Question

The root mean square velocity, $v_{rms}$ , the average velocity $v_{av}$ and the most probable velocity,$v_{mp}$ of the molecules of the gas are in the order:

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

Answer 1

Answer: (B)

$v _{ rms }=\sqrt{\frac{3 kT }{ m }}, v _{ av }=\sqrt{\frac{8 kT }{ m \pi}}$ and $v _{ mp }=\sqrt{\frac{2 kT }{ m }}$
$\Rightarrow v _{ rms }: v _{ av }: v _{ mp }=1: 0.92: 0.816$
$\therefore v _{ rms }> v _{ av }> v _{ mp } .$