Let `u_(av), u_(rms)` and `u_(mp)` are average, root means square and most probable speed the molcules in an ideal monoatomic gas at absolute temperature T. The mass of molecule is m, then :

Options

A. none of the moelcules can have a speed greater than `sqrt(2)u_(rms)`
B. none of the molecules can have a speed less than `sqrt(2)u_(mp)`.
C. `u_(av) lt u_(rms) lt u_(mp)`
D. the average kinetic energy of molecule is `3/4m u_(mp)^2`

Answer

D

Explanation

`K.E. = 1/2 mU_(rms)^2 = 1/2 m xx 3/2 xx U_(mp)^2 = 3/4 U_(mp)^2`.