Question

Let $v_{rms}, v_{mp}$ and $v_{avg}$ represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, $(v_{rms})^2 : (v_{mp})^2 : (v_{avg})^2$ is

• A. $8 : 3\pi : 2\pi$
• B. $8 : 2\pi : 3\pi$
• C. $3\pi : 2\pi: 8$
• D. $3 : 2 : 8$

Answer 1

Answer: (C)

$3\pi : 2\pi: 8$

Answer 2

$\because \:\: v_{rms} = \sqrt{\frac{3RT}{M}} , v_{mp} = \sqrt{\frac{2RT}{M}}$ and $v_{avg} = \sqrt{\frac{8RT}{ \pi M}}$
$\therefore \:\:\: (v_{rms})^2 : (v_{mp})^2 : (v_{avg})^2 = \frac{3RT}{M} : \frac{2RT}{M} : \frac{8RT}{\pi M}$
= $3 \pi : 2 \pi : 8$