Chemistry - Chemical Kinetics Question with Solution | TestHub

Radioactive disintegration is a Ist order reaction, hence $\begin{array}{rl}k& =\frac{2.303}{t}\log \frac{a}{a-x}\\ \therefore k& =\frac{2.303}{15}\log \frac{100}{100-50}\\ \text{ also }k& =\frac{2.303}{t}\log \frac{100}{100-99}\\ \therefore \frac{2.303}{15}\log \frac{100}{50}& =\frac{2.303}{t}\log \frac{100}{1}\\ \frac{1}{15}\log 2& =\frac{1}{t}\log 100\\ \frac{0.3010}{15}& =\frac{2}{t}\\ t& =\frac{2\times 15}{0.3010}=99\min \end{array}$