Question

In a gas at STP, if n is the number density of the molecules and r is the radius of the molecule, then the mean free path of the molecule is inversely proportional to

• A. nr²
• B. nr
• C. n²r
• D. \(\sqrt nr\)
• E. \(\sqrt{nr}\)

Answer 1

The Correct Option is A

The mean free path \( \lambda \) of a molecule is the average distance a molecule travels before colliding with another molecule. According to kinetic theory, the mean free path is inversely proportional to the number density \( n \) of molecules and the square of the radius \( r \) of the molecule. The formula for the mean free path is: \[ \lambda \propto \frac{1}{{n r^2}} \] Thus, the mean free path is inversely proportional to \( n r^2 \).

The correct option is (A) : \(nr^2\)

Answer 2

The mean free path \( \lambda \) of a gas molecule is given by the formula:  

$$ \lambda = \frac{1}{\sqrt{2} \pi r^2 n} $$ 
where \( r \) = radius of a molecule, \( n \) = number density of molecules (number per unit volume). 

From the formula, it is clear that: $$ \lambda \propto \frac{1}{n r^2} $$ 
So, mean free path is inversely proportional to \( nr^2 \). 

Correct answer: nr²