$ln\large\frac{k_2}{k_1}=\frac{E_a}{R}\big(\large\frac{1}{T_1}-\frac{1}{T_2}\big)$
$T_1=360K$
$T_2=400K$
$ln\large\frac{(t_{1/2})_1}{(t_{1/2})_2}=\frac{E_a}{R}\big(\frac{1}{360}-\frac{1}{400}\big)$
$ln \large\frac{45}{9}=\frac{E_a}{R}\big(\frac{1}{3600}\big)$
$E_a=5.81RKJ/mol$
Hence (b) is the correct answer.