Question

If $v_1,v_2$ and $v_3$ represents the root mean square speed, average speed and most probable speed of an ideal gas respectively, then $v_1:v_2:v_3$ is

• A. $\sqrt{3}:\sqrt{\frac{8}{\pi }}:\sqrt{2}$
• B. $\sqrt{\frac{8}{\pi }}:\sqrt{3}:\sqrt{2}$
• C. $\sqrt{\frac{2}{\pi }}:\sqrt{2}:\sqrt{3}$
• D. $1:1:1$

Answer 1

The correct option is A $\sqrt{3}:\sqrt{\frac{8}{\pi }}:\sqrt{2}$

We know that,
Root mean square speed,
$v_1=\sqrt{\frac{3RT}{M}}$ ...........(1)
Average speed,
$v_2=\sqrt{\frac{8RT}{\pi M}}$ ...........(2)
Most probable speed,
$v_3=\sqrt{\frac{2RT}{M}}$ ...........(3)

Using (1), (2) & (3) we get
$v_1:v_2:v_3=\sqrt{3}:\sqrt{\frac{8}{\pi }}:\sqrt{2}$