α, v and u represent most probable velocity, average velocity and...

\alpha, v

and

u

represent most probable velocity, average velocity and root mean square velocity respectively of a gas at a particular temperature. The correct order among the following is

Options

A $u>v>\alpha$
B $v>u>\alpha$
C $\alpha>u>v$
D $u>\alpha>v$

Correct answer

A. $u>v>\alpha$

Step-by-step solution

\begin{aligned}u: v: \alpha& =\sqrt{\frac{3 R T}{M}}: \sqrt{\frac{8 R T}{\pi M}}: \sqrt{\frac{2 R T}{M}}\\ & =\sqrt{3}: \sqrt{\frac{8}{\pi}}: \sqrt{2} \end{aligned}

=$1.224: 1.128: 1

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