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?

• A. 12.65 days
• B. 24.75 days
• C. 42.35 days
• D. 6.5 days

Answer 1

The correct option is A 12.65 days

We know that $K=\frac{0693}{t_{\frac{1}{2}}}=\frac{0.693}{3.8}=0.182da{y}^{-1}$
Let the initial amount of radon be N_0 and the amount left after t days be N which is equal to $\frac{N_0}{10}$
Applying the equation,
$t=\frac{2.303}{K}log\frac{N_0}{N}t=\frac{2.303}{0.182}log\frac{N_0}{\frac{N_0}{10}}=\frac{2.303}{0.182}log10=12.65days$