Question

The average velocity of a gas molecule is 400 m/s. the rms velocity at the same temperature will be:

• A. 550 m/s
• B. 434 m/s
• C. 750 m/s
• D. 350 m/s

Answer 1

The correct option is B 434 m/s

$C_{av}=\sqrt{\frac{8RT}{\pi M}}$ $C_{rms}=\sqrt{\frac{3RT}{M}}$

$\frac{C_{rms}}{C_{av}}=\sqrt{\frac{3RT}{M}}\times \sqrt{\frac{piM}{8RT}}=\sqrt{\frac{3\pi }{8}}=1.085$

$\therefore C_{rms}=1.085\times C_{av}=1.085\times 400=434m/s$