Mean Free Path (λ = 1/(√2·π·d²·n) = kBT/(√2·π·d²·P))
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λ = 1/(√2·π·d²·n) = kBT/(√2·π·d²·P)
What each symbol means
| Symbol | What it stands for |
|---|---|
| P | Pressure of gas (Pa) |
| T | Absolute temperature (K) |
| d | Effective diameter of a molecule (m) |
| n | Number density = N/V = P/(kBT) (molecules per m³) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| λ | Mean free path — average distance between consecutive collisions (m) |
When to use this
Valid for ideal gases. The √2 factor arises from using relative velocity between molecules (v_rel = √2 × v_avg for Maxwell distribution). πd² is the collision cross-section. λ ∝ T/P: increases with temperature, decreases with pressure. At STP for N₂: λ ≈ 10⁻⁷ m ≈ 1500 molecular diameters.