Collisional Cross Section Formula:
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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.
The calculator uses the formula:
Where:
Explanation: The formula calculates the effective target area for collisions between two spherical molecules.
Details: This measurement is crucial for understanding gas dynamics, reaction rates, diffusion processes, and designing chemical reactors.
Tips: Enter the radii of both molecules in meters. The radii are typically half the distance between nuclei in diatomic molecules.
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.