Question

The ratio of $V_{mp}:V_{avg}:V_{rms}$ is:

• A. $\sqrt{2} : \sqrt{3} : \sqrt{\frac{8}{\pi }}$
• B. $\sqrt{2} : \sqrt{\frac{8}{\pi }} : \sqrt{3}$
• C. $1 : \sqrt{2} : \sqrt{3}$
• D. $1 : 2 : 3$

Answer 1

Answer: (B)

Most probable velocity $V_{mp}=\sqrt{\frac{2 RT}{M}}$
Mean velocity $V_{\text{avg}}=\sqrt{\frac{8 RT}{\pi M}}$
Root mean square velocity $V_{\text{rms}}=\sqrt{\frac{3 RT}{M}}$
$V_{\text{MO}}\text{ : V}_{\text{avg}}\text{ : V}_{\text{rms}}=\sqrt{\frac{2 RT}{M}}:\sqrt{\frac{8 RT}{\pi M}}:\sqrt{\frac{3 RT}{M}} \\ \, =\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}$