Question

Calculate the time required for $60$% of a sample of radon to undergo decay. (Given $T_{\frac{1}{2}}$ of Radon $=3.8$ days)

Answer 1

We know that, $N=N_0{e}^{-\lambda t}$
So, $\frac{40}{100}{N}_0=N_0{e}^{-\lambda t}$
$e^{\lambda t}=\frac{10}{4}=2.5$
$\lambda t={\log }_{e}2.5$

$t=\frac{3.8\times {\log }_{10}2.5\times 2.3026}{0.6931}$
$t=5.022$ days