When ${^{232}_{92}Th}$ changes into ${^{208}_{82}Pb}$, the number of $α$ and $β^-$ particles emitted are

$α = 6;β=2$

The correct answer is Option (4) → $α = 6;β=2$

$^{232}_{92}\text{Th} \rightarrow \, ^{208}_{82}\text{Pb}$

$\text{Let number of } \alpha = a,\quad \beta^- = b$

$\text{Mass number: } 232 - 4a = 208$

$4a = 24 \Rightarrow a = 6$

$\text{Atomic number: } 92 - 2a + b = 82$

$92 - 12 + b = 82$

$80 + b = 82 \Rightarrow b = 2$