## 2 Materials and Methods
### Radiological Hazard Determination  
This study scrutinized the potential radiological risks in the surface soil samples in Mardin province by analyzing the activity concentrations of radioactive isotopes: Ra-226, Th-232, K-40, and Cs-137. The six radiological hazard indices, including radium equivalent activity (Ra\({}_{\text{eq}}\)), absorbed dose rate (D\({}_{\text{R}}\)), annual effective dose equivalent (AEDE), external radiation hazard index (H\({}_{\text{ex}}\)), annual gonadal dose equivalent (AGDE), and excess lifetime cancer risk (ELCR) were computed in this study. All radiological parameter equations are presented in Table 2.  
Radium equivalent activity (Ra\({}_{\text{eq}}\)) serves as a key parameter in assessing radiation safety for human populations [28; 29]. This metric, estimated using Equation (2), is derived from radionuclides Ra-226, Th-232, and K-40, for instance, in the surface soil samples. The equation adopts that 259 Bq\(\cdot\)kg\({}^{-1}\) of Th-232, 4810 Bq\(\cdot\)kg\({}^{-1}\) of K-40, and 370 Bq\(\cdot\)kg\({}^{-1}\) of Ra-226 contribute to a similar gamma dose rate [30]. The absorbed dose rate (D\({}_{\text{R}}\)) in air, a crucial factor in radiation exposure assessment, was calculated using Equation (3). This estimation was based on activity concentrations to calculate gamma radiation from soil sources. The dose rate (D\({}_{\text{R}}\)) was calculated using activity concentrations in this study, providing an estimation of the dose in the air 1 m above the ground [31]. To estimate the Annual Effective Dose Equivalent (AEDE), Equation (4) was applied. This calculation incorporated a conversion coefficient of 0.7 Sv/Gy and an outdoor occupancy factor of 0.2, \begin{table}
\begin{tabular}{c c} \hline \hline \(\text{Ra}_{\text{eq}}=\text{A}_{\text{Ra}}+0.077\)\(\text{A}_{\text{K}}+1.43\)\(\text{A}_{\text{Th}}\) & (2) \\ \(\text{D}_{\text{R}}=0.462\)\(\text{A}_{\text{Ra}}+0.604\)\(\text{A}_{\text{Th}}+0.0417\)\(\text{A}_{\text{K}}+0.03\)\(\text{A}_{\text{Cs}}\) & (3) \\ AEDE \((\mu\)Sv\(\cdot\)year\({}^{-1})=\text{DR}\)\((\text{nGyh}^{-1})\times 8760\)\((\text{h}\cdot\)year\({}^{-1})\times 0.7\)\((\text{SvGy}^{-1})\times 0.2\times 10^{-3}\) & (4) \\ \(\text{H}_{\text{ex}}=\frac{\text{A}_{\text{Ra}}}{370\)\(\text{B}_{\text{Eq}}\,\text{kg}^{-1}}+\frac{\text{A}_{\text{Th}}}{259\)\(\text{B}_{\text{Eq}}\,\text{kg}^{-1}}+\frac{\text{A}_{\text{K}}}{4810\) Bq\(\cdot\)kg\({}^{-1}}\) & (5) \\ AGDE \((\mu\)Sv\(\cdot\)year\({}^{-1})=3.09\)\(\text{A}_{\text{Ra}}+4.18\)\(\text{A}_{\text{Th}}+0.3147\)\(\text{A}_{\text{K}}\) & (6) \\ \(\text{ELCR}=\text{AEDE}\,\times\,\text{DL}\,\times\,\text{RF}\) & (7) \\ \hline \(\text{A}_{\text{Ra}}\), \(\text{A}_{\text{K}}\), and \(\text{A}_{\text{Th}}\) are the specific activities of Ra-226, K-40, and Th-232 & \\ \(\text{D}_{\text{R}}\) is the absorbed dose rate in the air (nGy h\({}^{-1}\)) & \\ DL is expectancy of life (estimated as 70 years), and RF is the risk factor provided as 0.05 & \\ Sv\({}^{-1}\) (fatal cancer risk per Siewert) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equations of radiological parameters. Figure 3: Geology Map of Mardin Province taken from [25] and modified. reflecting the dose absorbed in the air and its impact on adult exposure [32]. The external hazard index (H\({}_{\text{ex}}\)) is another important parameter for evaluating radiation exposure, particularly for individuals working outdoors. Equation (5) was utilized to determine this index [33]. Exposure to radiation beyond critical levels can have serious biological consequences, including cellular mutations and death [34]. The United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR, [1]) has reported that radiation particularly affects the bone marrow, bone surface cells, thyroid, lungs, and gonads [1]. Given the significance of radiation effects on reproductive organs, the annual gonadal dose equivalent (AGDE) was computed based on Equation (6).