Given below are two statements :

Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.

Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.

In the light of the above statements, choose the correct answer from the options given below :

<p>Let's analyze the given statements one by one in detail:</p> <p><b>Statement (I): The mean free path of gas molecules is inversely proportional to the square of molecular diameter.</b></p> <p>The mean free path ($ \lambda $) of gas molecules is the average distance a molecule travels before colliding with another molecule. The formula for the mean free path in terms of molecular diameter ($ d $) is given by:</p> <p>$\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$</p> <p>Here, $ k_B $ is the Boltzmann constant, $ T $ is the temperature, and $ P $ is the pressure. From this equation, it is evident that the mean free path ($ \lambda $) is inversely proportional to the square of the molecular diameter ($ d^2 $). Hence, Statement I is <b>true</b>.</p> <p><b>Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.</b></p> <p>The average kinetic energy ($ E_{\text{avg}} $) of gas molecules is given by:</p> <p>$E_{\text{avg}} = \frac{3}{2} k_B T$</p> <p>where $ k_B $ is the Boltzmann constant and $ T $ is the absolute temperature. This shows that the average kinetic energy is directly proportional to the absolute temperature of the gas. Hence, Statement II is <b>true</b>.</p> <p>Considering the analysis above, the correct answer is:</p> <p><b>Option B</b><br>Both Statement I and Statement II are true</p>