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