Question

The ratio among most probable velocity, mean velocity and root mean square velocity is given by:

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

Answer 1

The correct option is D $\sqrt{2}:\sqrt{8/\pi }:\sqrt{3}$

Most probable velocity,

$U_{RMS}=\sqrt{\frac{3RT}{M}}$

Average velocity,

$U_{avg}=\sqrt{\frac{8RT}{\pi M}}$

Root mean square velocity,

$U_{MP}=\sqrt{\frac{2RT}{M}}$

$\therefore$$U_{MP}:U_{avg}:U_{RMS}$

$=\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}$

Hence, option $D$ is correct.