Question

Among the following, which has the longest half life?

• A. ${}_{90}^{232}Th$
• B. ${}_{93}^{237}Np$
• C. ${}_{92}^{238}U$
• D. ${}_{92}^{235}U$

Answer 1

The correct option is A ${}_{90}^{232}Th$

If Number of neutrons $N=$ odd and Number of protons$P=$odd, Both are Unstable Nuclei.

and if Number of neutrons $N=$ even and Number of Protons $P=$even, Both are stable Nuclei.

Here ${}_{90}^{232}Th$ and ${}_{92}^{238}U$ is stable.

Now $\frac{N}{P}$ ratio of ${}_{90}^{232}Th\Rightarrow$$\frac{N}{P}=1.57$(Hence stable more closes to 1)

$\frac{N}{P}$ ratio of ${}_{92}^{238}U\Rightarrow$$\frac{N}{P}=\frac{146}{92}=1.59$

Now, the most stable element will have longest half-life.

Thus, option A is correct.