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(C) Let the parent nucleus be represented as ${}_Z^AX$.When one $\alpha$ particle $({}_2^4He)$ is emitted,the atomic number $Z$ decreases by $2$ and t

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isotope of parent

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(C) Let the parent nucleus be represented as ${}_Z^AX$.When one $\alpha$ particle $({}_2^4He)$ is emitted,the atomic number $Z$ decreases by $2$ and the mass number $A$ decreases by $4$.When one $\beta^-$ particle $({}_{-1}^0e)$ is emitted,the atomic number $Z$ increases by $1$ and the mass number $A$ remains unchanged.Given that the number of $\beta$ particles emitted is twice the number of $\alpha$ particles,let the number of $\alpha$ particles be $n$. Then the number of $\beta$ particles is $2n$.The change in atomic number $Z'$ of the daughter nucleus is given by: $Z' = Z - 2(n) + 1(2n) = Z - 2n + 2n = Z$.The change in mass number $A'$ of the daughter nucleus is given by: $A' = A - 4(n) + 0(2n) = A - 4n$.Since the atomic number $Z$ remains the same,the resulting daughter nucleus is an isotope of the parent nucleus.

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter nucleus is an

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