Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Most Probale speed $\left(C^{\ast }\right)=\sqrt{\frac{2RT}{M}}$

Average Speed ($\overline{C})=\sqrt{\frac{8RT}{\pi M}}$

Root mean square velocity $\left(\overline{C}\right)$ = $\sqrt{\frac{3RT}{M}}$

$C^{\ast }:\overline{C}:C=\sqrt{\frac{2RT}{M}}:\sqrt{\frac{8RT}{\pi M}}:\sqrt{\frac{3RT}{M}}$

$=1:\sqrt{\frac{4}{\pi }}:\sqrt{\frac{3}{2}}=1:1.128:1.225$