Information on radon occurrence in groundwater systems is important to assess risks from radon exposure. For this study we developed a novel passive method to measure for dissolved radon in groundwater using a coupled diffusive membrane encasing an alpha track (AT) detector. The membrane is gas permeable but water impermeable, which allows for the deployment of AT detectors in aqueous environments. The alpha track (AT) detectors measure the alpha decay of radon as it etches a film seated in the AT. Empirical relations have been developed to convert the etches or tracks from the film of the detectors to a radon concentration. Encasing the AT detectors in a membrane (called MAT detectors) prevents water from deteriorating the film and hindering the etching process. The datasets herein will be used to evaluate the efficacy of the MAT detectors to measure radon dissolved in groundwater . The datasets include (step 1) results from experiments to determine the diffusion rates of radon across various membrane types in a controlled, accredited, radon air chamber, and (step 2) field environmental samples of radon from wells to measure radon in the water column of the well and within the air above the water column of the well. Ambient radon air concentrations are also included as a background reference of radon in the environment. For step 1, the radon measurement results were used to quantify the diffusive properties of membranes subjected to a controlled radon air concentration within the radon air chamber. For step 2, the selected membrane and MAT detectors were deployed in the water column of wells and in the air column of wells located at several test sites throughout the country. Further for step 2, radon concentrations from the aqueous deployment of the MAT detectors were compared to concentrations from conventional radon groundwater samples measured with standard liquid scintillation analysis as a confirmatory measure.