Physics - Modern Physics Question with Solution | TestHub

$\begin{array}{l}{t}_{1/2}=3.8\text{ day }\\ \therefore \lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{3.8}=0.182\end{array}$ If the initial number of atom is $a=A_0$ then after time $t$ the number of atoms is $a/20=A$. We have to find $t$. $$\begin{array}{rl}t& =\frac{2.303}{\lambda }\log \frac{A_0}{A}=\frac{2.303}{0.182}\log \frac{a}{a/20}\\ & =\frac{2.303}{0.182}\log 20=16.46\text{ days }\end{array}$$