## 1 Introduction  
Radon (Rn-222), a naturally occurring radioactive gas from the decay of uranium in rocks, soils, and water, can accumulate to high concentrations indoors. Prolonged exposure can pose significant health risks, specifically lung cancer [1]. Thoron (Rn-220), like radon, is a geographically produced radioactive gas but is a decay product of thorium [1]. While both gases pose considerable health risks due to their radioactive nature, thoron is often less discussed than radon. Recent assessments indicate that the contribution of thoron to radiation dose was previously misunderstood and, therefore, underestimated [2]. This underestimation stems from a historical focus on radon and gamma radiation in regulatory frameworks, neglecting the synergistic effects of thoron (UNSCEAR, 2022 [3]). One reason for this omission is the shorter half-life of thoron (55.6 s), compared to that of radon (3.8 days), which limits its ability to diffuse far from its source. Consequently, thoron concentrations typically decrease rapidly with distance from emitting surfaces, making it more challenging to detect and measure accurately compared to radon [4]. Despite these challenges, recent assessments indicate that the decay products of thoron, which are the actual contributors to the dose, have long enough half-lives to reach indoor environments even from the soil beneath building foundations [5]. However, it is understood that building materials and natural stones used in interiors are the primary sources of thoron [6]. Radon, including exhalation from soil, building materials, and water, remains the main source of radiation exposure for the general public, contributing almost 60% to the annual average dose in Ireland, as highlighted by the Environmental Protection Agency (EPA) and the Health Information and Quality Authority (HIQA) in their recent 'Ionizing Radiation--National Dose Report--June 2024' [7]. The report, which assesses the radiation exposure received from various sources, estimates over 8% contribution from thoron. Notably, Ireland's thoron contribution exceeds the global average of 5% reported by the World Health Organization (WHO, 2021 [8]), while approximately 6% of the radiation dose comes from gamma radiation originating from the ground. More homes are at risk from radon than previously thought, and about half a million (10%) of the total Irish population may be affected by high indoor radon levels. Furthermore, the average radiation dose received is 4.2 mSv [7], with more than two-thirds arising from radon and thoron. This remains among the highest in Europe [9], highlighting the importance of addressing both radon and thoron exposure, the major contributors to the dose, in indoor environments. This study introduces a novel methodology to bridge critical gaps in radiation risk assessment by integrating gamma radiation with radon and thoron exhalation dynamics under varied ventilation scenarios--an approach not yet standardized in existing guidelines [10]. Both the methodology and findings are directly applicable to radiation protection in other countries. Rock and aggregate samples were collected from materials of both Irish origin (quarries and stone markets) and non-Irish origin (imported), covering a wide range of rock types. As there is no legal requirement on radon and thoron levels in building materials, models were developed for different housing types to convert radon and thoron activity to effective dose (mSv), which is the standard metric in scientific and regulatory contexts to assess and verify building and construction limits. A 1 mSv annual dose level is suggested as the threshold for building materials used indoors [11]. Existing studies, like [12], focus primarily on radon or gamma radiation in isolation, whereas our model quantifies combined thresholds and ventilation efficacy.