A nucleus has mass represented by m (A,Z). If mp and mn denote the mass of proton and neutron respectively and BE the binding energy (in MeV) then.
B.
In the case of the formation of the nucleus, the evolution of energy equals the binding energy of the nucleus takes place due to the disappearance of a fraction of total mass. If the quantity of mass disappearing is Δm, then the binding energy is
BE = Δmc2
From the above points, it is clear that the mass of the nucleus must be less than the sum of the masses of the constituent neutrons and protons. Thus,
Δm = Zmp - Nmn - m(A,Z)
Where m (A, Z) is the mass of the atom of mass number A atomic number Z. Hence, the binding energy of a nucleus is
BE = [Zmp + Nmn - m(A,Z)]c2
BE = [Zmp + (A-Z) mn - m(A,Z)] c2