JEE Advanced 2022 Paper 2, Physics Section 1 Q2: Radioactivity

JEE Advanced2022Paper 2Physics Section 1

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 _______.

Your answer

Solution

Let $n_{α}$ be the number of $α$ particles and $n_{β}$ the number of $β^{-}$ particles emitted.

Mass number balance: each $α$ removes 4 units while $β^{-}$ does not change $A$ . $230 - 214 = 4 n_{α} \Rightarrow n_{α} = 4$ .

Atomic number balance: each $α$ removes 2, each $β^{-}$ adds 1. $90 - 2 n_{α} + n_{β} = 84 \Rightarrow 90 - 8 + n_{β} = 84 \Rightarrow n_{β} = 2$ .

$∴ \frac{n _{α}}{n _{β}} = \frac{4}{2} = 2$ .

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JEE Advanced 2022 Paper 2, Physics Section 1 Q2: Radioactivity

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