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  4. The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is

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Q. The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is

IIT JEEIIT JEE 1981States of Matter

Solution:

The two types of speeds are defined as;
Root mean square speed $\left(u_{\text {rms }}\right)=\sqrt{\frac{3 R T}{M}}$
Average speed $\left(u_{ av }\right)=\sqrt{\frac{8 R T}{\pi M}}$
For the same gas, at a given temperature, $M$ and $T$ are same, therefore
$\frac{u_{ rms }}{u_{ av }} =\sqrt{\frac{3 R T}{M}}: \sqrt{\frac{8 R T}{\pi M}}=\sqrt{3}: \sqrt{\frac{8}{\pi}}$
$=\sqrt{3}: \sqrt{2.54}=1.085: 1$