### Molecular Collisions (How Far, How Fast, How Long)

#### 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
r^{2} ≈ 1, where r is the radius of a molecule.

This gives: λ = 1 / [(N/V) ^{}π
r^{2}]

Numerical estimates

Molecular cross-sectional area:
π r^{2} ≈ 10^{-19}
m^{2}

Molecular density (sea level):
N/V = P/kT ≈ 3 x 10^{25}
molecules/m^{3}

Mean free path (sea level): &lambda ≈ 10^{-7}m ≈ hundreds of
molecular diameters

Mean free path for air at different altitudes:

Altitude | Mean Free Path |

Sea Level | 0.1 μm |

100 km | 16 cm |

300 km | 20 km |

#### Typical Molecular Speed

Determine the typical molecular speed by:

½ mv^{2}
≈ KT → v &asymp
(kT/m)^{½} ≈ 500 m/s.

#### Typical Collision Time

Determine the typical collision time by:

τ = λ/v ≈ 10^{-10} sec.