Mean free path of molecules
Molecular model of gases · Physics
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Estimate the mean free path of nitrogen molecules in air at STP. Take molecular diameter d = 0.37 nm and number density n = 2.7 x 10^25 m^-3 (Loschmidt number). Solution: lambda = 1/(sqrt(2) n pi d^2) = 1/(1.414 x 2.7 x 10^25 x 3.1416 x (0.37 x 10^-9)^2). d^2 = 1.369 x 10^-19 m^2. Denominator = 1.414 x 2.7 x 10^25 x 3.1416 x 1.369 x 10^-19 = 1.64 x 10^7 m^-1. lambda = 6.1 x 10^-8 m = 61 nm - about 200 molecular diameters.