# Mean free path

1. Nov 21, 2009

### n.hirsch1

1. The problem statement, all variables and given/known data
A test tube of cylindrical shape having a length of 10 cm and a diameter of 2 cm contains 20 * 10 ^23 molecules (molecular size d = 3 * 10^-10 m). What is the mean free path of these molecules??

2. Relevant equations
λ = 1/ pi * d^2 * n

3. The attempt at a solution
This is an equation I have never used before and my text book doesn't help with either. I tried to solve it by:
1 / pi * (2 cm)^2 * (20 * 10^23 / 3*10^-12 cm)
I haven't ever done something like it before, am I on the right track with this?

2. Nov 21, 2009

### ehild

The mean free path is the distance between two subsequent collisions between the molecules. When the molecules touch each other, their centres are d distance apart (d is the diameter). The molecules are in motions and will collide with all molecules along their path get closer to centre -to centre than the diameter. Look at the blue molecule in the figure: When it travels along a path of length L it will collide with all molecules with centre confined in a cylinder of diameter 2d and length L.
If the density of molecules is n, the number of molecules in this cylinder is N= n*d^2*pi*L, there are N collisions along L length: the distance travelled between two subsequent collision is

$$\lambda = \frac{L}{N}= \frac{1}{d^2\pi n}$$

You know the number of the molecules in a known volume, so you can determine n.

ehild

Last edited: Jun 29, 2010