Question

If the r.m.s velocity of Hydrogen gas at a certain temperature is $c$, then the r.m.s velocity of Oxygen gas at the same temperature is

• A. $\frac{c}{8}$
• B. $\frac{c}{10}$
• C. $\frac{c}{4}$
• D. $\frac{c}{2}$

Answer 1

The correct option is C $\frac{c}{4}$

The rms velocity of a gas is expressed in terms of its temperature and molecular weight as $\sqrt{\frac{3RT}{M}}$.

Hence at same temperature, $c_{rms}\propto \frac{1}{\sqrt{M}}$

$⟹\frac{c_{O_2}}{c_{H_2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}$

$=\sqrt{\frac{2}{32}}$

$=\frac{1}{4}$

$⟹c_{O_2}=\frac{c}{4}$