Question

Root mean square velocity of a gas molecule is proportional to

• A. $m^{1/2}$
• B. $m^0$
• C. $m^{-1/2}$
• D. m

Answer 1

The Correct Option is C

To determine the correct answer, let's consider the concept of the root mean square (RMS) velocity of gas molecules as per the principles of kinetic theory of gases.

The RMS velocity is given by the formula:

v_{\text{rms}} = \sqrt{\frac{3kT}{m}}

where:

• v_{\text{rms}} is the root mean square velocity.
• k is the Boltzmann constant.
• T is the absolute temperature.
• m is the mass of the gas molecule.

In this formula, the RMS velocity is inversely proportional to the square root of the mass of the gas molecule. Therefore, we can express this relationship as:

v_{\text{rms}} \propto \frac{1}{\sqrt{m}} = m^{-1/2}

This confirms that the root mean square velocity of a gas molecule is proportional to m^{-1/2}.

Let's evaluate the given options to confirm:

• m^{1/2}: Suggests a direct proportion to the square root of mass, which is incorrect.
• m^0: Suggests no dependence on mass, which is incorrect.
• m^{-1/2}: Correctly indicates an inverse proportionality to the square root of mass.
• m: Suggests a direct proportion to mass, which is incorrect.

Thus, the correct answer is m^{-1/2}.