A clay cap is used to prevent water infiltration into soil that is uniformly contaminated with plutonium. The soil is contaminated to a depth of 10 meters and is covered on top by a 0.5 meter thick clay cap. The intergranular pores in the soil and clay are fully water saturated. The aqueous diffusion coefficient for plutonium is 3 x 10-5 cm2 /s. The concentration profile for an extended source of infinite extent is given by: . C(x,t) = 0.5Coerfc x 4Dt " # $ % & ' clay liner water with 100 mg/L phosphate rapidly flowing groundwater

a) Determine the concentration profile of plutonium in the clay cap after 1 week, 1 month, 1 year, and 10 years.

b) What is the maximum time for which the solution of an infinite source is valid?

c) Estimate how long it takes for the concentration at the center of the clay cap to reach 0.10 Co.