In a radioactive decay chain,   90 232 Th nucleus decays to   82 212 Pb nucleus. Let N α…

${\mathrm{ }}_{90}^{232}\mathrm{Th}$ is converting into ${\mathrm{ }}_{82}^{212}\mathrm{Pb}$
Change in mass number $\left(A\right)=232-212=20$

Mass number of an $\alpha$ particle $=4$
$\therefore$ No of $\alpha \text{ particle}=\frac{20}{4}=5$
Due to $5\alpha$ particle, $Z$ will change by $10$ unit.
Since given change is $8$, therefore no. of ${\beta }^{-}$ particle is $2$.