Study and Simulated the Natural Radioactivity (NORM) U-238, Th-232 and K-40 of Igneous and Sedimentary Rocks of Al-Atawilah (Al-Baha) in Saudi Arabia

In this work, gamma-ray spectroscopy based on semiconductor hyper pure germanium (HPGe) detector was used to evaluate the activity concentrations of the natural radionuclides (U-238 (Ra-226), Th-232 and K-40) and the fallout nuclide (Cs-137) for thirty samples of igneous and sedimentary rocks of Al-Atawilah (Al-Baha). The mean values of the activity concentrations of U-238 (Ra-226), Th-232, K-40 and Cs-137 in the igneous samples are found as (11.0, 11.50, 1172.71, 1.47) Bq/Kg respectively. In the sedimentary rocks, the mean values of the activity concentrations of the natural radionuclides (U-238 (Ra-226), Th-232 and K-40) and the fallout nuclide (Cs-137) equal to (12.04, 13.18, 1131.36, 1.60) Bq/Kg respectively. The averages of radiological hazards (Ra eq , H ex and I γ ) were calculated and found to be within the UNSCEAR permissible limit values (370 Bq/kg for Ra eq , and 1 for H ex and I γ ), except for a slight increase of average value of I γ in the igneous rock samples (1.36). The results indicate that the dose rate values depend on the kind of rocks (high in some igneous rock samples, and most of sedimentary rock samples have low dose rate). The activities of naturalnuclides were predicted and simulated in T time using a written MATLAB R2020a script based on the average activity concentrations and respective half-lives of U-238 and Th-232 series, and K-40, this is to evaluate the future effects of natural radionuclides on the population and estimate the human inputs in the future.


Introduction
Radiation activity exists everywhere on the surface of Earth and its interior. Uranium-238, thorium-232 (and their progenies) and potassium-40 are most important sources of radiation. These nuclei are found in any type of rocks, especially in igneous and sedimentary rocks. U-238 decays by ejection an alpha particle to generate daughter radionuclide Th-234 which followed by other decays to produce other radionuclides such as Ra-226 and its progeny Rn-222. Similarly, Th-232 disintegrates to produce Rn-228 and followed by other radionuclides [1]. These radionuclides constitute risks by the external exposure to gamma radiation emissions and internally by radon and its progenies. Radon is a human carcinogen, and it is considered the second leading cause of lung cancer [2]. Knowledge of radionuclide distribution is important because it gives helpful information in the observation of natural environmental radioactivity and connected external exposure that resulting from gamma radiation primary based on the geological and geographical conditions and can be seen at various levels in the rocks of each area of the world [3]. The aim of this study is to determine the radionuclides activity concentration of Ra-226, Th-232 and K-40 for igneous and sedimentary rock samples collected from Al-Atawilah (north of Al-Baha region), and to estimate the doses and hazard indices originate from the existence of the natural radionuclides in the surrounding area. Moreover, Ra-226, Th-232 and K-40 activity concentrations were used to simulate and predict the range of decay by using an appropriate program. The results are used to assess the future effect of these radionuclides and evaluate the future of radiation hazards.

Sampling and Samples Preparation
Eighteen igneous rock samples and twelve sedimentary rock samples were collected from Al-Atawilah (20.273351˚N, 41.358325˚E), north of Al-Baha region, southeast of Saudi Arabia, Figure 1. The samples were collected from the study region at depth ≈ 5 cm, by cracking the rock with hammer after removing a thin layer of the mother rock. Then, the collected samples were dried, pulverized and then sieved through less than 1mm-mesh size [4]. All crushed sieved rock samples were filled into Polyethylene Marinelli beakers. The samples were pulverized into fine-grained powder for uniform distribution of radon and its decay products and to avert any accumulation in the top [5]. The weight of each sample was recorded and then hermetically sealed from outside using a thick tape for more than a month so as to establish the secular equilibrium between Ra-226 and Th-232 (and their decay products) [6] [7].

