Question

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

• A. $\begin{array}{ccc}{C}^{\ast }& \overline{C}& C\\ 1.225& 1.128& 1\end{array}$
• B. $\begin{array}{ccc}{C}^{\ast }& \overline{C}& C\\ 1& 1.128& 1.225\end{array}$
• C. $\begin{array}{ccc}{C}^{\ast }& \overline{C}& C\\ 1.128& 1.225& 1\end{array}$
• D. $\begin{array}{ccc}{C}^{\ast }& \overline{C}& C\\ 1& 1.125& 1.128\end{array}$

Answer 1

The correct option is B $\begin{array}{ccc}{C}^{\ast }& \overline{C}& C\\ 1& 1.128& 1.225\end{array}$

As
$C^{\ast }=\sqrt{\frac{2RT}{M}};\overline{C}=\sqrt{\frac{8RT}{\pi M}};C=\sqrt{\frac{3RT}{M}}$
$C^{\ast }:\overline{C}:C=\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}=1.414:1.596:1.732$
$=1:1.128:1.225$