Mean free path

Intermediate

Average distance between collisions.

Key relationλ = 1/(√2 π d² n)

The average distance between collisions is λ = 1/(√2 π d²n). At STP air λ ≈ 70 nm; in a vacuum chamber it can be metres.

Worked example

Nitrogen at 1 atm: 68 nm.

Common mistake

Decreases with pressure and molecular size.

In more detail

The mean free path is the average distance a molecule travels between collisions. It depends on molecular size and gas density.

Vacuum systems are designed with mean free paths longer than the chamber size.
Electron microscopes operate in vacuum for long mean free paths.
Vacuum engineers use the mean free path to decide how low a pressure must be for particles to travel without colliding.

How does density affect it?

Higher density means shorter mean free path, because collisions are more frequent.

Is mean free path large in air?

At atmospheric pressure it is about 70 nanometres.

Does mean free path increase with temperature?

Only through its dependence on density. At a fixed pressure, a hotter gas is less dense, so the mean free path is longer.