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A number of studies have used C-14 to estimate ages of unconfined ground water and to infer recharge rates. Some of these studies have been in arid or semi-arid regions, and the inferred recharge rates have been very low. The implicit assumption has been that the vertical movement of C-14 within the unconfined ground water is entirely by convective processes. In this paper we extend the ground water C-14 model of previous workers to include diffusion within the aquifer, and show that for recharge rates less than approximately 1 mm year-1, diffusion can be important in defining the C-14 distribution. For this reason it is not possible to use C-14 profiles to estimate recharge in these cases. We also show how neglecting diffusion can lead to serious underestimates of groundwater ages in unconfined aquifers where recharge rates are similarly low.