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

Explanation

One moles of an ideal gas at S.T.P occupies a volume of `22.4xx10^(-3)m^3`
`("Number of moles")/m^3=(6.023xx10^23)/(22.4xx10^(-3))`
`n = 2.69xx10^(25)("moles")/m^3`
In terms of number of molecules and radius the mean free path at S.T.P can be written as,
`lamda=1/(4pisqrt2r^2n)`
Radius `r=3/2xx10^(-10)=1.5xx10^(-10)`
`:.lamda=1/(4xx3.14xx1.414xx(1.5xx10^(-10))^2xx2.69xx10^(25))`
`{:("Mean free"),("path"):}}=9xx10^(-8)m`.