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 will be

Answer 1

$$\displaystyle t_{1/2}=3.8$$ day

$$\displaystyle \therefore \lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{3.8}=0.182$$

If the initial number of atom is $$\displaystyle a=A_{0}$$ then after time t the number of atoms is $$a/20=A$$.

$$\displaystyle t=\frac{2.303}{\lambda}\log \frac{A_{0}}{A}=\frac{2.303}{0.182}\log \frac{a}{a/20}$$

$$\displaystyle =\frac{2.303}{0.182}\log 20=16.46$$