Calculate the ratio of the mean free path of molecules of two gases ig the ratio of the numbers denusity per `cm^(3)` of the gases is `5:3` and the ratio of the diameters of the molecules of the gases is `4:5`

Explanation

Given, ratio of the numers density `n_(1)/n _(2)=5/3`
Ratio of the diameters, `d_(1)/d_(2)=4/5`
Mean free path of the molecules of first gas, `lambda_(1)=1/(sqrt2pin_(1)d_(1)^(2))`
Simlary, mean free path of the second gas, `lambda_(2)=1/(sqrt2pin_(2)d_(2)^(2))`
`therefore` Ration of `lambda_(1)` and `lambda_(2)`
`lambda_(1)/(lambda2)=(n_(2)d_(2)^(2))/(n_(1)d_(1)^(2))=3/5xx5/4xx5/1=15/16`
`rArr" " lambda_(1):lambda_(2)=15:16`