Answer to Question #202401 in Atomic and Nuclear Physics for Pranali Patil

Question

The most common isotope of oxygen is oxygen-16 with a measured mass of 15.994915u.  

1. Determine the mass defect;
2. Determine the binding energy;
3. Determine the binding energy per nucleon.

Answer 1

The mass defect is $\Delta m = 8m_p + 8m_n + 8m_e - m_{\text{isotope}}$ , because the atom consists of 8 protons, 8 neutrons and 8 electrons.

$\Delta m = 8(m_p + m_n + m_e) - m_{\text{isotope}}, \\\Delta m = 8(1.00728 + 1.00866+0.00055) - 15.994915, \\\Delta m = 0.137\,\mathrm{u} = 0.137\cdot 1.6605\cdot10^{-27} = 0.227\cdot10^{-27}\,\text{kg}.$

The binding energy is $\Delta m c^2 = 0.227\cdot10^{-27}\cdot(3\cdot10^8)^2 = 2\cdot10^{-11}\,\mathrm{J}.$

The binding energy per nucleon is $\dfrac{\Delta mc^2}{16} = 0.128\cdot10^{-11}\,\mathrm{J}.$