Which element has a relatively more stable nucleus? — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Nuclear Stability and Binding Energy per Nucleon The stability of a nucleus is determined by its binding energy per nucleon ($\overline{B} = E_b/A$). Higher $\overline{B}$ means nucleons are more tightly bound and the nucleus is more stable. Step 2 - The Binding Energy Curve When $\overline{B}$ is plotted vs. mass number $A$: - **Light nuclei** ($A < 30$): low $\overline{B}$; tendency to undergo fusion. - **Medium nuclei** ($50 \le A \le 60$): peak stability; $\overline{B}$ is maximum. - **Heavy nuclei** ($A > 90$): $\overline{B}$ decreases; electrostatic repulsion makes them unstable. Step 3 - Approximate Binding Energies | Element | $A$ | $\overline{B}$ (MeV/nucleon) | |---------|-----|-------------------------------| | $\ce{H}$ | 1 | ~0 (single proton, no binding) | | $\ce{Fe}$ | 56 | ~8.8 (**maximum**) | | $\ce{Ra}$ | 226 | ~7.7 | | $\ce{U}$ | 238 | ~7.6 | Step 4 - Evaluate Options - **(A) U** — Incorrect. Heavy radioactive element; $\overline{B} \approx 7.6$ MeV/nucleon; decays spontaneously. - **(B) H** — Incorrect. Lightest element; essentially no inter-nucleon binding. - **(C) Fe** — Correct. $\ce{^{56}Fe}$ sits at the peak of the binding energy curve ($\approx 8.8$ MeV/nucleon); most stable nucleus. - **(D) Ra** — Incorrect. Highly radioactive heavy element; lower binding energy than Fe. $$\boxed{\text{Answer: C (Fe)}}$$