The half-life of radon is 3.5 days. After how many days will only one twentieth of radon sample be left over. $\left(\ln 20 = 3 ; \ln 2=0.7\right)$

Disintegration constant $\mathrm{\lambda }=\frac{\ln 2}{{\mathrm{t}}_{1/2}}=\frac{\ln 2}{3.5}$ per day

The number of particles left after time t

$\mathrm{N}={\mathrm{N}}_0{\mathrm{e}}^{-\mathrm{\lambda t}}$   or   $\frac{{\mathrm{N}}_0}{20}={\mathrm{N}}_0{\mathrm{e}}^{-\mathrm{\lambda t}}$   or   ${\mathrm{e}}^{\mathrm{\lambda t}}=20$   or   $\mathrm{t}=\frac{\mathrm{In}20}{\mathrm{\lambda }}=\frac{\mathrm{In}20}{\ln 2}\left(3.5\right)=15 \mathrm{days}$