Question

In a radioactive decay chain, ${}_{90}^{232}Th$ nucleus decays to ${}_{82}^{212}Pb$ nucleus. Let $N_{\alpha }$ and $N_{\beta }$ be the number of $\alpha$ and ${\beta }^{-}$ particles respectively, emitted in this decay process. Which of the following statements is (are) true?

• A. $N_{\alpha }=5$
• B. $N_{\alpha }=6$
• C. $N_{\beta }=2$
• D. $N_{\beta }=4$

Answer 1

Answer: (A), (C)

The correct options are
A $N_{\alpha }=5$
C $N_{\beta }=2$

${}_{90}^{232}$Th has converted into ${}_{82}^{212}Pb$

Change in mass number (A) = $20$

$\therefore$ no of $\alpha$ particle $=\frac{20}{4}=5$

Due to $5\alpha$ particle, z will change by $10$ unit.

Since given change is $8$, therefore no. of the beta particle is $10-8=2$