Question

The half life period of radon is $3.8$ days. After how many days will only one-twentieth of radon sample be left over?

Answer 1

$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{3.8}=0.182{day}^{-1}$

Let the initial amount of radon be $N_0$ and the amount left after $t$ days be $N$ which is equal to $\frac{N_0}{20}$.

Applying the equation,
$t=\frac{2.303}{\lambda }{\log }_{10}\frac{N_0}{N}$

$=\frac{2.303}{0.182}{\log }_{10}\frac{N_0}{N_0/20}=\frac{2.303}{0.182}{\log }_{10}20$

$=16.54$ days