Mass defect (Δm): It is found that the mass of a nucleus is always less than the sum of masses of it's constituent nucleons in free state. This difference in volumes is known as mass defect. Hence mass defect

        Δm = Sum of masses of nucleons - Mass of nucleus

where m_p = Mass of proton, m_n = Mass of each neutron, m_e = Mass of each electron

             M = Mass of nucleus, Z = Atomic number, A = Mass number, M¢ = Mass of atom as a whole.

Packing fraction: Mass defect per nucleon is called packing fraction

            Packing fraction (f) = Δm/A = M-A/A   where M = Mass of nucleus, A = Mass number

Binding energy (B.E.): The neutrons and protons in a stable nucleus are held together by nuclear forces and energy is needed to pull them infinitely apart (or the same energy is released during the formation of the nucleus). This energy is known as the binding power of the nucleus.

If Dm is mass defect then according to Einstein's mass energy relation

Binding energy = Δm.mc² = [{m_pZ + m_n(A - Z)} - M] .c² 

(This binding energy is expressed in joule, because Δm is measured in kg)

If Δm is measured in amu then binding energy = Δm.amu = [{m_pZ + m_n(A - Z)} - M] amu = Δm * 931 MeV

Binding energy per nucleon: The average energy required to release a nucleon from the nucleus is called binding energy per nucleon.

Binding energy per nucleon

Binding energy per nucleon ∝ Stability of nucleus

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