Atoms and Nuclei Part 3

Concept:Higher binding energy means higher nuclear stability.In an exothermic reaction (energy released), products are more stable than reactants.In an endothermic reaction (energy absorbed), products are less stable than reactants.Explanation:First reaction: ${}_{2}^{3}\mathrm{He}+{}_{0}^{1}\mathrm{n} \rightarrow {}_{2}^{4}\mathrm{He}+20\,\mathrm{MeV}$ (Q = +20 MeV).Since energy is released, ${}_{2}^{4}\mathrm{He}$ is more stable than ${}_{2}^{3}\mathrm{He}$.Thus $\mathrm{X}_{4} > \mathrm{X}_{3}$.Second reaction: ${}_{2}^{4}\mathrm{He}+{}_{0}^{1}\mathrm{n} \rightarrow {}_{2}^{5}\mathrm{He}-0.9\,\mathrm{MeV}$ (Q = –0.9 MeV).Since energy is absorbed, ${}_{2}^{5}\mathrm{He}$ is less stable than ${}_{2}^{4}\mathrm{He}$.Thus $\mathrm{X}_{4} > \mathrm{X}_{5}$.Comparing $\mathrm{X}_{5}$ and $\mathrm{X}_{3}$:The stability increase from $\mathrm{X}_{3}$ to $\mathrm{X}_{4}$ is large (20 MeV).The stability decrease from $\mathrm{X}_{4}$ to $\mathrm{X}_{5}$ is small (0.9 MeV).Therefore $\mathrm{X}_{5}$ is still much more stable than $\mathrm{X}_{3}$.Overall order: $\mathrm{X}_{4} > \mathrm{X}_{5} > \mathrm{X}_{3}$.Answer:Option (A): $X_{4} > X_{5} > X_{3}$