How Long to Achieve Uniform Mixture in Helium Gas Experiment?

[Jameskd]

Homework Statement

Estimating how long it would take to achieve a uniform mixture.

Relevant Equations

J = DA dC/dx, C=N/V

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.

I am unsure how to begin this question, for starters I thought of a high concentration to a low concentration, so where the valve is to the rest of the sphere. But I'm just struggling to start. Any tips?

Thank you in advance.

 

[Chestermiller]

Start out by writing down for us the equation for the time dependence of the rms distance in random walk.