Question

Identify the correct order as indicated in the given diagram of different kind of speed of molecules of same gas.


$f\left(v\right)\to$ Maxwell speed distribution function
$v_{mp}\to$ Most probable speed
$v_{rms}\to$ Root mean square speed
$v_{av}\to$ Average speed

• A. $v_{mp}-3,v_{av}-2,v_{rms}-1$
• B. $v_{mp}-1,v_{av}-2,v_{rms}-3$
• C. $v_{mp}-2,v_{av}-1,v_{rms}-3$
• D. $v_{mp}-3,v_{av}-1,v_{rms}-2$

Answer 1

The correct option is B $v_{mp}-1,v_{av}-2,v_{rms}-3$

We know that,
$v_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{3}k=1.7k$
[Let $\sqrt{\frac{RT}{M}}=k$]
$v_{av}=\sqrt{\frac{8RT}{\pi M}}=\sqrt{\frac{8}{\pi }}k=1.6k$
$v_{mp}=\sqrt{\frac{2RT}{M}}=\sqrt{2}k=1.4k$
We can see that, $v_{rms}>v_{av}>v_{mp}$ and speed at $3>2>1$
Therefore, correct order is $v_{mp}-1,v_{av}-2,v_{rms}-3$