# Mass Defect

Experimentally, it is found that the mass of a nucleus is smaller than the sum of the masses of the constituent nucleons in free state. This mass difference is known as mass defect.

Let Z be atomic number, A be mass number of an element. Let mp, mn and M be the masses of proton, neutron and nucleus respectively.
Mass defect (∆m) = Sum of masses of protons and neutrons – mass of nucleus

Thus, ∆m = [Zmp + (A – Z)mn] – M

## Packing Fraction

The mass defect per nucleon is called packing fraction. It is the ratio of mass defect and the mass number.

Packing fraction (f) = ∆m/A

Packing fraction is a measure of the comparative stability of the atom. It is also defined as $f=\frac{\text{Isotopic mass – Mass number}}{\text{Mass number}}×104$

If packing fraction is negative, then the isotopic mass is less than the mass number. In such cases, a part of mass gets converted into energy during the formation of the nucleus in accordance with Einstein’s mass-energy relation, E=mc². These nuclei are more stable. If packing fraction is positive, then it means that the nucleus is not stable. But this is not applicable to the elements of low atomic mass.

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