## 3 Materials and Methods  
Six different stone samples, i.e., Lecce stone, Modica stone, Ignimbrite Campana, Comiso stone, Mendicino stone, and Viterbo tuff, were prepared in the laboratory by cutting large blocks into smaller cubes with sides of \(\sim\)5 cm, using a circular saw. Prior to testing, samples were oven-dried at 110 \({}^{\circ}\)C for 24 h to eliminate moisture, and surfaces were left untreated to represent real construction conditions [49]. The prepared specimens were subsequently analyzed to assess the radon exhalation rate, through the closed chamber method (CCM) [31]. In detail, the experimental setup consisted of a sealed cylindrical steel chamber (2.75 L), connected in a closed-loop configuration with a Rad7 (Durridge, Billerica, MA, USA) detector. The loop included CaSO\({}_{4}\) desiccant, vinyl tubing, a particle filter to remove moisture, and charged radon progeny (see Figure 1) [49; 61; 62]. An internal pump circulates air continuously. As radon decays within the chamber, alpha particles from radon progeny (\({}^{218}\)Po, \({}^{214}\)Po, \({}^{216}\)Po) are detected by using a silicon solid-state detector. The alpha energies (from 6 MeV to 8.8 MeV) allow quantification of radon through progeny equilibrium, typically reached within 15-20 min [63]. The Rad7 detector was calibrated before measurements using a standard radon source, as per the manufacturer's protocol [61]. Daily background checks and zero calibrations were performed to confirm detector stability. Desiccant replacement and system integrity (leak testing) were ensured before each test to minimize humidity and back diffusion interference. The calibration uncertainty (\(\pm\)5%) was factored into the total uncertainty budget for exhalation rate calculations, following recommended practice [63]. These quality control steps ensured data accuracy and compliance with international standards. Thus, experimental data were analyzed using two distinct protocols. The first, referred to as _Method 1_, involved tracking the radon accumulation curve over a 10-day period until an equilibrium condition was achieved. The radon exhalation rate (E, expressed in Bq h\({}^{-1}\)) was then calculated using the following equation [63; 64; 65]:  
\[\mathrm{E}=\frac{(\mathrm{C}-\mathrm{C}_{0}\mathrm{e}^{-\lambda\mathrm{T}})}{1- \mathrm{e}^{-\lambda\mathrm{T}}}\lambda\mathrm{V} \tag{1}\]  
In the above equation, C and C\({}_{0}\) account for the equilibrium and initial radon concentration (Bq m\({}^{-3}\)) values, respectively, while \(\lambda\) (h\({}^{-1}\)) refers to the effective decay constant,  
Figure 1: Experimental set-up of the Durridge Rad7 for the radon exhalation assessment. which encompasses the intrinsic radon decay, potential back diffusion, and any leakage from the chamber. V denotes the total volume of the measurement system (m\({}^{3}\)), and T corresponds to the duration of exposure, which in our case was set to 240 h.  
The second approach, referred to as _Method 2_, involved tracking the linear increase in radon concentration over a shorter period, i.e., 24 h. From the obtained linear profiles, the specific exhalation rate of \({}^{222}\)Rn (E, in Bq h\({}^{-1}\)) was calculated using the following relation [63]:  
\[\mathrm{E}=(\mathrm{m}+\lambda_{222}\mathrm{C}_{0})\mathrm{V} \tag{2}\]  
with m (Bq m\({}^{-3}\) h\({}^{-1}\)) representing the initial slope of the radon concentration increase over time. The constant \(\lambda_{222}\), approximately equal to 7.55 \(\times\) 10\({}^{-3}\) h\({}^{-1}\), corresponds to the radioactive decay constant of \({}^{222}\)Rn. As in the previous method, C\({}_{0}\) represents the initial radon concentration (Bq m\({}^{-3}\)) and V represents the total volume of the experimental setup (m\({}^{3}\)). _Method 2_ is designed for faster, practical assessments. Literature confirms that early radon growth follows a linear trend, allowing accurate estimations before saturation [63].