Question

The $rms$ velocity of a gas at a certain temperature is found to be 12,240 $cm/sec$. The most probable velocity of that gas in $cm/sec$ is:

• A. ${10}^3$
• B. ${10}^4$
• C. $11280$
• D. $1128$

Answer 1

The correct option is B ${10}^4$

r.m.s velocity $=\sqrt{\frac{3RT}{M}}=u_{rms}$

Most probable velocity $=\sqrt{\frac{2RT}{M}}=u_{mp}.$

$\frac{u_{mp}}{u_{rms}}=\frac{\sqrt{2}}{\sqrt{3}}$

$\frac{u_{mp}}{12240}=\frac{\sqrt{2}}{\sqrt{3}}⟹u_{mp}=\frac{\sqrt{2}}{\sqrt{3}}\times 12240=9993\simeq 10000={10}^4$

$\therefore$ Most probable velocity is ${10}^4$ times rms velocity.