Question #202401

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.
1
Expert's answer
2021-06-03T09:16:35-0400

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

Δm=8(mp+mn+me)misotope,Δm=8(1.00728+1.00866+0.00055)15.994915,Δm=0.137u=0.1371.66051027=0.2271027kg.\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 Δmc2=0.2271027(3108)2=21011J.\Delta m c^2 = 0.227\cdot10^{-27}\cdot(3\cdot10^8)^2 = 2\cdot10^{-11}\,\mathrm{J}.

The binding energy per nucleon is Δmc216=0.1281011J.\dfrac{\Delta mc^2}{16} = 0.128\cdot10^{-11}\,\mathrm{J}.


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