Expressions are developed for the maximum concentrations and discharge rates of radioactive nuclide chains migrating through an adsorbing medium. These expressions are presented in terms of nondimensional parameters. Conditions are established that quantify the reconcentration effort of radionuclide chain migration in terms of the non-dimensional parameters. This approach provides a relatively simple mechanism for determining an upper bound to the concentrations or release rates of parent and daughter radionuclides in groundwater.