Calculate the fraction of gas molecules which have the mean-free-path in the range λ to 2λ.
Fraction of gas molecules that do not undergo collisions after path length x is exp(−x/λ). Therefore the fraction of molecules that has free path values between λ to 2λ is
f = exp(−λ/λ) − exp(−2λ/λ)
= exp(−1) − exp(−2)
= 0.37 − 0.14 = 0.23
