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Mean Free Path

The average distance a particle travels between collisions, a key parameter in describing transport phenomena within a fluid or gas.
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The statement of the theorem

Let nn be the number density of particles in a volume VV, and let dd be the effective molecular diameter. Define the collision cross-section σ\sigma as σ=πd2\sigma = \pi d^2. The collision frequency ν\nu (collisions per unit time per particle) is given by the integral over relative velocities v⃗rel\vec{v}_{rel}: ν=⟨v⃗rel⋅A⃗⟩/⟨r⃗⋅A⃗⟩\nu = \langle \vec{v}_{rel} \cdot \vec{A} \rangle / \langle \vec{r} \cdot \vec{A} \rangle, where A⃗\vec{A} is the relative velocity vector and ⟨… ⟩\langle \dots \rangle denotes the ensemble average. For an ideal gas, the mean free path λ\lambda is defined as the average particle speed vˉ\bar{v} divided by the collision frequency ν\nu. Specifically, λ\lambda is derived from the relationship:\n\nλ=12πd2n\lambda = \frac{1}{\sqrt{2} \pi d^2 n}
Source: Wikipedia