Question

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

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

Answer 1

Answer: (C)

$c^* : \overline{c} : c = 1 : 1.128 : 1.225$

Answer 2

C * = Most probable speed $\sqrt{\frac{2RT}{M}}$
$\overline{C}$= Average speed = $\sqrt{\frac{8RT}{\pi M}}$
C = Root square speed corrected as root means square speed, i.e
$rms=\sqrt{\frac{3RT}{M}}$ and as we know $\, ^{*}_{C} < \overline{C} < C$
$\, ^{*}_{C} : \overline{C} : C=1 : \sqrt{\frac{4}{p}} : \sqrt{\frac{3}{2}}= 1 : 1.128 : 1.225$
NOTE
As no option correspond to root square speed, it is understood as misprint. It should be root mean square speed.