Two gaseous molecules `A` and `B` are traveling towards each other. Let the mean free path of the molecule be `sigma` and `Z` be the collision number with other molecules at pressure `1 atm`. Answer the following questions
If the collision frequency of a gas at `1 atm` pressure is `Z`, then its collision frequency at `0.5 atm` is

Options

A. `1.0Z`
B. `0.707Z`
C. `2Z`
D. `0.5Z`

Explanation

To solve the problem, we need to understand the relationship between collision frequency and pressure. The collision frequency \( Z \) is inversely proportional to the pressure \( P \) of the gas.

### Step-by-Step Solution:

1. **Understanding Collision Frequency**:
The collision frequency \( Z \) at a given pressure is defined as the number of collisions per unit time. It is given that at a pressure of \( P_1 = 1 \, \text{atm} \), the collision frequency is \( Z_1 = Z \).

2. **Relationship Between Collision Frequency and Pressure**:
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