calculate the molecular diamter of He from its van der waal's constant b=24?? proper explanation reqd.!

Dear student!
b = 4 x volume occupied by molecules of 1 mole of the gas.

Since volume of each molecule of a gas = (4/3 πr³ ) no. of molecules /mol = avogadro no. N_A 

So, b = 4 x N_A x (4/3 πr³ )

So, r =  (3b/ 16 N_A x π)^1/3 

putting all the values we get 

 r = (3 x 24 / 16 x 6.022 x 10²³ x 3.14)^1/3  = 1.335 x 10⁸ cm³ = 133.5 pm 

Since, molecular diameter (d) = 2r

So, molecular diameter of He gas = 2 x  133.5 pm = 267 pm