Estimate the mean free path and collision frequency of a nitrogen molecule in a cylinder containing nitrogen at 2 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 nitrogen = 28.0 u).

Explanation

Mean free path `lambda=(1)/(sqrt(2)pid^(2)n)`
`lambda=(k_(B)T)/(sqrt(2)pi d^(2)P)(P=nK_(B)T)`
`lambda=((1.38xx10^(-23))(290))/((1.414)(3.14)(2xx10^(-10))^(2)(2.026xx10^(5)))=1.1xx10^(-7)`
`v_(rms)=sqrt((3k_(B)T)/(m))=sqrt((3xx1.38xx10^(-23)xx290)/(28xx1.66xx10^(-27)))=5.1xx10^(2)m//s`
`therefore f=(v_(rms))/(lambda)=(5.1xx10^(2))/(1.1xx10^(-7))=4.6xx10^(9)s^(-1)`