## 3 Materials and Methods
It is worth noting that environmental factors, particularly humidity and temperature, can affect radon exhalation from building materials [63]. Elevated humidity can inhibit radon diffusion by partially saturating pore spaces, whereas temperature changes can modify the radon emanation coefficient due to changes in mineral structure and air density [63]. Although our laboratory experiments were carried out under controlled conditions using oven-dried samples and a constant ambient temperature, field applications may show variability. Therefore, in situ measurements should be supported with environmental monitoring in order to adapt and interpret radon data properly. To assess the accuracy between results derived from the two analytical approaches, the statistical u-test was used to compare the methods, being suitable for small datasets and when comparing paired values with known uncertainties. In particular, the u-test (u\({}_{\mathrm{test}}\)) statistical parameter was quantified considering, as input values, the radon exhalation rates obtained by _Method 1_ and _Method 2_ for each analyzed stone sample [66]:  
\[\mathrm{u}_{\mathrm{test}}=\frac{\mathrm{E}_{\mathrm{Method}}-\mathrm{E}_{ \mathrm{method2}}}{\sqrt{\mathrm{u}_{\mathrm{Emethod1}}^{2}+\mathrm{u}_{ \mathrm{Emethod2}}^{2}}}\leq 2 \tag{3}\]  
In detail, u\({}_{\mathrm{E\;method\;1}}\) and u\({}_{\mathrm{E\;method\;2}}\) represent the uncertainties associated with measurements obtained using _Method 1_ and _Method 2_, respectively. If the computed u\({}_{\mathrm{test}}\) value is less than or equal to 2, the predefined significance threshold, the null hypothesis (H\({}_{0}\)) is confirmed--indicating no statistically significant difference between the two methods, and thus their substantial equivalence in determining the radon exhalation rates in stones [66]. Going on, to further assess the potential radiological risks associated with long-term exposure in indoor environments, a simulation was carried out using the Markkanen room model [67]. This theoretical framework estimates the steady-state concentration of radon within an indoor space, based on the exhalation rates measured experimentally. The model incorporates two primary components: the accumulation of radon exhaled from construction materials (walls, ceiling, and floor) into the room, and the effect of ventilation, which influences the removal and dilution of radon-laden air. Key input parameters for the model include the volume of the room, the surface area of the building materials in contact with the indoor air, and the ventilation rate, defined as the volume of outdoor air exchanged with indoor air per hour. The time-dependent radon concentration C(t) within the room is described using a mass balance equation that incorporates the radon exhalation rate, its radioactive decay, and the dilution effect from ventilation [67]\[\frac{\mathrm{d}C(t)}{\mathrm{d}t}=\frac{\mathrm{J}\cdot\mathrm{A}}{\mathrm{V}}- \bigg{(}\lambda_{222}+\frac{1}{\tau}\bigg{)}C(t) \tag{4}\]  
The parameter \(\mathrm{J}\) indicates the specific radon exhalation rate from building materials (\(\mathrm{Bq\,m^{-2}\,h^{-1}}\)), while \(\mathrm{A}\) is the total surface area (\(\mathrm{m^{2}}\)) of the materials contributing to radon emission. \(\mathrm{V}\) stands for the indoor volume (\(\mathrm{m^{3}}\)) of the room under analysis. The decay constant of \(\mathrm{222 Rn}\) is denoted as \(\lambda_{222}\), and \(\tau\) represents the air exchange time, i.e., the time required to replace the air within the room through ventilation (in hours).