Explanation

(b)
We know that,$\frac{(t_{1/2})}{(t_{1/2})} = \left\lbrack \frac{a_{2}}{a_{1}} \right\rbrack^{n - 1}$
Where, n=order of reaction
Given, $\left( t_{1/2} \right) = 0.1s,\ a_{1} = 400$
$\left( t_{1/2} \right) = 0.8s,\ a_{1} = 50$
On substituting the values
$\frac{0.1}{08} = \left\lbrack \frac{50}{400} \right\rbrack^{n - 1}$
On taking log both sides
$\log\frac{0.1}{0.8} = (n - 1)\log\frac{50}{400}$
$\log\frac{1}{8} = (n - 1)\log\frac{1}{8}$
0.90=(n-1)0.90
n-1=1
n=2