The relationship among most probable velocity, average velocity and root mean square velocity is respectively

For an ideal gas at absolute temperature $$T$$, molecular velocities are expressed as:

• Most probable (peak) velocity: $$v_{mp} = \sqrt{\frac{2RT}{M}}$$

• Average (mean) velocity: $$\overline{v} = \sqrt{\frac{8RT}{\pi M}}$$

• Root-mean-square velocity: $$v_{rms} = \sqrt{\frac{3RT}{M}}$$

Here $$R$$ is the gas constant and $$M$$ is the molar mass. Since all three contain the common factor $$\sqrt{\frac{RT}{M}}$$, divide each velocity by that factor to obtain their dimensionless ratio:

$$v_{mp} : \overline{v} : v_{rms} = \sqrt{2} : \sqrt{\frac{8}{\pi}} : \sqrt{3}$$

This order matches Option B.

Option B which is: $$\sqrt{2} : \sqrt{8/\pi} : \sqrt{3}$$