(a) Write the relation for binding energy (in MeV) of a nucleus `" "_(Z)^(A)X` of atomic number ‘Z’ and mass number ‘A’ in terms of the masses of its constituents — neutrons and protons.
(b) Draw a plot of binding energy per nucleon versus mass number ‘A’ for `2 le A le 240`. Use this graph to explain the release of energy in the process of nuclear fusion of two light nuclei.

Explanation

(a) If `m_(n)` and `m_(p)` be the masses of neutron and proton respectively and m(`" "_(Z)^(A)X`) be the mass of given nucleus, all expressed in atomic mass units, then the binding energy of the nucleus is given as per relation:
BE =[`Zm_(p) + (A-Z)m_(n) - m(" "_(z)^(A)X )] xx 931.5 MeV`
(b) When we consider fusion of two very light nuclei (A < 10) fusing to forma single heavier nucleus, the binding energy per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei. Thus, the fused nuclei is more tightly bound than the initial lighter nuclei and as a result energy is released in the fusion process.