GATE 2026 CY – Question 60
The sum of alpha and beta particles emitted in $^{238}_{92}\mathrm U\to{}^{206}_{82}\mathrm{Pb}$ is _____ (in integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 14
Explanation
In the decay chain $^{238}_{92}\text{U}\to{}^{206}_{82}\text{Pb}$ the nuclide emits alpha particles ($^4_2\text{He}$, mass number 4 and charge 2) and beta particles ($\beta^-$, charge −1, no change of mass number).
**Number of alpha particles** from the change in mass number (beta emission does not change it):
$$\frac{238-206}{4}=\frac{32}{4}=8 .$$
**Number of beta particles** from the change in atomic number. Eight alpha particles lower $Z$ by $8\times2=16$, from 92 to 76. To reach 82, $Z$ must increase by 6, and each $\beta^-$ raises it by 1:
$$82-76=6\text{ beta particles}.$$
**Total emitted:** $8+6=\mathbf{14}$.