The mean free path of collision of gas melecules varies with its diameter (d) of the molecules as

Options

A. `d^(-1)`
B. `d^(-2)`
C. `d^(-3)`
D. `d^(-4)`

Explanation

To determine how the mean free path (λ) of gas molecules varies with the diameter (d) of the molecules, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Mean Free Path**: The mean free path (λ) is defined as the average distance traveled by a gas molecule between successive collisions. It is influenced by the size of the molecules and the density of the gas.

2. **Mean Free Path Formula**: The mean free path can be expressed mathematically as:
\[ \lambda = \frac{1}{\sqrt{2} \pi d^2} \]
where:
- \( \lambda \) is the mean free path,
- \( d \) is the diameter of the gas molecules.

3. **Analyze the Formula**: From the formula, we can see that the mean free path is inversely proportional to the square of the diameter of the molecules. This means that as the diameter increases, the mean free path decreases.

4. **Expressing the Relationship**: We can express the relationship mathematically:
\[ \lambda \propto \frac{1}{d^2} \]
This indicates that the mean free path is directly proportional to \( d^{-2} \).

5. **Conclusion**: Therefore, the mean free path of gas molecules varies with the diameter of the molecules as:
\[ \lambda \propto d^{-2} \]

### Final Answer:
The mean free path (λ) of gas molecules varies with the diameter (d) of the molecules as \( \lambda \propto d^{-2} \).

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