The heat conductivity of helium is `8.7` times that of argon (under standard conditions). Find the radio of effective diameters of argon and helium atoms.

Explanation

`k = (1)/(3) lt v gt lamda rho c_v`
=`(1)/(3) sqrt((8 kT)/(m pi)) (1)/(sqrt(2) pi d^2 n) mn (C_V)/(M)`
`(C_V` is the specific heat capacity which is `(C_V)/(M) )`. Now `C_V` is the same for all monoatomic gases such as `He` and `A`. Thus
`k alpha (1)/(sqrt(M) d^2)`
or `(k_(He))/(k_A) = 8.7 = (sqrt(M_A) d_A^2)/(sqrt(M_(He) d_H^2)) = sqrt(10) (d_A^2)/(d_(He)^2)`
`(d_A)/(d_(He)) = sqrt((8.7)/(sqrt(10))) = 1.658 ~~ 1.7`.