Mass Defect - Definition and mathematically

Mass Defect

The mass of a stable nucleus is always found to be less than the sum of the masses of the constituent nucleons.

Definition

The difference between the sum of the masses of the nucleons constituting a nucleus and the rest mass of the nucleus is known as mass defect.

Derivation

Consider a nucleus of an atom ^A_ZX. In this case, the nucleus of the atom contains Z protons and (A-Z) neutrons.

Let mass of a proton = m_p

Mass of a neutron = m_n

Mass of the nucleus of atom ^A_ZX = M

Then mass defect is given by
Δm = [Zm_p + (A-Z)m_n] - M