# Mean Free Path

## Mean free Path

- On the basis of kinetic theory of gases, it is assumed that the molecules of a gas are continuously colliding against each other.

- Molecules move in straight line with constant speeds between two successive collisions.

- Thus path of a single molecule is a series of zig-zag paths of different lengths as shown in fig -.

- These paths of different lengths are called free paths of the molecule

- Mean Free Path is the average distance traversed by molecule between two successive collisions.

- If s is the Total path travelled in N
_{coll} collisions, then mean free path

λ= s/N_{coll}

Expression for mean free path :

- Consider a gas containing n molecules per unit volume.

- We assume that only one molecule which is under consideration is in motion while all others are at rest.

- If σ is the diameter of each molecule then the moving molecule will collide with all these molecules where centers lie within a distance from its centre as shown in fig

<

- If v is the velocity of the moving molecule then in one second it will collide with all molecules with in a distance σ between the centres.

- In one second it sweeps a volume πσ
^{2}v where any other molecule will collide with it.

- If n is the total number of molecules per unit volume, then nπσ
^{2}v is number of collisions a molecule suffers in one second.

- If v is the distance traversed by molecule in one second then mean free path is given by

λ = total distance traversed in one second /no. of collision suffered by the molecules

=v/πσ^{2}vn

=1/πσ^{2}n

- This expression was derived with the assumption that all the molecules are at rest except the one which is colliding with the others.

- However this assumption does not represent actual state of affair.

- More exact statement can be derived considering that all molecules are moving with all possible velocities in all possible directions.

- More exact relation found using distribution law of molecular speeds is

λ=1/(√2)πσ^{2}n

its derivation is beyond our scope.

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