With increase in pressure, the mean free path

Options

A. increase
B. becomes zero
C. decrease
D. remains constant

Explanation

To solve the question regarding the relationship between pressure and mean free path, we will follow these steps:

### Step 1: Understand the Mean Free Path
The mean free path (λ) is the average distance a particle travels between collisions. It is influenced by factors such as the number of particles and their effective cross-sectional area.

### Step 2: Identify the Formula
The mean free path is given by the formula:
\[ \lambda = \frac{1}{\sqrt{2} \pi \sigma^2 \frac{n}{V}} \]
where:
- \( \sigma \) is the effective cross-sectional area for collisions,
- \( n \) is the number of particles,
- \( V \) is the volume.

### Step 3: Relate Pressure to Number of Particles
Pressure (P) in a gas is related to the number of particles per unit volume (n/V). As pressure increases, the number of particles per unit volume also increases, assuming temperature remains constant.

### Step 4: Analyze the Inverse Relationship
From the formula, we see that:
\[ \lambda \propto \frac{1}{\frac{n}{V}} \]
This indicates that as the number of particles per unit volume increases (which happens when pressure increases), the mean free path (λ) decreases.

### Step 5: Conclusion
Thus, with an increase in pressure, the mean free path decreases. Therefore, the answer to the question is that the mean free path decreases with an increase in pressure.

### Summary
- As pressure increases, the number of particles per unit volume increases.
- The mean free path is inversely proportional to the number of particles per unit volume.
- Therefore, with an increase in pressure, the mean free path decreases.

---