Calculate the mean free path of air molecules at STP. The diameter of `N_(2)` and `O_(2)` is about `3xx10^(-10)m`

Explanation

`P=1 atm =1.01xx10^(5)Pa,k_(B)=1.38xx10^(-23)JK^(-1),T=273K`
from ideal fgas law,`n=P/(kT)`
`n=(1.01xx10^(5))/(1.38xx10^(-23)xx273)=(1.01xx10^(5)xx10^(23))/(376.74)=2.68xx10^(-3)xx10^(28)`
`n=2.68xx10^(25)" molecules"//m^(3)`
Mean free path of the air molecule,
`gamma=1/(sqrt2pind^(2))=1/(1.414xx3.14xx2.68xx10^(25)xx(3xx10^(-10))^(2))`
`1/(1.0709xx10^(-18)xx10^(25))=0.9338xx1^(-7)`
` gamma =9.3xx10^(-8)m`