Question

Identify the correct labels of $A,B$ and $C$ in the following graph from the options given below:
Root mean square speed $\left(u_{rms}\right)$; most probable speed $\left(u_{mp}\right)$; Average speed $\left(u_{av}\right)$

• A. $A-u_{mp};B-u_{av};C-u_{rms}$
• B. $A-u_{mp};B-u_{rms};C-u_{av}$
• C. $A-u_{av};B-u_{rms};C-u_{mp}$
• D. $A-u_{rms};B-u_{mp};C-u_{av}$

Answer 1

The correct option is A $A-u_{mp};B-u_{av};C-u_{rms}$

$u_{\text{av}}=\sqrt{\frac{8RT}{\pi M}},u_{\text{rms}}=\sqrt{\frac{3RT}{M}}$
$u_{\text{mp}}=\sqrt{\frac{2RT}{M}}$
Ratio of the speeds are:
$u_{rms};u_{av};u_{mp}=1.22:1.12:1$
$u_{rms}$ is greater magnitude than $u_{av}$ and $u_{mp}$ is smallest in magnitude.
Therefore correct option is (a) i.e. $A-u_{mp};B-u_{av};C-u_{rms}$