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(A) Let the nucleus $R$ be represented as $_Z A^m$. $1$. After $\alpha$-decay: $_Z A^m \xrightarrow{\alpha} _{Z-2} X^{m-4}$. $2$. After first $\beta$-

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Isotopes

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(A) Let the nucleus $R$ be represented as $_Z A^m$. $1$. After $\alpha$-decay: $_Z A^m \xrightarrow{\alpha} _{Z-2} X^{m-4}$. $2$. After first $\beta$-decay: $_{Z-2} X^{m-4} \xrightarrow{\beta} _{Z-1} Y^{m-4}$. $3$. After second $\beta$-decay: $_{Z-1} Y^{m-4} \xrightarrow{\beta} _Z Z^{m-4}$. Thus,$R$ $(_{Z} A^m)$ and $Z$ $(_{Z} Z^{m-4})$ have the same atomic number $(Z)$ but different mass numbers ($m$ and $m-4$). Therefore,$R$ and $Z$ are isotopes.

In the following radioactive transformation given below $R$ $\xrightarrow{\alpha} X$ $\xrightarrow{\beta} Y$ $\xrightarrow{\beta} Z$; the nuclei $R$ and $Z$ are

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