## 4 Results and Discussion
### Radiological Hazards Indices  
In order to assess the radiological hazard for populations exposed to the radiations emitted by the granite samples, several indices were calculated based on the concentrations obtained in this work for \({}^{40}\)K (C\({}_{\text{K}}\)), \({}^{232}\)Th (C\({}_{\text{Th}}\)) and \({}^{226}\)Ra (C\({}_{\text{Ra}}\)) [2, 37, 38, 39]. The external hazard index (H\({}_{\text{ex}}\)) commonly used to evaluate radiation dose rate due to external exposure to gamma radiation from natural radionuclides in soil/rock samples is presented in the next equation. The calculated average external hazard index was found to be less than unity for the radiation hazard to be insignificant. \[\text{H}_{\text{ex}}\ =\ \frac{\text{C}_{\text{k}}}{4810}+\frac{\text{C}_{ \text{Th}}}{259}+\frac{\text{C}_{\text{Ra}}}{370}\ \leq 1\]  
Figure 5: Linear regression LR with residuals analysis of \({}^{232}\)Th to \({}^{238}\)U of granitic rocks samples. Figure 6: Activity concentrations (Bq kg\({}^{-1}\)) of the radioelements (\({}^{238}\)U, \({}^{226}\)Ra, \({}^{232}\)Th and \({}^{40}\)K) found in granitic rock samples (right scale is for \({}^{40}\)K). Figure 7: Frequency distribution of the \({}^{238}\)U, \({}^{226}\)Ra, \({}^{232}\)Th and \({}^{40}\)K radionuclides in granitic rocks samples. The internal exposure to \({}^{222}\)Rn and its radioactive progeny is controlled by the internal hazard index (H\({}_{\text{in}}\)). The internal hazard index (H\({}_{\text{in}}\)) is a parameter for estimating the negative effect of radioactive materials on the lungs and other respiratory organs. For example, the risk of internal exposure due to the natural radionuclides \({}^{40}\)K, \({}^{226}\)Ra, and \({}^{232}\)Th can be assessed from the value of the H\({}_{\text{in}}\) equation:  
\[\text{H}_{\text{in}}\ =\ \frac{\text{C}_{\text{k}}}{4810}+\frac{\text{C}_{ \text{Th}}}{259}+\frac{\text{C}_{\text{Ra}}}{185}\]  
The European Commission (1999) [37] proposed the gamma-ray index (I\(\gamma\)), which is strongly related to the annual effective dose. The gamma-ray index is calculated considering a standard room model with dimensions of 4 m \(\times\) 5 m \(\times\) 2.8 m and 20 cm-thick walls. The formula calculates this index factor associated to the external exposure:  
\[\text{I}\gamma\ =\ \frac{\text{C}_{\text{Ra}}}{300}+\frac{\text{C}_{\text{Th}}}{2 00}+\frac{\text{C}_{\text{k}}}{3000}\]  
The excess alpha radiation due to radon inhalation originating from building materials is estimated using the relation below:  
\[\text{I}\alpha\ =\ \frac{\text{C}_{\text{Ra}}}{200}\leq 1\]  
I\(\alpha\) should be lower than the maximum permissible value of I\(\alpha\) = 1, which corresponds to 200 Bq kg\({}^{-1}\). For alpha radiation is considered that a building material with Ra concentration lower than 200 Bq kg\({}^{-1}\) could not cause an indoor radon concentration higher than 200 Bq m\({}^{-3}\). The internal hazard index (H\({}_{\text{in}}\)) for the studied Aswan granites ranged from 0.07 to 0.9. These values are within the limit of safety value of 1 as recommended by the European Commission [37], except for sample No. 14 for the Gandolla 2 sample, which had H\({}_{\text{in}}\) of 1.11, which is higher than the safety limit. Furthermore, the external hazard index (H\({}_{\text{ex}}\)) must also be less than the unity to maintain a negligible radiation hazard. Therefore, the external hazard index estimated for the studied Aswan granite samples was less than the safety limit as given in Figure 9.  
Figure 8: Range, mean, median line and outliers for \({}^{238}\)U, \({}^{226}\)Ra, \({}^{232}\)Th, and \({}^{40}\)K activities in the measured samples in interested area. The gamma-ray index is correlated with the annual dose rate due to gamma radiation (external exposure). Materials having I\(\gamma\) < 2 would increase the yearly effective dose by 0.3 mSv, while for 2 < I\(\gamma\) < 6, the gamma-ray index corresponds to an increase in effective dose by 1 mSv y-1.