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

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The radioactive decay process involves alpha and beta decay sequences. We can break down the steps as follows: The original $^{230}_{90}Th$ nucleus undergoes alpha decay, emitting an alpha particle ($\alpha$). After this decay, the resulting nucleus is $^{226}_{88}Ra$. The $^{226}_{88}Ra$ nucleus undergoes alpha decay again, resulting in $^{222}_{86}Rn$, emitting another alpha particle ($\alpha$). The $^{222}_{86}Rn$ nucleus undergoes alpha decay to form $^{218}_{84}Po$, emitting another alpha particle ($\alpha$). The $^{218}_{84}Po$ nucleus undergoes alpha decay to form $^{214}_{82}Pb$, emitting yet another alpha particle ($\alpha$). The $^{214}_{82}Pb$ nucleus undergoes beta decay, emitting a beta particle ($\beta$), and transforming into $^{214}_{83}Bi$. The $^{214}_{83}Bi$ nucleus undergoes beta decay again, emitting a second beta particle ($\beta$), and transforming into $^{214}_{84}Po$, which is the final product. Thus, we see that there are 4 alpha decays and 2 beta decays. Therefore, the ratio of the number of alpha particles to beta particles is: $$ \text{Ratio of } \alpha \text{ to } \beta = \frac{4}{2} = 2 $$ Final Answer: The ratio of the number of alpha particles to the number of beta particles emitted in this process is $2$.

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

Correct Answer: 2

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