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 option given below:

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) Both Statement \(I\) and Statement \(II\) are true.

Detailed explanation

The mean free path \( \lambda \) of gas molecules is given by:

\( \lambda = \frac{1}{\sqrt{2}\,\pi d^2 n} \)

where \( d \) is the molecular diameter and \( n \) is the number density. Hence,

\( \lambda \propto \frac{1}{d^2} \)

Therefore, Statement (I) is true.

The average kinetic energy of a gas molecule is:

\( \langle E_k \rangle = \frac{3}{2}kT \)

which shows that the average kinetic energy is directly proportional to the absolute temperature \( T \). Hence, Statement (II) is also true.

However, the mean free path depends on molecular diameter and number density, not directly on the average kinetic energy or temperature.

Both Statement (I) and Statement (II) are true, but Statement (II) is not the correct explanation of Statement (I).

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