Question

$v_{rms}$, $v_{av}$ and $v_{mp}$ are root mean squate,average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

• A. $v_{rms}<v_{av}<v_{mp}$
• B. $v_{rms}>v_{av}>v_{mp}$
• C. $v_{mp}<v_{rms}<v_{av}$
• D. $v_{mp}>v_{rms}<v_{av}$

Answer 1

The correct option is B $v_{rms}>v_{av}>v_{mp}$

Root mean square speed

$v_{rms}=\sqrt{\frac{3kT}{m}}$

Most probable speed

$v_{mp}=\sqrt{\frac{2kT}{m}}$

Average speed
$v_{av}=\sqrt{\frac{8kT}{\pi m}}$

$u_{mp}:u_{av}:u_{rms}=1:1.128:1.224$

So, $v_{rms}>v_{av}>v_{mp}$