Question

The ratio of average speed, most probable speed and root mean square speed of a gas sample will be:

• A. $\sqrt{\frac{4}{\pi }}:\sqrt{3}:\sqrt{2}$
• B. $\sqrt{\frac{8}{\pi }}:\sqrt{2}:\sqrt{3}$
• C. $\sqrt{\frac{16}{\pi }}:\sqrt{2}:\sqrt{3}$
• D. $\sqrt{2}:\sqrt{\frac{9}{\pi }}:\sqrt{3}$

Answer 1

Answer: (B)

$\sqrt{\frac{8}{\pi }}:\sqrt{2}:\sqrt{3}$

$v_{avg}=\sqrt{\frac{8RT}{\pi M}}$

$v_{mp}=\sqrt{\frac{2RT}{M}}$

$v_{rms}=\sqrt{\frac{3RT}{M}}$

Therefore $V_{avg}:v_{mp}:v_{rms}=\sqrt{\frac{8}{\pi }}:\sqrt{2}:\sqrt{3}$