Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters `1Å` and `2Å`. The gases may be considered under indentical conditions of temperature pressure and volume.

Explanation

Mean free path of a molecule is given by
`l=(1)/(sqrt(2)d^(2)n)`
Where n = number of molecules`//`volume
d= diameter of the molecule
Now . We can write `l prop (1)/(d^(2))`
`" Given "" "d_(1) =1 Å, d_(2) = 2Å`
`" As "" "l_(1) prop (1)/(d_(1)^(2)) " and " l_(2) prop (1)/(d_(2)^(2))`
`rArr So " "(l_(1))/(l_(2)) =((d_(2))/(d_(1)))^(2) =((2)/(1))^(2)=(4)/(1)`
`"Hence "" "l_(1) : l_(2) = 4 :1`