Question

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

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

Answer 1

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

According to the question,
$\begin{array}{c}226\\ 88\end{array}Ra\to \begin{array}{c}206\\ 82\end{array}Pb+n\begin{array}{c}4\\ 2\end{array}He+m\begin{array}{c}0\\ -1\end{array}\beta$
where $n$ and $m$ are respectively the required number of $\alpha$ and $\beta$ particles
$226=206+4n$
$n=5$
$88=82+2n-m$
$m=4$
only (C) satisfies the above reaction