A nucleus ${}_n^{m}X$ emits one $\alpha$ particle and two $\beta$ -particles. The resulting nucleus is:

1. $\alpha$ emission: Mass number decreases by 4, Atomic number decreases by 2.
$${}_n^{m}X\stackrel{\alpha }{\to }{}_{n-2}^{m-4}Y$$
2. Two ${\beta }^{-}$ emissions: Mass number remains unchanged, Atomic number increases by 1 for each $\beta$.
$${}_{n-2}^{m-4}Y\stackrel{2\beta }{\to }{}_{n-2+2}^{m-4}X={}_n^{m-4}X$$
The resulting nucleus has the same atomic number $n$ but a different mass number $m-4$, making it an isotope of the original element $X$.