Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2.0 atm and temperature `17^(@)C`. Take the radius of a nitrogen molecule to be roughly 1.0 Å. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of `N_(2)` = 28.0 u).

Explanation

Mean free path `lambda=(1)/(sqrt2 pid^(2)lambda)`
`lambda=(K_B T)/(sqrt2 pid^(2)p) (p=nK_B T)`
`lambda=((1.38 xx 10-23) (290))/((1.414) (3.14) (2 xx 10^(-10)) (2.026 xx 10^(5)))=1.1 xx 10-7`
`V_(rms)=sqrt((3K_BT)/(m))=sqrt((3 xx 1.38 xx 10^(-23) xx 290))/(28 xx 1.66 xx 10^(-27)) =5.1 xx 10^(2)m//s`
collisioin frequency
`f=(V_(rms))/(lambda)=(5.1 xx 10^(2))/(1.1 xx 10^(-7))=4.6 xx 10^(9)s^(-1)`.