Question

The half life of radioactive Radon is 3.8 days. Find the time during which $\frac{1}{20}$ of Radon sample will remain undecayed.

Answer 1

From the law of radio activity, $N=N_0{e}^{-\lambda t}$

Given, half life $t_{1/2}=3.8$ days, so decay constant $\lambda =\frac{0.693}{t_{1/2}}=0.693/3.8=0.182$

here, $N=N_0/20$

Thus, $N_0/20=N_0{e}^{-\lambda t}$

or $\lambda t=ln20$

or $t=\frac{ln20}{0.182}=16.46$ days