E_{bn} = \dfrac{1565.52}{197} \approx 7.94 \text{ MeV}