At 300K, the rms speed of oxygen molecules is $\sqrt{\frac{α + 5}{α}}$ times to that of its average speed in the gas. Then the value of $α$ will be
(used $π = \frac{22}{7})$

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answer is D.

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Detailed Solution

$\begin{array}{l} \sqrt{\frac{3 RT}{M}} = \sqrt{\frac{α + 5}{α}} \sqrt{\frac{8 RT}{πM}} \\ 3 = (\frac{α + 5}{α}) \frac{8}{(\frac{22}{7})} \Rightarrow \frac{α + 5}{α} = \frac{33}{28} \Rightarrow α = 28 \end{array}$

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