The largest stable nucleus is — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Stability Limit of Nuclei The two competing forces inside a nucleus: 1. **Strong nuclear force** (attractive, short-range, nearest-neighbor only) 2. **Electrostatic (Coulomb) force** (repulsive, long-range, $\propto Z(Z-1)$) For $Z > 83$, Coulomb repulsion exceeds strong nuclear attraction → all elements with $Z > 83$ are radioactive. Step 2 - Bismuth-209 as the Heaviest Stable Nucleus $\ce{^{209}_{83}Bi}$: $Z = 83$, $N = 126$, $A = 209$ Bismuth-209 is classically defined as the heaviest stable nucleus. *(Note: Ultra-sensitive experiments in 2003 detected extremely slow $\alpha$-decay: $t_{1/2} \approx 1.9 \times 10^{19}$ years — about $10^9 \times$ the age of the universe. For JEE/standard curricula, it is treated as stable.)* Step 3 - Evaluate Options - **(A) $\ce{U_{238}}$** — $Z = 92 > 83$; radioactive ($\alpha$ emitter, $t_{1/2} = 4.47 \times 10^9$ yr). Incorrect. - **(B) $\ce{Bi_{209}}$** — $Z = 83$; the heaviest stable nucleus. Correct. - **(C) $\ce{U_{235}}$** — $Z = 92 > 83$; radioactive (fissile). Incorrect. - **(D) $\ce{Pb_{206}}$** — $Z = 82$, $A = 206$; stable, but smaller than $\ce{Bi_{209}}$. Incorrect. $$\boxed{\text{Answer: B} \quad \ce{^{209}_{83}Bi}}$$