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Q.

In a radioactive decay chain reaction, $_{90}^{230} Th$ nucleus decays into $_{84}^{214} Po$ nucleus. The ratio of the number of $α$ to number of $β^{-}$ particles emitted in this process is _________.

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answer is 2.

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Detailed Solution

$T h_{90}^{230} \to P o_{84}^{214} + n α_{2}^{4} + m β_{- 1}^{0}$
By conservation of mass, we have
$230 = 214 + 4 n$
$n = \frac{16}{4} = 4$
By conservation of charge, we have
$90 = 84 + n \times 2 - m \times 1 \Rightarrow 90 = 84 + 4 \times 2 - m \times 1 \Rightarrow m = 92 - 90 = 2 \Rightarrow \frac{n}{m} = \frac{4}{2} = 2$

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