Question

At the point of intersection of the two curves shown, the conc. of $B$ is given by ____ for, $A \longrightarrow n B$ :

• A. $\frac{n A_{0}}{2}$
• B. $\frac{A_{0}}{n-1}$
• C. $\frac{n A_{0}}{n+1}$
• D. $\left(\frac{n-1}{n+1}\right) A_{0}$

Answer 1

Answer: (C)

From the fig. $[ A ]_{\text {left }}=[ B ]_{\text {formed }}=n \times[ A ]_{\text {decayed }}$
$\therefore \left[A_{0}\right]_{e}^{-\lambda t}=n \times A_{0}\left[1-e^{-\lambda t}\right] $
$\therefore e^{-\lambda t}=\frac{n}{n+1}$
$[ B ]_{\text {formed }}=n \times A_{0} \times\left[1-\frac{n}{n+1}\right]=\frac{n A_{0}}{n+1}$