What is the mean free path?

• A. The average distance traveled by a gas molecule between collisions
• B. The average speed of a gas molecule
• C. The average distance between energy levels
• D. The average time between collisions

Answer: (A)

The mean free path is the average distance a gas molecule travels before it collides with another molecule. It’s a length scale, not a speed or a time, so it tells you how far a molecule goes between interactions rather than how fast it moves.

This distance gets smaller as the gas becomes denser or as the molecules get larger (larger collision cross section), because collisions become more frequent. Conversely, in a dilute gas or with smaller molecules, the mean free path is longer. A handy way to think about it is that you’re measuring how far, on average, a molecule can go in a straight line before bumping into another one.

In kinetic theory, the mean free path is often written as λ ≈ 1/(√2 n σ) for hard-sphere molecules, where n is the number density and σ is the collision cross section. This shows the inverse relationship with both how many particles are around and how big the effective target area is.

Note how this differs from the mean free time, which is the time between collisions (τ = λ/v, with v a characteristic speed). The other options refer to speed or to energy-level spacing, which are not what the mean free path measures.