In this page of Hyperphysics, I am puzzled as to why there isn't any mass dependence in the expressions for mean free path.

Here are the two equations as mentioned in the website:

When only one molecule is moving: $$ l = \frac{1}{\pi d^2 n_v}$$

The mean free path when motion of all molecules is accounted for($l'$):

$$ l' = \frac{l}{\sqrt{2}}$$

Is there any intuitive way to understand this aspect of the result?

Why I expect mass to be there in the expression: We know that collisions, the quantity always conserved is momentum and that is product of mass and velocity, since there is a mass factor in momentum (something which is related to collisions) I suspected that there must be some dependence on the mean free path as well.

  • 1
    $\begingroup$ Can you clarify precisely why you'd expect there to be mass dependence? That might help focus the question somewhat. $\endgroup$
    – J. Murray
    Commented Jun 1, 2021 at 21:25
  • $\begingroup$ Note that the "size" of a particle seen by another particle changes with energy (really the cross-section interaction) and has little to do with rest mass. Some interactions do care about the type of particle, obviously, but not really the rest mass. $\endgroup$ Commented Jun 11, 2021 at 12:51

1 Answer 1


Small correction: the first expression is when only one molecule is moving and all of the "target" molecules are stationary.

Some intuition for lack of mass dependence: the mean free path concerns the distance between collisions. If you consider a billiard ball thrown across a table filled with billiard balls, the distance before the first collision only depends on the speed you throw the ball and the radius of the balls. The mass plays no role here, as in the molecule case.

Possible misconception: you might be thinking that bigger molecules will lead to a small mean free path. Indeed, molecules with a larger diameter will have a smaller mean free path. However, two molecules with the same diameter but different masses will have the same mean free path. The key factor is diameter, not mass.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.