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An element ' $Y$ ' emits one $\alpha$-and two $\beta$-particles to give ' X '. $X$ and $Y$ are
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isotopes
Let atomic mass and atomic number of $Y$ are ' $a$ ' and ' $b$ ' respectively. Hence,
\({ }_b Y^a \xrightarrow{-\alpha}{ }_{b-2} M^{a-4} \xrightarrow{-\beta}{ }_{b-1} N^{a-4}\xrightarrow{-\beta}{ }_b X^{a-4}\)
Hence, $X$ and $Y$ are isotopes (i.e., having equal atomic number but differing in mass number)
\({ }_b Y^a \xrightarrow{-\alpha}{ }_{b-2} M^{a-4} \xrightarrow{-\beta}{ }_{b-1} N^{a-4}\xrightarrow{-\beta}{ }_b X^{a-4}\)
Hence, $X$ and $Y$ are isotopes (i.e., having equal atomic number but differing in mass number)
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