Diffusion is an important mechanism in the transport and deposition of very small particles from gas streams to the surfaces of a conduit. Based on the heat/mass analogy, an analytical model has been formulated for the deposition of the precursor (i.e., the fission product that first enters the gas stream) and for its first and second daughter products from laminar, and turbulent gas streams under steady-state conditions. The model is strictly applicable to deposition in the isothermal regions; axial temperature gradients have been found to alter the deposition pattern. Activity deposited on the surfaces of a conduit has been correlated with this model both for the molecular and larger size particles (0.004 μ) assuming a perfect-sink condition at the wall surface. There is experimental evidence that wall surfaces do not always act as a perfect sink for the colliding particles; effects of an imperfect-retention scheme have been included in the analysis by introducing a factor for the effectiveness of the wall surfaces in retaining the particles. No rational evaluation of this factor is known. However, activity deposited on such surfaces can be correlated with the model developed if a suitable value is chosen for this factor.