I was able to get the expression of probability P = ##e^{-x/\lambda}##. I followed the approach that the probability of no collision over ##f(x+dx) = f(x)(1-\frac{dx}{\lambda})## then expanded LHS using Taylor series. Then by taking the first two terms and neglecting the higher order terms, I...
If the distance between the centres of two molecules is σ, then imagining a a cylinder with radius σ the number of molecules can be given by πσ²cn where c = average velocity.
So mean free path can be given by λ = c/πσ²cn = 1/nπσ². But do I derive it from exp(-x/λ)?