## 2 Materials and Methods
### Dose Conversion and Ventilation Models
#### 2.4.2 Dose from Radon and Thoron  
Calculating the dose from radon and thoron in indoor environments is a complex process due to the various factors influencing the concentration and distribution of these gases [5]. Radon and thoron levels depend on several variables, including the type of building materials used, the ventilation rate, the design of the building, and the time occupants spend indoors. To address these complexities, three common housing scenarios are considered: a one-bedroom house, a two-bedroom house, and a three-bedroom house. A model of each housing scenario was created to estimate the effective (net) volumes for different building type scenarios. This technique helped to visualize and calculate the surface areas of potential radon sources in homes, determine the total volume of furniture  
Figure 1: Radon/thoron and gamma measurement setup at the Environmental Radioactivity Laboratory, Trinity Center for the Environment.  
inside the house, estimate the net air volumes for different housing types, and analyze data from numerous real-world cases. By studying dozens of actual instances, we approximated the range of surface areas of natural stones--recognized sources of radon and thoron in indoor environments--that could be present in each housing type (Table 1). Additionally, to calculate the effective volume of indoor spaces, we subtracted the volume occupied by furniture and appliances from the total volume of the house. This allowed an estimation of the effective space in which radon and thoron can accumulate, providing a more accurate calculation of the potential exposure doses for the occupants.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & \multicolumn{2}{c}{**1-Bedroom House**} & \multicolumn{2}{c}{**2-Bedroom House**} & \multicolumn{2}{c}{**3-Bedroom House**} \\  & \multicolumn{2}{c}{**(See Figure 2)**} & & \\ \hline V effective (V\({}_{\text{eff}}\)) m\({}^{3}\) & 121.16 & 230 & 380 \\ Stone Surface Area (s) range m\({}^{2}\) (10 & & & \\ to 30\% of the total Surface Area of & 42–80 & 72–123 & 118–180 \\ the house) & & & \\ \hline \hline \end{tabular}  
* F\({}_{\text{Rn-222}}\) and F\({}_{\text{Rn-220}}\) are radon and thoron conversion factors equal to 2.7 \(\times\) 10\({}^{-6}\) and 7.0 \(\times\) 10\({}^{-6}\) mSv per Bqm\({}^{-3}\), respectively. C\({}_{\text{Rn-222}}\) and C\({}_{\text{Rn-222}}\) represent the average radon and thoron exhalation per surface Area (Bqm\({}^{-2}\)).  
\end{table}
Table 1: Annual gamma, radon, and thoron doses (mSv/year) for Irish building materials. Altered granites show the highest combined doses.  
Figure 2: Schematic model for the visualization of radon and thoron emission and the sources of radioactive gases and gamma radiation (including kitchen worktops, kitchen island, floor, tiles, and hand basin top) within a one-bedroom house. In this instance, the effective volume is estimated at 121.6 m\({}^{3}\), with stone (e.g., granite, limestone and sandstone) coverage ranging from 42 to 80 m\({}^{2}\).  
Equation (4) for calculation of Dose [20; 21]:  
\[\text{Dose (mSv)}=(\text{F}_{\text{Rn-222}}\text{ C}_{\text{Rn-222}}\text{ (Bqm}^{-2})+\text{F}_{\text{Rn-220}}\text{ C}_{\text{Rn-220}}\text{ (Bqm}^{-2}))\text{ S(m}^{2})/\text{V}_{\text{eff}}\text{ (m}^{3}) \tag{4}\]