Which of the following is least likely to be stable? — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Nuclear Stability Rules For light nuclei ($Z \le 20$), stability requires $n/p \approx 1.0$. Magic numbers (2, 8, 20, 28, 50, 82, 126) confer extra stability. Step 2 - Evaluating Each Isotope - $\ce{^{40}_{20}Ca}$: $Z=20, N=20$, $n/p=1.0$, doubly magic → extremely stable - $\ce{^{30}_{13}Al}$: $Z=13, N=17$, $n/p=17/13\approx 1.31$ — far too high for $Z=13$; highly neutron-rich, unstable (half-life 3.6 s) - $\ce{^{119}_{50}Sn}$: $Z=50$ is magic number → 10 stable Sn isotopes, very stable - $\ce{^{55}_{25}Mn}$: $n/p=30/25=1.20$, appropriate for this mass range → stable monoisotope Step 3 - Conclusion $\ce{^{30}Al}$ has the most unfavourable $n/p$ ratio for its mass and is the least likely to be stable. $$\boxed{B}$$