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. `(upsilon)_(P) lt vec(upsilon) lt (upsilon)_(rms)`
B. no molecule can have a speed greater than `sqrt(2) (upsilon)_(rms)`
C. no molecule can have speed less than `(upsilon)_(P)//(sqrt(2))`
D. the average kinetic energy of a molecule is `(3)/(4)m (upsilon)^(2)_(P)`

Answer

A, D

Explanation

Mean speed, `bar(upsilon) = sqrt((8kT)/(pi m)) = 0.92 upsilon_(rms)`
rms speed, `upsilon_(rms) = sqrt((3kT)/(m))`
most probable speed, `upsilon_(p)= sqrt((2kT)/(m)) = 0.816upsilon_(rms)` ltbr. As is clear from the formulae, `upsilon_(p) lt bar(upsilon) lt upsilon_(rms)`
Average kinetic energy of a molecule
`=3/2 kT = 3/4 m. ((2kt)/(m)) = 3/4 m upsilon_(p)^(2)`.