13.3 Obtain the binding energy (in MeV) of a nitrogen nucleus \(\left({ }_{7}^{14} \mathrm{~N}\right)\), given mass of nitrogen nucleus, \(m_\left({ }_{7}^{14} \mathrm{~N}\right)\)=14.00307 u.
Hint: The binding energy can be obtained by finding the mass defect in the nitrogen nucleus. Step 1: Find the mass defect in the nitrogen nucleus.
The atomic mass of nitrogen, m = 14.00307 u
A nucleus of nitrogen contains 7 protons and 7 neutrons.
Hence, the mass defect of this nucleus,
where,
Mass of a proton, = 1.007825 u
mass of a neutron, = 1.008665 u
Mass defect,
Step 2: Find the binding energy of nitrogen nucleus.
Hence, the binding energy of the nucleus is given as:
where, c= speed of light
Hence, the binding energy of a nitrogen nucleus is 104.66334 MeV.
