Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be:
( Molecular weight of oxygen is $32 g / m o l;$ $R = 8.3 J K^{- 1} m o l^{- 1})$

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$\sqrt{\frac{8 π}{3}}$

$\sqrt{\frac{3}{3}}$

$\sqrt{\frac{8}{3}}$

$\sqrt{\frac{3 π}{8}}$

answer is C.

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Detailed Solution

$V_{r m s} = \sqrt{\frac{3 R T}{M}} and V_{a v g} = \sqrt{\frac{8 R T}{π M}} D i v i d i n g w e g e t, \frac{V_{r m s}}{V_{a n g}} = \sqrt{\frac{3 π}{8}}$

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