Question

The number of $\alpha$ and ${\beta }^{-}$ emitted during the radioactive decay chain starting from ${}_{88}^{226}Ra$ and endjg at ${}_{82}^{206}Pb$ is

• A. $3\alpha$ and $6{\beta }^{-}$
• B. $4\alpha$ and $5{\beta }^{-}$
• C. $5\alpha$ and $4{\beta }^{-}$
• D. $6\alpha$and $6{\beta }^{-}$

Answer 1

The correct option is C $5\alpha$ and $4{\beta }^{-}$

$\begin{array}{c}\text{Let no of}\alpha \text{particle emitted}=x\\ \text{no of}\beta \text{panticle emitted}=y\end{array}$

${\text{Now,}}_{88}^{226}Ra{\to }_{82}^{206}Pb+x_2^4\alpha +y_{-1}^0\beta$

$\begin{array}{c}\text{balancing atomic mass}\\ \begin{array}{cc}226& =206+4x+0\\ 4x& =20\\ x& =5\end{array}\end{array}$

$\begin{array}{c}\text{balancing atomic no.}\\ \begin{array}{cc}88& =82+2x+(-1)y\\ 6& =10\cdots y\\ y& =4\end{array}\end{array}$

$\text{So,}5\alpha \text{and}4{\beta }^{-}$