Question

The half-life of radioactive radon is 3.8 days. The time at the end of which 1/20th of the radon sample will remain undecayed is (given $lo{g}_{10}e=-0.4343)$:

• A. 3.8 day
• B. 16.5 day
• C. 33 day
• D. 76 day

Answer 1

The correct option is B 16.5 day

$t_{\frac{1}{2}}=3.8$days

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{T_{\frac{1}{2}}}}$

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{3.8}}$

We have to find t,

$N=\frac{N_0}{20}$

$\frac{N_0}{20}=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{3.8}}$

$\ln \left(\frac{1}{20}\right)=\frac{t}{3.8}\ln \frac{1}{2}t=16.5$ days