Question

The half life of radioactive radon is 3.8 days. The time at the end of which $\frac{1}{20}$th of the Radon sample will remain undecayed is (given ${\log }_{10}e=0.4343$)

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

Answer 1

The correct option is B 16.5 days

$t_{1/2}=3.8$ day
$\therefore \lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{3.8}=0.182$
If the initial number of atom is $a=A_0$ then after time t the number of atoms is $a/20=A$.
$t=\frac{2.303}{\lambda }\log \frac{A_0}{A}=\frac{2.303}{0.182}\log \frac{a}{a/20}$
$=\frac{2.303}{0.182}\log 20=16.46$