Question

The ratio of most probable velocity $\left(\alpha \right)$, average velocity $\left(\overline{v}\right)$, root mean square velocity $\left(u\right)$ is :

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

Answer 1

The correct option is A $\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}$

The ratio of most probable velocity $\left(\alpha \right)$ average velocity $\left(\overline{v}\right)$ root mean square velocity $\left(u\right)$ is $\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}$

$\alpha :v:u=\sqrt{\frac{2RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{3RT}{M}}$

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

$=1.414:1.595:1.732$

$=1:1.128:1.224$

Therefore, the option is A.