## 4 Results and Discussion
### Analysis of Radionuclides
The activity concentration ranges of \({}^{226}\)Ra, \({}^{232}\)Th, and \({}^{40}\)K of the granite samples of this study were compared to those of different localities in the Eastern Desert of Egypt, with 137 granite samples from different countries all over the world, as shown in Table 2. The results showed that the activity concentrations of \({}^{226}\)Ra, \({}^{232}\)Th, and \({}^{40}\)K in the studied samples are lower than most values of granitic rocks in the Eastern Desert and the international samples. Figure 5 shows the correlation between \({}^{238}\)U and \({}^{232}\)Th radionuclides in all measured samples: there is a positive correlation between \({}^{238}\)U and \({}^{232}\)Th with fitting the equation \({}^{232}\)Th = 0.01877 \(\times\)\({}^{238}\)U + 56.84 and standard error \(\pm\) 0.13. The band with the orange color around the fit line is the confidence band, which depicts the upper and lower confidence bounds for all points on a fitted line within the range of data; for example, the model indicates with 95 confidence that in a sample, if \({}^{238}\)U = 80, this indicates that in the same sample, there is a proximity of 45 to 75 \({}^{232}\)Th, which are the y-values of the lower and upper confidence bands at \({}^{238}\)U = 15. The same applies to the prediction band. The results include a 4-panel residuals plot. Residuals are also analyzed for normality using the Anderson-Darling test. Looking at the Fitted Y (Bq/kg) figure of the residuals, we can see how they are constant from left to right, which is called the constant variance of the residuals; also, in the percentiles figure, we can see how they are distributed around the fitted line, which proves the initial assumption. The residual count figure shows that most of the residuals are between 0 and 0.5, while the last figure explains the relationship between the residuals against each independent variable; as we can see, there is no pattern clearly related to one of the independents. The sampling site-specific variations of \({}^{238}\)U, \({}^{226}\)Ra, \({}^{232}\)Th, and \({}^{40}\)K radioactivity concentrations (Bq kg\({}^{-1}\)) with minimum, mean and maximum values for the studied samples shown in Figure 6. G2 sample has the highest values of \({}^{238}\)U (148.20 Bq kg\({}^{-1}\)) and \({}^{226}\)Ra (88.80 Bq kg\({}^{-1}\)), while the BA3 and R2 samples have the highest values of \({}^{232}\)Th (105.56, Bq/kg) and \({}^{40}\)K (1483.62 Bq kg\({}^{-1}\)), respectively. In Figure 7, the histograms are presented for the data of the activity concentration results for \({}^{238}\)U, \({}^{232}\)Th, \({}^{226}\)Ra, and \({}^{40}\)K in twenty-nine different samples of Aswan granites. The data present a strong normal distribution from this figure, and all the values of activity concentrations are nearly within the computed mean value for each natural radionuclide. The statistical distribution of the results, the activity concentration results for \({}^{238}\)U, \({}^{232}\)Th, \({}^{226}\)Ra, and \({}^{40}\)K in the studied points of Aswan granites, are presented in Figure 8 using boxplots. The \({}^{40}\)K has the highest values of the range, median, mean, and outliers of Aswan granites.