Question

For gaseous state, most probable speed is denoted by $C^{\ast }$, average speed by $\overline{C}$ and root mean square speed by $C$ respectively. For the same number of molecules at same temperature, the ratios of these speeds are:

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

Answer 1

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

Most probable speed $\left(C^{\ast }\right)=\sqrt{\frac{2RT}{M}}$
Average Speed $\left(\overline{C}\right)=\sqrt{\frac{8RT}{\pi M}}$
Root mean square speed $\left(C\right)=\sqrt{\frac{3RT}{M}}$
When we take a ratio,
$C^{\ast }:\overline{C}:C=\sqrt{\frac{2RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{3RT}{M}}$
Since all the velocities are measured for same mass and at same temperature, the ratios become,
$=>1:\sqrt{\frac{4}{\pi }}:\sqrt{\frac{3}{2}}=1:1.128:1.225$