Mean Free Path

The mean free path is the distance that a molecule travels between collisions.

The mean free path is determined by the criterion that there is one molecule within the "collision tube" that is swept out by a molecular trajectory.

The criterion is: λ (N/V) π r² ≈ 1, where r is the radius of a molecule.

This gives:   λ = 1 / [(N/V) π r²]

Numerical estimates
Molecular cross-sectional area:   π r² ≈ 10^-19 m²
Molecular density (sea level):   N/V = P/kT ≈ 3 x 10²⁵ molecules/m³
Mean free path (sea level):   &lambda ≈ 10^-7m ≈ hundreds of molecular diameters

Mean free path for air at different altitudes:

Typical Molecular Speed

Determine the typical molecular speed by:

½ mv² ≈ KT   →   v &asymp (kT/m)^½ ≈ 500 m/s.

Typical Collision Time

Determine the typical collision time by:

τ = λ/v ≈ 10^-10 sec.