Question

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

• A. 1.085:1
• B. 01:01.1
• C. 2 . 1.086
• D. 1.086: 2

Answer 1

The Correct Option is A

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