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. 1 : 1.086
• C. 2 : 1.086
• D. 1.086 : 2

Answer 1

Answer: (A)

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