## 3 Results and Discussion
### Effect of Ventilation  
Table 5 presents a worst-case scenario model for radon and thoron dose reduction in a one-bedroom house, focusing on samples with radon and thoron dose contributions higher than 0.3 mSv. The analysis considers two configurations: 10% and 30% of the surface area covered by stone, and the impact of varying air ventilation rates. At a ventilation rate of 0.5 m\({}^{3}\)/h, with 10% surface coverage, doses range from approximately 0.041 to 1.327 mSv. Increasing the ventilation to 2 m\({}^{3}\)/h reduces these doses to a range of 0.079 to 0.662 mSv, representing a reduction of about 50-80%. When the surface coverage is increased to 30%, the doses are generally higher due to the greater exposure, but the relative reduction remains similar. At the highest ventilation rate of 10 m\({}^{3}\)/h, the doses decrease to a range of 0.005 to 0.126 mSv, corresponding to a reduction of approximately 90-95%, regardless of surface coverage.  
Notably, the reduction in thoron dose is more significant than the reduction in radon dose due to ventilation. This can be attributed to the shorter half-life of thoron (approximately 55.6 s) compared to radon (3.8 days). Thoron decays more rapidly, meaning that effective ventilation can remove thoron gas from indoor environments before it has a chance to decay and contribute significantly to radiation dose. As a result, higher ventilation rates are particularly effective in reducing thoron levels, leading to the observed substantial  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{4}{c}{**Dose mSv.**} & \multicolumn{4}{c}{**Surface Activity Bq m\({}^{-2}\)**} & \multicolumn{4}{c}{**Air Ventilation Rate**} \\ \cline{4-11} \multicolumn{1}{c}{**(Worst Case Scenario with No Ventilation)**} & \multicolumn{4}{c}{**Surface Activity Bq m\({}^{-2}\)**} & \multicolumn{4}{c}{**Low**} & \multicolumn{2}{c}{**Medium**} & \multicolumn{2}{c}{**High**} \\ \hline Sample & I index & Radon & Thoron & Thoron & Radon & 0.5 m\({}^{3}\)/h & 2 m\({}^{3}\)/h & 10 m\({}^{3}\)/h \\
37 & 0.291 & 1.627 & 3.612 & 782 & 95.28 & 1.327 & 2.528 & 0.332 & 0.632 & 0.066 & 0.126 \\
12 & 0.188 & 0.916 & 2.034 & 440 & 45.09 & 0.685 & 1.305 & 0.171 reductions in thoron dose across different ventilation scenarios. Based on the charts of Figure 6, a formula was developed to calculate the reduced dose from radon and thoron because of active air ventilation.  
\[\text{Reduced Dose after Ventilation = 0. 1192Q}^{-1.001}\times\text{e}(^{0.7805. Dose Initial}) \tag{6}\]  
To mitigate indoor radiation exposure, practitioners first measure the annual radiation dose from radon, thoron, and gamma sources using detectors, such as the RAD7 (Durridge, Billerica, MA, USA). In Ireland, where the average annual radiation dose is 4.2 mSv, approximately 60% (2.5 mSv/year) comes from radon and thoron. If 0.4 mSv/year is also attributed to gamma radiation (total = 2.9 mSv/year), to meet the recommended safety threshold of 1 mSv/year, the radon/thoron contribution must be reduced to 0.6 mSv/year (because 1 mSv/year total \(-\) 0.4 mSv/year gamma = 0.6 mSv/year). Using an empirical model derived from experimental data, the required ventilation rate (Q) is calculated to be 1.4 m\({}^{3}\)/h. This airflow can be achieved with a small exhaust fan or mechanical ventilation system. Because of the extremely short half-life of thoron (55.6 s), even modest ventilation drastically reduces its dose contribution. However, the longer half-life of radon (3.8 days) means additional measures--such as sealing foundation cracks, installing radon barriers, or substituting high-exhalation building materials (e.g., granite) with low-emission alternatives (e.g., limestone)--are often necessary for long-term mitigation. Post-installation validation using RAD7 detectors confirms compliance with the 1 mSv/year threshold and accounts for real-world variables, like uneven airflow or material heterogeneity.