Mean free path of a gas molecule is

Options

A. inversely proportional to number of molecules per unit volume
B. Inversely proportional to diameter of molecule
C. directly proportional to square root of absolute temperature
D. directly proportional to molecular mass

Explanation

To find the mean free path of a gas molecule, we can follow these steps:

### Step 1: Understand the Definition
The mean free path (λ) is the average distance a molecule travels between collisions with other molecules. It is an important concept in the kinetic theory of gases.

### Step 2: Identify the Formula
The mean free path can be expressed mathematically using the formula:
\[ \lambda = \frac{1}{\sqrt{2} \pi d^2 n} \]
where:
- \( \lambda \) = mean free path
- \( d \) = diameter of the gas molecule
- \( n \) = number density of gas molecules (number of molecules per unit volume)

### Step 3: Analyze the Variables
From the formula, we can see that:
- The mean free path (λ) is inversely proportional to the number density (n). This means that as the number of molecules per unit volume increases, the mean free path decreases.
- The mean free path (λ) is also inversely proportional to the square of the diameter (d) of the molecules. This means that larger molecules will have a shorter mean free path due to more frequent collisions.

### Step 4: Relate to Temperature and Pressure
Another expression for the mean free path can be given in terms of temperature (T) and pressure (P):
\[ \lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P} \]
where:
- \( k_B \) = Boltzmann's constant
- \( T \) = absolute temperature
- \( P \) = pressure of the gas

### Step 5: Conclusion
From the analysis, we conclude that the mean free path is inversely proportional to the number density of gas molecules and the square of the diameter of the molecules. Therefore, the correct statement regarding the mean free path of a gas molecule is that it is inversely proportional to the number density of the gas.

### Final Answer
The mean free path of a gas molecule is inversely proportional to the number density of gas molecules.

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