The relation between vrms velocity, and the most probable velocity, vmp , of a gas is:

Question

The relation between vrms velocity, and the most probable velocity, vmp , of a gas is: (A) vrms = vmp (B) vrms = √(3/2)vmp (C) vrms = √(2/3)vmp (D) vrms = (2/3)vmp

Tardigrade Admin · Accepted Answer

V text rms =√(3 R T/M) Vm p=√(2 R T/M) (V text rms /V text mp )=(√3/√2) ⇒ V text rms =√(3/2) ⋅ V text mp

Q. The relation between $v_{r m s}$ velocity, and the most probable velocity, $v_{m p}$ , of a gas is:

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

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

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

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

$V_{rms} = \frac{3 RT}{M}$
$V_{m p} = \frac{2 RT}{M}$
$\frac{V _{rms}}{V _{mp}} = \frac{3}{2}$
$\Rightarrow V_{rms} = \frac{3}{2} \cdot V_{mp}$

Q. The relation between vrms​ velocity, and the most probable velocity, vmp​ , of a gas is:

vrms​=vmp​

vrms​=23​vmp​​

vrms​=32​vmp​​

vrms​=32​vmp​

Vrms ​=M3RT​​ Vmp​=M2RT​​ Vmp ​Vrms ​​=2​3​​ ⇒Vrms ​=23​​⋅Vmp ​

Q. The relation between $v_{r m s}$ velocity, and the most probable velocity, $v_{m p}$ , of a gas is:

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

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

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

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

$V_{rms} = \frac{3 RT}{M}$
$V_{m p} = \frac{2 RT}{M}$
$\frac{V _{rms}}{V _{mp}} = \frac{3}{2}$
$\Rightarrow V_{rms} = \frac{3}{2} \cdot V_{mp}$