Measurements Equipment
Measurement of radionuclides activity concentrations in the rock samples were evaluated by using high-resolution gamma-ray spectrometry system includes hyper-purity closed-end coaxial germanium detector. The detector had resolution of 2 keV at 1332.5 keV of Co-60 and 25% relative efficiency and peak to Compton ratio of 50:1. The detector is placed in a cylinder-heavy lead shield to minimize the radiation background values. Activity concentration calculations were based on the establishment of secular equilibrium in the measured sample between 226 Ra and 232 Th and their progenies of smaller lifetime [8]. 226

Equations for Calculations
The radionuclide activity concentration (A c ) in the investigated rocks samples were determined in Bq•kg −1 . The activity concentration calculations were carried out using the following formula [9] [10]: where: N c is the net peak area per unit time (second), m is sample mass in kg, ε is the detector absolute efficiency at the photo-peak energy and β is the branching ratio of gamma radiation.
Radium equivalent (Ra eq ) is calculated by applying the following equation [11] [12]: ( ) To keep the radiation hazard insignificant, the calculated value of the external hazard index must be less than unity [13].
Representative level index (I γ ) is determined with following equation [14]: The absorbed dose rate (D R ) in air at 1m overhead the ground level was evaluated from the activity concentrations of the relevant natural radionuclides according to the following equation [15]:

Decay Simulation of Natural Radionuclides
The mean activity concentrations in the rock samples of Al-Atawilah were used to simulate and predict the range of decay. The decay of the radionuclides U-238 (Ra-226), Th-232 and K-40 of the rocks samples were simulated using written MATLAB R2020ascript according to the exponential law of radioactive decay [16]: where: A is the change of the radioactive nuclei number with time, A 0 is the initial activity, t is the time and λ is the constant of the decay.
In this study, Forward Different Interpolation Method was applied to reconstruct the activity concentrations of radionuclides. The term e −λt of the radionu- " (n to a 4 th order) was used in Taylor polynomial form. The decay factor e −λt was approximated to a polynomial form by the following analysis for the fourth order: Since: this yields the polynomial as: The coefficients a, b, c and e were calculated for the equation (8), and it was used with MATLAB R2020a to simulate the decay of the radionuclides 238 U, 232 Th and 40 K using their half-lives [17].

Activity Concentrations
Analytical results for the samples have been applied to evaluate the activity concentration of 226 Ra, 232 Th and 40 K, and the artificial radionuclide ( 137 Cs) in Bq•kg −1 together with their total uncertainties. The results are presented in

Natural Radionuclides Decay Simulation of the Rock Samples
The decay of 226 Ra ( 238 U equivalent), 232 Th and 40 K of the rock samples were predicted over 10 3 years, 10 6 years, 10 9 years and finally over 10 10 Ra,232 Th and 40 K, respectively. The graphics have been zoomed in to clarify 238 U ( 226 Ra) and 232 Th decay curves. The following observations from the simulation outcomes can be indicated as: 1) According to the Equation (6), the decay curves were expected to give an exponential graph, the lines approach zero if the background radiation is ignored.
2) The decay will be almost constant in the several next years in the study area, as the decay was not observed in Figure 2 and Figure 3, this due to the extremely long half-lives of the terrestrial radionuclides, thus the decay that the radionuclides will undergo during thousands or millions years will be insignificant.
3) From Figure 4 and Figure 5, a significant collapse was observed in the decay curve of 40 K compared to 232 Th and 238 U ( 226 Ra), this due to its shorter half-life compared to 238 U and 232 Th half-lives. World Journal of Nuclear Science and Technology    4) This study evaluates the future effect of natural radionuclides on the population of this region and any increase in the concentration of radioactivity should be due to human inputs.

Conclusion
Gamma-ray spectroscopy of hyper-purity Germanium (HPGe) detector is a good experimental tool for studying levels of the radioactivity in various environmental samples such as rocks. The mean activity concentrations of 226 Ra, 232 Th and 40 K in the igneous rock samples are 11, 11.5, 1172.71 Bq•kg −1 , respectively. For the sedimentary rock samples, the activity concentrations are found to be 12.04, 13.18, 1131.36 Bq•kg −1 for 226 Ra, 232 Th and 40 K, respectively. Fallout nuclide ( 137 Cs) was found in the most of the rock samples under investigation, the low mean values of 137 Cs are not of radiologically significant. The calculated mean values of radium equivalent (Ra eq ), external hazard index (H ex ), representative level index (I γ ) and absorbed dose rate (D R ) are within the suggested limit values, except for a slight increase of I γ in igneous rock samples. This study also evaluated the radioactivity levels in the future and their effects on the population of the study region and any increase in the concentration of radioactivity should be due to human inputs. The results of the present study can help us to understand the distribution of natural radionuclides in the environment of Al-Baha region and provide a main map of radioactivity levels in Saudi Arabia.