The rms velocity $\left(\mathrm{u}_{\mathrm{rms}}\right)$, mean velocity $\left(\mathrm{u}_{\mathrm{av}}\right)$ and most probability ( $\mathrm{u}_{\mathrm{mp}}$ ) of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?

• A

  $\frac{u_{r m s}}{u_{a v}}=1.20$
• Correct answer
  B

  $\frac{u_{a v}}{u_{m p}}=1.12$
• C

  $\frac{u_{r m s}}{u_{m p}}=1.15$
• D

  $\frac{u_{a v}}{u_{r m s}}=0.98$

Solution

rms velocity $\left(\mu_{\mathrm{rms}}\right)=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$ Mean velocity $\left(\mu_{\mathrm{av}}\right)=\sqrt{\frac{8 \mathrm{RT}}{\pi \mathrm{M}}}$ Most probability $\left(\mu_{m p}\right)=\sqrt{\frac{2 R T}{M}}$
Option (2) is correct.

Hence, the correct answer is option: 'B'.