Question

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

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

Answer 1

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

$\stackrel{\ast }{C}:\overline{C}:C=\sqrt{\frac{2RT}{m}}:\sqrt{\frac{8RT}{\pi m}}:\sqrt{\frac{3RT}{m}}$
$=\sqrt{2}:\sqrt{\frac{8}{\pi }}:\sqrt{3}$
$=1.414:1.596:1.732$
$=1:1.128:1.225$.