Question

A radioactive sample undergoes decay as per the following graph. Dotted line represents the slope of the curve at t = 0. If this dotted line intersects the time axis at t = T, choose the correct alternative (Given $t_{\frac{1}{2}}=$half life,$t_{avg}=$ mean life)

• A. $t_{\frac{1}{2}}>T$
• B. $t_{avg}=T$
• C. $t_{\frac{1}{2}}=T$
• D. $t_{avg}>T$

Answer 1

The correct option is B $t_{avg}=T$

$N=N_0{e}^{-\lambda t}$
${\begin{array}{c}\frac{dN}{dt}\end{array}|}_{t-0}=-\lambda N_0$
$\left(\lambda N_0\right)T=N_0$
$T=\frac{1}{\lambda }=t_{avg}$