Question

If average velocity of a sample of gas molecules at $300K$ is $5cm.s^{-1}$, what is RMS velocity of the same sample of a gas molecule at the same temperature? (Given, $\alpha :u:v=1:1.224:1.127$)

• A. $6.112cm/s$
• B. $4.605cm/s$
• C. $4.085cm/s$
• D. $5.430cm/s$

Answer 1

The correct option is D $5.430cm/s$

Given that $\alpha$ (most probable velocity) $:u$ (RMS velocity) $:v$ (average velocity) $=1:1.224:1.127$

$\therefore \frac{u}{v}=\frac{1.224}{1.127}$

or $\frac{u}{5}=\frac{1.224}{1.127}$

or $u=\frac{1.224\times 5}{1.127}=5.430cm/s$