Question

For gaseous state, if most probable speed is denoated by $C^{\ast }$, average speed by $\overline{C}$ and mean square speed by $C$, then for a large number of molecules the ratios of these speeds are:

• A. $C^{\ast }:\overline{C}:C=1.128:1.225:1$
• B. $C^{\ast }:\overline{C}:C=1:1.128:1.225$
• C. $C^{\ast }:\overline{C}:C=1:1.125:1.128$
• D. $C^{\ast }:\overline{C}:C=1.225:1.128:1$

Answer 1

The correct option is B $C^{\ast }:\overline{C}:C=1:1.128:1.225$

Most probable speed $=C^{\ast }=\sqrt{\frac{2RT}{M}}$

Average speed $=\overline{C}=\sqrt{\frac{8RT}{\pi M}}$

Mean square speed $=C=\sqrt{\frac{3RT}{M}}$

$C^{\ast }:\overline{C}:C=1:1.128:1.225$

So, the correct option is $B$