. Explain Packing fraction of Nuclear Stability
The difference of actual isotopic mass* and the mass number in terms of packing fraction is defined as
Carbon12 has zero packing fraction because it is taken as a reference on the atomic scale and its actual isotopic mass (12) is equal to its mass number (12).
The negative or zero value of the packing fraction means that the actual isotopic mass is less or equal to the mass number. This in turn indicates that some mass has been transformed into energy (binding energy) during formation of nucleus. Such nuclei are, therefore, more stable.
The positive packing fraction should imply the opposite, i.e., the nuclei of such isotopes should be unstable. However, this generalization is not strictly correct especially for elements of low mass numbers. For these the actual masses of protons and neutrons (of which the nuclei are composed) are slightly greater than unity.
In general, lower the packing fraction, greater is the binding energy per nucleon and hence greater is the stability. The relatively low packing fraction of He, C and O implies their exceptional stability. Packing fraction is least for Fe (negative) and highest for H (+78).