States of Matter - Result Question 24
####24. The ratio among most probable velocity, mean velocity and root mean square velocity is given by
[1993]
(a) $1: 2: 3$
(b) $1: \sqrt{2} \cdot \sqrt{3}$
(c) $\sqrt{2}: \sqrt{3}: \sqrt{8 / \pi}$
(d) $\sqrt{2}: \sqrt{8 / \pi}: \sqrt{3}$
Show Answer
Solution:
- (d) Most probable velocity $(\alpha)=\sqrt{\frac{2 R T}{M}}$ Mean velocity $(\bar{{}v})=\sqrt{\frac{8 R T}{\pi M}}$
Root mean square velocity $(u)=\sqrt{\frac{3 R T}{M}}$
$ \begin{aligned} \therefore \alpha: \bar{{}v}: u & =\sqrt{\frac{2 R T}{M}}: \sqrt{\frac{8 R T}{\pi M}}: \sqrt{\frac{3 R T}{M}} \\ & =\sqrt{2}: \sqrt{\frac{8}{\pi}}: \sqrt{3} \end{aligned} $
