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The ratio of average speed of an oxygen molecule to the RMS speed of a nitrogen molecule at the same temperature is :

$(a)\;(\large\frac{3\pi}{7})^{\large\frac{1}{2}}\qquad(b)\;(\large\frac{7}{3\pi})^{\large\frac{1}{2}}\qquad(c)\;(\large\frac{3}{7\pi})^{\large\frac{1}{2}}\qquad(d)\;(\large\frac{7\pi}{3})^{\large\frac{1}{2}}$
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$U_{av}\;\;\;O_2 = \sqrt{[\large\frac{8RT}{\pi \times 32}]}$
$U_{rms}\;\;\;N_2 = \sqrt{[\large\frac{3RT}{28}]}$
$\large\frac{U_{av}\;\;O_2}{U_{rms}\;\;N_2} = \sqrt{[\large\frac{8\times28}{\pi \times32\times3}]}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\sqrt{[\large\frac{7}{3\pi}]}$
Hence answer is (b)
answered Mar 6, 2014 by sharmaaparna1
 

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