Question

$\alpha ,v\text{and}u$ represent most probable velocity, average velocity and root mean square velocity of a gas at a particular temperature. Which one of the following relationship is correct?

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

Answer 1

The correct option is D $u>v>\alpha$

Kinetic Molecular Theory of Gases:
As we know,
$u:v:\alpha =\sqrt{\frac{3RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{2RT}{M}}$

$\Rightarrow u:v:\alpha =\sqrt{3}:\sqrt{\frac{8}{\pi }}:\sqrt{2}$

$\Rightarrow u:v:\alpha =1.73:1.59:1.41$


$\text{Root mean square velocity}>\text{average velocity}>\text{most prolable velocity}$.
Hence, option D is correct answer.