In a radioactive decay chain, ${}_{90}^{232}\mathrm{Th}$ nucleus decays to ${}_{82}^{212}\mathrm{~Pb}$ 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) $N_{\alpha}=5$; (C) $N_{\beta}=2$

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Modern Physics

In a radioactive decay chain,

_{90}^{232} Th

nucleus decays to

_{82}^{212} Pb

nucleus. Let

N_{α}

and

N_{β}

be the number of

α

and

β^{-}

particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

Answer: (A), (C)

In the decay

_{90}^{232} Th \to_{82}^{212} Pb

, the mass number decreases by

232 - 212 = 20

. Each

α

particle has mass number 4, so

N_{α} = \frac{20}{4} = 5

(A is correct, B is incorrect). Each

α

decay reduces the atomic number by 2, so 5

α

decays reduce it by 10, from 90 to 80. To reach atomic number 82, we need 2

β^{-}

decays (each increases atomic number by 1), so

N_{β} = 2

(C is correct, D is incorrect).

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · One or more correct options