Question

The rms velocity of a gas molecule of mass \( m \) at a given temperature is proportional to

• A. \( m^0 \)
• B. \( m \)
• C. \( \sqrt{m} \)
• D. \( \frac{1}{\sqrt{m}} \)

Hint:

The rms velocity is inversely proportional to the square root of the molecular mass. This relationship is important in understanding the kinetic theory of gases.

Answer 1

The Correct Option is D

The rms velocity of a gas molecule is given by the formula: \[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \] where \( k \) is the Boltzmann constant, \( T \) is the temperature, and \( m \) is the mass of the molecule. Thus, the rms velocity is inversely proportional to the square root of the mass: \[ v_{\text{rms}} \propto \frac{1}{\sqrt{m}} \] So, the correct answer is \( \frac{1}{\sqrt{m}} \).