Question

A radioactive reaction is ${}_{92}{U}^{238}\to {}_{82}P{b}^{206}.$ How many $\alpha$ and $\beta$ particles are emitted?

• A. 10,6
• B. 8,8
• C. 12,6
• D. 8,6

Answer 1

Answer: (D)

${}_{92}{U}^{238}\to {}_{82}P{b}^{206}$
Let the number of $\alpha$ and $\beta$ particles emitted be $x$ and $y$ respectively. Then
${}_{92}{U}^{238}\to {}_{82}P{b}^{206}+x_{2}H{e}^4+y_{-1}{e}^0$
Equating the mass and atomic numbers on both sides, we get
$206+4x=238$
$\Rightarrow x=\frac{238-206}{4}=8$
$82+2x-y=92$
$\Rightarrow y=82+2\times 8-92=6$
$\therefore$ The number of $\alpha$ and $\beta$ particles emitted are $8$ and $6$ respectively