JEE Advanced 2022 Paper 2 · Q02 · Nuclear Physics
In a radioactive decay chain reaction, $^{230}_{90}\text{Th}$ nucleus decays into $^{214}_{84}\text{Po}$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^-$ particles emitted in this process is ____.
Reveal answer + step-by-step solution
Correct answer:2
Solution
Let $n_\alpha$ alpha and $n_\beta$ beta-minus particles be emitted. Mass-number balance: $230 = 214 + 4 n_\alpha$, so $n_\alpha = 4$. Charge balance: $90 = 84 + 2 n_\alpha - n_\beta = 84 + 8 - n_\beta$, giving $n_\beta = 2$. Therefore $n_\alpha/n_\beta = 4/2 = 2$.
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