  We give a very simple method for finding the exact analytical solution for
the problem of a particle undergoing diffusive motion on a flat potential in
the presence of a gaussian sink function. The diffusion process is modelled by
using one dimensional Smoluchowski equation. Our method provides solution in
Laplace domain, which is used to derive an analytical expression for time
average rate constant. Our solution can be used to analyze several related
problems involving diffusion-reaction systems.
