Recently I have been studying Kinetic Theory Of Gases, with one of the topics as collision frequency. I know that collision frequency is inverse of relaxation time which is also the measure of number of collisions per unit volume per unit time. But I am stuck while calculating "number of collisions per unit distance". I looked up on internet and somewhere it was mentioned that it was the inverse of mean free path. Please help me through this.
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The number of collisions $n$ per distance $d$, so the calculation $n/d$, is a measure with a unit like this: $\frac{1}{\mathrm m}$. This is a measure of how many times a particle will collide with structural atoms if it moves over e.g. one metre (or nanometre or other preferred unit of distance). In intuitive terms, maybe a particle collides with 5 atoms per metre.
Now turn this around.
How many metres can the particle move before colliding with an atom? If it collides with 5 for every metre it has moved, then on average it will collide after every $1/5$ metre. In other words, it's path is only free for it to travel along undisturbed for on average $1/5$ metres. This value is found as simply the reciprocal, $\lambda=d/n$, and the unit will be $\mathrm m$.
Instead of "collisions per metre" we are here looking at "metres per collision". Remember that this is an average, a mean. We refer to this measure as the mean free path $\lambda$.
