Question

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

• A. $1.086:1$
• B. $1:1.086$
• C. $2:1.086$
• D. $1.086:2$

Answer 1

Answer: (A)

$1.086:1$

The expression for the root mean square velocity is $\left(u_{rms}\right)=\sqrt{\frac{3RT}{M}}$.

The expression for the average speed is $\left(u_{avg}\right)=\sqrt{\frac{8RT}{\pi M}}$.

For a particular gas, at a particular temperature, M and T are constant.

Hence, the ratio of the root mean square velocity to average speed is:

$\frac{u_{rms}}{u_{avg}}=\sqrt{\frac{3RT}{M}}:\sqrt{\frac{8RT}{\pi M}}=\sqrt{3}:\sqrt{\frac{8}{\pi }}=\sqrt{3}:\sqrt{2.54}=1.181:1$.

Hence, the correct answer is option $\text{A}$.