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) 8.54 days

(B) 20 days

(C) 11.28 days

(D) 16.46 days

Answer 1

We know that, $\lambda=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{3.8}=0.182$ day $^{-1}$

Let the initial amount of radon be $N_0$ and the amount left after $t$ days be $N$ which is equal to $\frac{N_0}{20}$. Applying the equation,

$\begin{aligned}t & =\frac{2.303}{\lambda} \log _{10} \frac{N_0}{N} \\& =\frac{2.303}{0.182} \log _{10} \frac{N_0}{N_0 / 20}=\frac{2.303}{0.182} \log _{10} 20 \\& =16.46 \text { days }\end{aligned}$

So, The correct option is (D).