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  4. Calculate the ratio of rms speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

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Q. Calculate the ratio of $ rms $ speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

AMUAMU 2010Kinetic Theory

Solution:

Root mean square velocity
$V_{rms} \propto\frac{1}{\sqrt{M}}$
so $\frac{\left(V_{rms}\right)O_{2}}{\left(V_{rms}\right)H_{2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}$
$=\sqrt{\frac{2}{32}}=\frac{1}{4}$