Sutton's diffusion equation, which is commonly used for the computation of atmospheric dispersion of fission products, is modified to account for the effect of dilution of the fission products due to mixing of the contaminated air inside the reactor building with clean air prior to exhaust. The effect of radioactive decay is also considered. The resulting integral equation is solved for a specific example using a Romberg integration subroutine and the application of the equation to a washout calculation is described.