Q149 / 180 · AIIMS 2004 · Physics
$v_{r m s}, v_{a v}$ and $v_{m p}$ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?
- A$v_{m s} < v_{a v} < v_{m p}$
- Correct answerB$v_{r m s}>v_{a v}>v_{m p}$
- C$v_{m p} < v_{r m s} < v_{a v}$
- D$v_{m p}>v_{r m s}>v_{\alpha v}$.
Solution
$$
\begin{aligned}
& \text { } v_{r m s}=\sqrt{\frac{3 K_B T}{m}}=1.73 \sqrt{\frac{K_B T}{m}} \\
& v_{a v}=\sqrt{\frac{8 K_B T}{\pi m}}=1.60 \sqrt{\frac{K_B T}{m}} \\
& v_{m p}=\sqrt{\frac{2 K_B T}{m}}=1.41 \sqrt{\frac{K_B T}{m}}
\end{aligned}
$$
From these equations, $v_{r m s}>v_{a v}>v_{m p}$.
Hence, the correct answer is option: 'B'.