Question

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

• A. $6,8$
• B. $8,6$
• C. $16,6$
• D. $32,12$

Answer 1

The correct option is B $8,6$

$\begin{array}{c}\text{For each.}\alpha \text{-decay Mass number}\\ \text{decreases by}{}^{\prime \prime }{4}^{\prime \prime }\text{and}Z\text{by "}{2}^{\prime \prime }\\ 238⟶206\end{array}$

$\begin{array}{c}\text{Decrease in mass aumber is}{}^{\prime \prime }{32}^{\prime \prime }\\ \text{Let number of}{}^{\prime \prime }{\alpha }^{\prime \prime }\text{particles and}\\ {}^{\prime \prime }{\beta }^{\prime \prime }\text{particles emitted be "}{x}^{\prime \prime }\text{and "y"}\\ \begin{array}{c}4x=32\\ x=8\end{array}\end{array}$

$\begin{array}{c}\therefore \text{No. of}\alpha \text{-particles emitted will be}8.\\ \text{Now, due to this emission}z\text{decrease}\\ \text{by}16.\\ \therefore z=76\\ 76\to 82\\ \therefore y=6\\ \text{No of}\beta \text{-particles emitted is "}6".\end{array}$