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 log10e=0.4343)

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

Answer 1

Answer: (B)

16.5 days

Answer 2

The correct option is B)
t$_\frac{1}{2}$ =3.8 day
∴ λ = $\frac{0.693}{t_\frac{1}{2}}$=$\frac{0.693}{3.8}$= 0.182
If the initial number of atoms is a=A0​ then after time t the number of atoms is $\frac{a}{20}$ = a
$t=\frac{2.303}{\lambda}log\frac{A_0}{A}=\frac{2.303}{0.182}log\frac{a}{a/20}$
$=\frac{2.303}{0.182}log 20 = 16.46$
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