## 3 Results and Discussion  
### Radon/Thoron Exhalation Rates vs. Radionuclide Activity  
For each sample, radon and thoron exhalation rates were calculated based on the equilibrium thoron activity and radon growth model as shown in Figure 3. Supplementary Table S2 shows the detailed measurements of gamma radiation and radon thoron exhalation rates for each sample. Table 2 shows the statistics of the radionuclide activity of the samples grouped based on their geology. Along with Figure 4, the table provides a comprehensive comparison of radionuclide activity and radon/thoron exhalation rates across various building materials, with an emphasis on the range and mean values to highlight differences in  
Figure 3: Radon and thoron growth models for an Irish granite (sample #37). radiological properties. Granite displays the widest range in thorium (Th) concentrations (2.09 to 7.94 mg/kg) and the highest variability in thoron (Rn-220) exhalation rates, ranging from 10 to 45,889 Bq m\({}^{-2}\) h\({}^{-1}\), with a mean of 6396 Bq m\({}^{-2}\) h\({}^{-1}\). This significant variation is largely due to the differing mineralogical composition of granite, which can include minerals, like thorite and monazite, that are rich in thorium and contribute to higher thoron emissions. Some of the granites with high thoron exhalation rates were found to be highly altered (e.g., Donegal and Galway areas). Higher modal % of Th-bearing accessory minerals and the secondary porosity and fractured nature of altered granite could facilitate the escape of thoron gas, enhancing its potential to contribute to indoor radiation exposure [25]. Quartzite also exhibits notable radiological properties, with thoron exhalation rates ranging from 103 to 6091 Bq m\({}^{-2}\) h\({}^{-1}\) and a mean of 1637 Bq m\({}^{-2}\) h\({}^{-1}\). The variability in thoron exhalation from quartzite can be attributed to the presence of thorium-bearing minerals, such as monazite and zircon, which contribute to higher emissions. This suggests that quartzite, like granite, can potentially contribute to indoor radiation levels, particularly when used extensively in building construction [17,26]. In contrast, materials, like gypsum and rock-types, such as limestone, show much lower and more consistent thoron exhalation rates. For instance, gypsum has a uniform thoron exhalation rate of 21 Bq m\({}^{-2}\) h\({}^{-1}\), with a mean thorium concentration of 2.31 mg/kg, indicating a lower radiological risk. The consistency in the thoron exhalation rates of gypsum can be linked to its homogeneous mineral composition. Limestone exhibits a broader range of thoron exhalation (15 to 15,213 Bq m\({}^{-2}\) h\({}^{-1}\)), but with a much lower mean of 1352 Bq m\({}^{-2}\) h\({}^{-1}\), which is still significantly lower than that of granite. This is likely due to the predominance of CaCO\({}_{3}\) with minimal thorium content, leading to reduced thoron emissions [2]. The Pearson correlation coefficients in Table 3 provide important insights into the relationships between various radon and thoron exhalation rates, surface emissions, and radionuclide activities. The strong positive correlations between thoron exhalation rates (E220 Rn) and its surface emission (r = 0.96), as well as between radon exhalation rates (E222 Rn) and its surface emission (r = 0.89), underscore a direct and robust link between the amount of these gases emitted and their measurable surface presence. This indicates that increases in the exhalation rates of thoron and radon correspond to proportional increases in their respective surface emissions. In contrast, the moderate correlation between E220 Rn and E222 Rn (r = 0.60) suggests a more nuanced relationship. While there is some association between thoron and radon exhalation rates, the correlation is less pronounced compared to the correlation between each gas's exhalation rate and its surface emission. This implies that factors influencing the emission of radon may not directly impact thoron, and vice versa.