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$υ_{a v}, υ_{m s} a n d υ_{m p}$ are average speed, root mean square speed and most probable speed of the gas respectively at constant temperature T. Molar mass of the gas is ‘m’. Then:

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$υ_{m p} < υ_{a v} < υ_{r m s}$

The average kinetic energy of a molecule is $\frac{3}{4} m υ_{m p}^{2}$

No molecules can have a speed less than

No molecules can have a speed greater than $\sqrt{2} υ_{r m s}$

answer is C, D.

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Detailed Solution

$υ_{m p} < υ_{a v} < υ_{r m s}; υ_{m p} = \sqrt{\frac{2 R T}{m}}; υ_{m p}^{2} = \frac{2 R T}{m}$

$\frac{3}{4} m υ_{m p}^{2} = \frac{3}{2} R T = Kinetic energy of gas molecule (per mol)$

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