The four passive samplers (quatrefoil) already described in a parallel paper, make it possible to obtain thin radiation sources, useful for alpha and beta counting by any passive and real-time detector. In the present paper, the applications of this quatrefoil for measuring radon gas by etch-track detectors will be described. In the case of radon measurements, different solids have been identified, with radon-sorption partition coefficients related to air from 1 to 2000. Uniquely compact radon badges can be obtained by using a layer of these solids facing an alpha track-etch detector. These radon badges make it possible to overcome most of the shortcomings of existing passive monitors. Moreover, these badges show promise for studying the radon solubility of polymer films.