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Calculate the ratio of the mean free pat...

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

Text Solution

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`l_1 = (1)/(sqrt(2) pi n_ d_2^2)`
`l_2 = (1)/(sqrt(2) pi n_2 d_2^2)`
`(l_1)/(l_2) = (n_2 d_2^2)/(n_1 d_1^2)`
`(n_1 )/(n_2) =(5)/(3) rArr (n_2)/(n_1) = (3)/(5)`
`(d_1)/(d_2)= (4)/(5) rArr (d_2)/(d_1) = (5)/(4)`
`(l_1)/(l_2) = (3)/(5) xx (5)/(4) xx (5)/(4) = (15)/(16)`
`l_1 : l_2 = 15: 16`
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