In the atomic nucleus, the protons and the neutrons are bound together by a strong, short range and charge independent, attractive force called the nuclear force. It is necessary to supply energy to break the nucleus. The minimum energy required to separate a nucleus into its free constituents, i.e., protons and neutrons, is known as the nuclear binding energy. It is the mass energy of the nucleons minus the mass energy of the nucleus.
The mass defect of a nucleus, of mass M, mass number A, proton number Z and neutron number N = A – Z, is
∆m = (Zmp + Nmn) – M
where, mp is the proton mass and mn is the neutron mass. Then, from Einstein’s massenergy relation,
nuclear binding energy = ∆mc2
= [(Zmp -(- Nmn) – M] c2 (in joule)
= [(Zmp + Nmn) – M] c2/e(in eV)
where c is the speed of light in free space and e is the elementary charge. In calculations using the above equations, mp is replaced by mH (mass of hydrogen atom). M is taken to be the atomic mass and not nuclear mass because the electron masses cancel out and the difference in electronic binding energies can be ignored as these are 106 times smaller than the nuclear binding energy.
∴ Nuclear binding energy
≅ [(ZmH + Nmn) – Matom ] c2 (in joule)
The minimum energy required on the average to separate a nucleon from a given nucleus is called the binding energy per nucleon for that nucleus. It is the nuclear binding energy for a nucleus divided by its mass number. ∴ Binding energy per nucleon = Δmc2/A
= [(Zmp+ Nmn) – M] c2/A
≅ [(ZmH + Nmn) – Matom] c2/A
