Explanation

(d) Root mean square velocity of gas molecules
$v_{rms} = \sqrt{\frac{3RT}{M}}\ \ \ \ \ \ \ $
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v_{rms} \propto \frac{1}{\sqrt{M}}\ \ \ \ \ \ $
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{{v_{O}}_{3}}{{v_{O}}_{2}} = \sqrt{\frac{{M_{O}}_{2}}{{M_{O}}_{3}}}$
Here, ${M_{O}}_{2} = 32,\ \ \ \ \ {M_{O}}_{3} = 48$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{{v_{O}}_{3}}{{v_{O}}_{2}} = \sqrt{\frac{32}{48}} = \frac{\sqrt{2}}{\sqrt{3}}$