In a radioactive decay chain reaction, nucleus decays into nucleus. The ratio of the number of to number of particles emitted in this process is ____. [2022]

Question

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 ____. [2022]

Smart Achievers · Accepted Answer

(2)

${}_{90}^{230}{Th} ⟶ {}_{84}^{214}{Po} + n {}_{2}^{4}{He} + m {}_{- 1}^{0}e$

$\Rightarrow 230 = 214 + 4 n$ and $90 = 84 + 2 n - m$

$\Rightarrow 16 = 4 n$ and $6 = 2 n - m$

$\Rightarrow n = 4$ $\Rightarrow 6 = 8 - m$ $(∵ n = 4)$

$\Rightarrow m = 2$

So, $\frac{n}{m} = \frac{4}{2} = 2$

Solution

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 ____. [2022]

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Solution

Q. In a radioactive decay chain reaction, Th90230 nucleus decays into Po84214 nucleus. The ratio of the number of α to number of β- particles emitted in this process is ____. [2022]

Ans. (2) Th90230⟶Po84214+n He24+m e-10 ⇒230=214+4n and 90=84+2n-m ⇒16=4n and 6=2n-m ⇒n=4 ⇒6=8-m (∵n=4) ⇒m=2 So, nm=42=2

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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 ____. [2022]