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Numerical · Q23

Q.Calculate the mass defect, the total binding energy, and the binding energy per nucleon of 816O^{16}_{8}\text{O}, given: mass of 816O^{16}_{8}\text{O} atom =15.994915 u= 15.994915\ \text{u}, mass of hydrogen atom =1.007825 u= 1.007825\ \text{u}, mass of neutron =1.008665 u= 1.008665\ \text{u}.

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For 816O^{16}_{8}\text{O}, Z=8Z=8 protons and A−Z=8A-Z=8 neutrons. The mass defect is

Δm=[8mH+8mn]−M=[8(1.007825)+8(1.008665)]−15.994915\Delta m = [8m_H + 8m_n] - M = [8(1.007825) + 8(1.008665)] - 15.994915

=[8.06260+8.06932]−15.994915=16.13192−15.994915=0.137005 u= [8.06260 + 8.06932] - 15.994915 = 16.13192 - 15.994915 = 0.137005\ \text{u}

The total binding energy is

BE=0.137005×931.5≈127.6 MeVBE = 0.137005\times931.5 \approx 127.6\ \text{MeV}

and the binding energy per nucleon is …

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