Question

The particles emitted during the sequential radioactive decay of ${}^{238}{U}_{92}$ to ${}^{206}P{b}_{82}$ are

• A. $5\alpha$ and $6\beta$
• B. $6\alpha$ and $8\beta$
• C. $8\alpha$ and $4\beta$
• D. $8\alpha$ and $6\beta$

Answer 1

Answer: (D)

Let number of $\alpha$-particles emitted during radioactive decay $=n_1$
Let number of $\beta$-particles emitted during radioactive decay $=n_2$
${}^{238}{U}_{92}⟶{}^{206}P{b}_{82}+n_1{\alpha }^{+1}+n_2{\beta }^{-1}$
The $\alpha$-particle represents a helium atom. In $\alpha$-decay the atomic mass is reduced to four units.
$\therefore 238-206=4n_1$
$\Rightarrow \frac{238-206}{4}=n_1$
$n_1=8$
In $\beta$ decay the atomic number is reduced to two units.
$\therefore 92-82=2n_2$
$\Rightarrow \frac{12}{2}=n_2$
$n_2=6$