Question

Calculate the mass defect (in g/mol) and the binding energy (in V/nucleon) for the following nuclides: ${}^{54}Zn$ (atomic mass $=63.92915$ amu)

• A. Mass defect $=0.45$ g/mol, Binding energy $=6.56$ MeV/neucleon
  
• B. Mass defect $=0.6$ g/mol, Binding energy $=12.36$ MeV/neucleon
  
• C. Mass defect $=0.6$ g/mol, Binding energy $=8.76$ MeV/neucleon
  
• D. none of the above

Answer 1

Answer: (C)

Mass defect $=0.6$ g/mol, Binding energy $=8.76$ MeV/neucleon

${}_{30}^{64}Zn$ has 30 electrons, 30 protons and 34 neutrons. The expected mass of Zn is
$30\left(0.000543\right)+30\left(1.00758\right)+34\left(1.00893\right)=64.54731$ amu.
The actual mass is 63.92915 amu
The mass defect $\Delta m=64.54731-63.92915=0.61816$ amu $\simeq 0.6$ g/mol
The binding energy $E=\Delta m\times 931.5$ MeV $=0.61816\times 931.5=575.816$ MeV.
This binding energy is for 64 nucleons. For 1 nucleon, the binding energy will be $\frac{575.816}{64}=8.99$