Question

The relation between $RMS$ velocity,average velocity and most probable velocity is:

• A. $RMS$ velocity > Average velocity > Most probable velocity.
• B. Average velocity > $RMS$ velocity > Most probable velocity
• C. $RMS$ velocity $=$ Average velocity > Most probable velocity
• D. Most probable velocity > Average velocity > $RMS$ velocity

Answer 1

The correct option is A $RMS$ velocity > Average velocity > Most probable velocity.

Relationship among the velocities are:

RMS velocity= Crms

Average velocity= Cav

Most probable velocity= Cmp

Crms : Cav : Cmp =$\sqrt{\frac{3RT}{M}}$ :$\sqrt{\frac{8RT}{piM}}$ : $\sqrt{\frac{2RT}{M}}$

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

=1.732:1.596: 1.414

Hence, RMS velocity > Average velocity > Most probable velocity