Question

The relation between $v_{rms}$ velocity, and the most probable velocity, $v_{mp}$ , of a gas is:

• A. $v_{rms} = v_{mp}$
• B. $v_{rms} = \sqrt{\frac{3}{2}v_{mp}}$
• C. $v_{rms} = \sqrt{\frac{2}{3}v_{mp}}$
• D. $v_{rms} = \frac{2}{3}v_{mp}$

Answer 1

Answer: (B)

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

Answer 2

$V_{\text {rms }}=\sqrt{\frac{3 R T}{M}}$ $V_{m p}=\sqrt{\frac{2 R T}{M}}$ $\frac{V_{\text {rms }}}{V_{\text {mp }}}=\frac{\sqrt{3}}{\sqrt{2}}$ $\Rightarrow V_{\text {rms }}=\sqrt{\frac{3}{2}} \cdot V_{\text {mp }}$