Question

Let \( \bar{V} \), \( V_{\text{rms}} \), \( V_p \) denote the mean speed, root mean square speed, and most probable speed of the molecules of mass \( m \) in an ideal monoatomic gas at absolute temperature \( T \) Kelvin. Which statement(s) is/are correct?

• A. No molecules can have speed greater than \( \sqrt{2} V_{\text{rms}} \).
• B. No molecules can have speed less than \( \frac{V_p}{\sqrt{2}} \).
• C. \( V_p<\bar{V}<V_{\text{rms}} \).
• D. Average kinetic energy of a molecule is \( \frac{3}{4} m V_p^2 \).

Hint:

In an ideal monoatomic gas, the most probable speed, the mean speed, and the root mean square speed are related by the formulas \( V_p<\bar{V}<V_{\text{rms}} \). Always remember that the distribution of molecular speeds is not uniform, and different speeds correspond to different probabilities.