1. What is Collisional Cross Section?

Definition: Collisional cross section is defined as the area around a particle in which the center of another particle must be in order for a collision to occur.

Purpose: It's a fundamental concept in gas kinetics and molecular physics used to calculate collision rates and mean free paths.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sigma_{AB} \) — Collisional cross section (m²)
• \( r_A \) — Radius of Molecule A (m)
• \( r_B \) — Radius of Molecule B (m)
• \( \pi \) — Archimedes' constant (~3.14159)

Explanation: The formula calculates the effective target area for collisions between two spherical molecules.

3. Importance of Collisional Cross Section

Details: This measurement is crucial for understanding gas dynamics, reaction rates, diffusion processes, and designing chemical reactors.

4. Using the Calculator

Tips: Enter the radii of both molecules in meters. The radii are typically half the distance between nuclei in diatomic molecules.

5. Frequently Asked Questions (FAQ)

Q1: What if the molecules are the same?
A: For identical molecules (A = B), the formula becomes \( \sigma_{AA} = \pi \times (2r_A)^2 \).

Q2: How does temperature affect the cross section?
A: This simple hard-sphere model doesn't account for temperature. For more accuracy, consider potential energy surfaces.

Q3: What units should I use?
A: The calculator uses meters for radius inputs, resulting in m² for the cross section. Convert from Ångströms (1Å = 10⁻¹⁰m) if needed.

Q4: Is this valid for non-spherical molecules?
A: This is a simplified model. For complex shapes, consider orientation-dependent cross sections.

Q5: How does this relate to mean free path?
A: Mean free path \( \lambda = 1/(\sqrt{2}n\sigma) \), where n is number density.