The relation between root mean square speed ( v rms ) and most probable speed ( v p ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :-

Question

The relation between root mean square speed ( v rms ) and most probable speed ( v p ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :- (A) v rms =√(2/3) v p  (B) v rms =√(3/2) v p  (C) v rms = v p  (D) v rms =√(1/3) v p

Tardigrade Admin · Accepted Answer

v rms =√(3 RT / M ) and v mp =√(2 RT / M ) Thus v rms =√(3/2) v mp

Q. The relation between root mean square speed $(v_{r m s})$ and most probable speed $(v_{p})$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300 K$ will be :-

$v_{r m s} = \frac{2}{3} v_{p}$

$v_{r m s} = \frac{3}{2} v_{p}$

$v_{r m s} = v_{p}$

$v_{r m s} = \frac{1}{3} v_{p}$

$v_{r m s} = \frac{3 RT}{M}$
and $v_{m p} = \frac{2 RT}{M}$
Thus $v_{r m s} = \frac{3}{2} v_{m p}$

Q. The relation between root mean square speed (vrms​) and most probable speed (vp​) for the molar mass M of oxygen gas molecule at the temperature of 300K will be :-

vrms​=32​​vp​

vrms​=23​​vp​

vrms​=vp​

vrms​=31​​vp​