The sensitivities of LR-115 detectors to 222Rn and 220Rn chains in front of hemispherical surfaces of different radii are calculated by the Monte Carlo method. The optimum radii of hemispherical caps are determined, as a result contributions of the different α-emitter nuclei to the track density are differentiated and non-uniform track distribution is avoided. It is demonstrated that if eight detectors are exposed separately in front of the same number of hemispherical surfaces of different radii, the concentrations of each α emitter in airborne and deposited states can be determined. A passive integrating system to calculate the concentrations of radon, thoron and their progenies in free air is given. © 2008 Elsevier Ltd. All rights reserved.