A mathematical model to calculate the234U/238U activity ratio (AR) in an aqueous phase in contact with rock/soil is presented. The model relies on the supply of238U by dissolution and that of234U by dissolution and preferential release from radiation damaged regions (recoil tracks). The model predicts that values of234U/238U AR>1 in the aqueous phase can be obtained only from weathering “virgin” surfaces. Thus, to account for the observed steady-state supply of234U excess to the oceans by the preferential leaching model, ‘virgin’ rock/soil surfaces would have to be continually exposed and weathered. The238U concentration and234U/238U AR in continental waters allow us to estimate the exposure rates of “virgin” rock/soil surfaces.