Question

The nucleus of which of the following atoms whose atomic mass numbers '$A$' are given in the options would have the highest binding energy per nucleon?

• (A) 200
• (B) 100
• (C) 50
• (D) 20

Answer 1

The Correct Option is B

Explanation:
The binding energy of a particle can be defined as the minimum energy required to remove nucleons (Proton or neutron) to an infinite distance from the nucleus. It can be expressed as:$\mathrm{\Delta }\mathrm{E}=({\mathrm{Zm}}_{\mathrm{p}}+(\mathrm{A}-\mathrm{Z}){\mathrm{m}}_{\mathrm{n}}-\mathrm{M}){\mathrm{c}}^2\times 931.5\mathrm{MeV}$This is derived by using Einstein's mass-energy relation and we can consider binding energy per nucleons as an average energy per nucleon needed to separate a nucleus into its individual nucleons.

According to the graph of binding energy per nucleons vs the atomic mass number of atoms, we can see that,Iron (Fe) is most stable element since binding energy needed to remove 1 nucleon is highest for iron and as we increase atomic mass the binding energy needed to remove 1 nucleon decreases because of coloumbic repulsion between protons inside nucleus which makes it less stable. So among the give option ${}^{100}\mathrm{Mo}$ is most stable. i.e., among all option atom with an atomic mass number of 100 will have the highest binding energy per nucleon.Hence, the correct option is (B).