Question

In the uranium radioactive series the initial nucleus is ${}_{92}^{238}\text{U}$ and the final nucleus is ${}_{82}^{206}\text{Pb}$. When the uranium nucleus decays to lead, number of $\alpha$-particles emitted is ...............and the number of $\beta$-particles emitted is ...............

Answer 1

When an $\alpha$ particle is emitted, the atomic number decreases by 2 and the mass number decreases by 4.
The number of alpha particles emitted is $\frac{238-206}{4}=\frac{32}{4}=8$
When 8 alpha particles are emitted the atomic number decreases by $2\times 8=16$ from 92 to $92-16=76$
When a $\beta$ particle is emitted, the atomic number increases by 1.
The number of $\beta$ particles emitted $=82-76=6$.