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- Homework Statement
- The probability of gas molecules surviving a distance x without collision is given by exp(-x/λ), use this expression to prove λ = 1/nπσ² where σ = mean diameter and n = number density.

- Relevant Equations
- f(x) = exp(-x/λ)

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)?

So mean free path can be given by λ = c/πσ²cn = 1/nπσ². But do I derive it from exp(-x/λ)?