Question

The average velocity of gas molecules is $400m/sec$. Calculate its rms velocity at the same temperature.

• A. $432m/sec$.
• B. $434m/sec$.
• C. $438m/sec$.
• D. $440m/sec$.

Answer 1

The correct option is B $434m/sec$.

As we know that,

$\text{Root mean square velocity}\left(V_{rms}\right)=\sqrt{\frac{3RT}{M}}$

$\text{Average velocity}\left(V_{average}\right)=\sqrt{\frac{8RT}{\pi M}}$

$\Rightarrow \frac{V_{rms}}{V_{av.}}=\frac{\left(\sqrt{\frac{3RT}{M}}\right)}{\left(\sqrt{\frac{8RT}{\pi M}}\right)}$

$\Rightarrow \frac{V_{rms}}{400}=\sqrt{3}\times \sqrt{\frac{\pi }{8}}$

$\Rightarrow V_{rms}=400\times 1.085=434.14\approx 434m/sec$