JEE Advanced 2022 · Paper 2 · Physics Q2

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PhysicsInteger+3 / -1Question 20 of 54

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

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Answer and worked solution

Official answer: 2

Alpha particles. Only $\alpha$ decay changes the mass number: $230-214=16=4n_\alpha$ , so $n_\alpha=4$ .

Beta particles. Four $\alpha$ decays lower $Z$ by 8, but $Z$ falls only from 90 to 84, i.e. by 6. So $n_\beta=2$ .

Ratio. $n_\alpha:n_\beta=4:2=2$ .

Topics:Radioactive decay

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JEE Advanced 2022 · Paper 2, Physics question 2