An element ' Y ' emits one α -and two β -particles to give ' X '. X...

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)