Question

The half life of two samples are $0.1$ and $0.4$ second. Their respective concentrations are $200$ and $50$ respectively. What is the order of the reaction?

Answer 1

$t_{1 / 2} \propto a^{1-n}$
$\therefore \frac{0.1}{0.4}=\frac{(200)^{1-n}}{(50)^{1-n}}=\left(\frac{200}{50}\right)^{1-n}$
$\therefore \frac{1}{4}=(4)^{1-n}$
or $(4)^{-1}=(4)^{1-4}$ of
or $(4)^{-1}=(4)^{1-n}$ or $-1=1-n$ or $n=2$