First slide

Rms speed

Question

The ratio of most probable speed and the rms speed of gas molecules at a given temperature is

Easy

A

$\sqrt{\frac{2}{3}}$
B

$\frac{\sqrt{3}}{8}$
C

$\frac{3}{8}$
D

$\frac{2}{3}$

Solution

We know that
$V_{m p} = \sqrt{\frac{2 RT}{M}} V_{r m s} = \sqrt{\frac{3 RT}{M}} \frac{V_{m p}}{V_{r m s}} = \sqrt{\frac{2 RT}{M}} x \sqrt{\frac{M}{3 RT}} = \sqrt{\frac{2}{3}}$

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