Solving Diffusion Question: Estimating Time for Uniform Mixture

[Ryan Hillier]

1.
Homework Statement Question
This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of
diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small
amount of 3He gas is introduced through a valve on one side of the vessel. Make a
rough estimate of how long one must wait before a uniform mixture has formed (use
the result for the time dependence of the root mean square travel distance in a
random walk in 1D.) Suggest a better way to make a uniform mixture.

Homework Equations

Area = pi (diameter/2)^2 , pv =nrt , ficks law of diffusion , Mass flux = 1/3lv

The Attempt at a Solution

I am not sure where to start from. I am reading about fick's law of diffusion right now however I'd love tobe pointed out in the right direction.

Since the question asks for time dependence then isn't second law the most obvious equation to use ?
edit: hm.. as i was reading i came across this idea.. how about i get the area first, then divide volume by area to give me the 'length' which i can plug into ficks equation if I am not mistaken.
Appreciate your help.

 

[mfb]

If you need a length, there is one given in the problem statement: 1 meter. A factor of 2 does not matter here.