Question

The ratio of root mean square velocity to 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

The correct option is A 1.086:1

As we know, the 2 types of speed are defined as-

Root mean square speed, $v_{rms}=\sqrt{\frac{3RT}{M}}$

Average speed, $v_{average}=\sqrt{\frac{8RT}{\pi M}}$

Therefore, their ratio becomes, $\frac{v_{rms}}{v_{average}}=\sqrt{\frac{3}{8\pi }}=1.086:1$

So, the correct option is $A$