Question

The root mean square speed of the molecules of a gas is $1260\text{m/s}$. The average speed of the molecules is

• A. $1260\text{m/s}$
• B. $1161\text{m/s}$
• C. $1671\text{m/s}$
• D. $1061\text{m/s}$

Answer 1

The correct option is B $1161\text{m/s}$

Given:
Root mean square speed, $v_{rms}=1260\text{m/s}$
To find:
Average speed, $v_{av}=?$

We know that,
$v_{rms}=\sqrt{\frac{3RT}{M}}$ and $v_{av}=\sqrt{\frac{8RT}{\pi M}}$
So, $\frac{v_{av}}{v_{rms}}=\frac{\sqrt{8/\pi }}{\sqrt{3}}$
$\Rightarrow \frac{v_{av}}{1260}=\sqrt{\frac{8}{3\pi }}$
$\Rightarrow v_{av}=1260\times \sqrt{\frac{8}{3\pi }}=1161\text{m/s}$