JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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:
- A Statement \(I\) is false but Statement \(II\) is true.
- B Statement \(I\) is true but Statement \(II\) is false.
- C Both Statement \(I\) and Statement \(II\) are false
- D Both Statement \(I\) and Statement \(II\) are true.
Answer & Solution
Correct Answer
(D) Both Statement \(I\) and Statement \(II\) are true.
Step-by-step Solution
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…
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