Question

Which of the following is likely to be least stable?

• A. ${}_{20}^{40}Ca$
• B. ${}_{25}^{55}Mn$
• C. ${}_{50}^{119}Sn$
• D. ${}_{13}^{30}Al$

Answer 1

The correct option is D ${}_{13}^{30}Al$

$\frac{n}{P}$ratio is important in the stability of radioactive substance.

If $n$ and $p$ value is magic number.i.e

$2,8,20,28,50,82,126$

then extremely stable nuclei.

${}_{20}^{40}Ca\Rightarrow$ P=20(Magic Number)

${}_{25}^{55}Mn\Rightarrow$p=25 and n=30 (No magic Number)

${}_{50}^{119}Sn\Rightarrow$p=50 (Magic Number)

${}_{13}^{30}Al\Rightarrow$ p=13 and n=17( No magic Number)

If $\frac{N}{P}$ ratio is equal(approx) to 1 then radioactive substance is stable

Her ${}_{25}^{55}Mn\Rightarrow$$\frac{N}{P}=\frac{30}{25}=1.2$

${}_{13}^{30}Al\Rightarrow$$\frac{N}{P}=\mathrm{1.31.}$(Hence least stable)