Question

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

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

Answer 1

Answer: (A)

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

As we know,
$u_{m.p.}:u_{av}:u_{rms}=\sqrt{\frac{2RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{3RT}{M}}$

$=\sqrt{2}:\sqrt{8/\pi }:\sqrt{3}=1:1.128:1.225$

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

Hence, the correct answer is option $\text{A}$.