Question

The root mean square velocity of a gas is given by

• A. $\sqrt{\frac{3RT}{M}}$
• B. $\sqrt{\frac{8RT}{\pi M}}$
• C. $\sqrt{\frac{2RT}{M}}$
• D. $\sqrt{\frac{8RT}{M}}$

Hint:

Formula Tip: RMS velocity is always given by \[ u_{rms}=\sqrt{\frac{3RT}{M}} \] Remember: \[ u_{rms} > u_{avg} > u_{mp} \]

Answer 1

The Correct Option is A

Concept:
According to kinetic theory of gases, RMS velocity represents the square root of the average of squares of molecular velocities.
Step 1:
The RMS velocity is: \[ u_{rms}=\sqrt{\frac{3RT}{M}} \]
Step 2:
Where:
• $R$ = gas constant
• $T$ = absolute temperature
• $M$ = molar mass
Step 3:
\[ u_{avg}=\sqrt{\frac{8RT}{\pi M}} \] \[ u_{mp}=\sqrt{\frac{2RT}{M}} \] Thus options (2) and (3) correspond to average and most probable velocity.
Step 4:
Hence RMS velocity is: \[ \boxed{\sqrt{\frac{3RT}{M}}} \] \[ \boxed{\text{Correct Option = (1)}} \]