Let `barv,v_(rms) and v_p` respectively denote the mean speed. Root mean square speed, and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m. Then

Options

A. No molecule can have speed greater than `sqrt(2)v_("rms")`
B. No molecule can have speed less than `(v_(p))/(sqrt(2))`
C. `v_(p) lt overlinev lt v_("rms")`
D. The average kinetic energy of a molecule is `(3)/(4) mv_(p)^(2)`

Answer

C, D

Explanation

`V_(P) = sqrt((2kT)/(m)) , overlinev = sqrt((8kT)/(pim)) , V_("rms") = sqrt((3kT)/(m)) implies V_(P) lt overlinev lt V_("max") = (3)/(2) kT = (3)/(4)mv_(P)^(2)`