Introduction

Assessing the natural radioactivity levels in the environment is crucial for determining the radiation exposure levels of individuals. One reason for radioactivity in rocks, water, and air is naturally occurring radioactive materials found in the Earth’s crust [1]. More than 60 naturally occurring radioactive elements may be found in rock, soil, water, and the air, among other sources of natural radiation. These radiations are mostly contributed by the decay series of 226Ra, 232Th, and singly occurring isotopes such as 40K [2]. Since the earth’s origin, radiation has come from a variety of natural sources. The fact that 226Ra, 232Th, and 40K naturally occurring sources expose an average individual to around four to five times as much as man-made sources is not unexpected [3]. Exposure to radionuclides can occur by direct contact, inhalation of contaminated dust particles, or consumption of contaminated food and drink [4]. There are varying degrees of radioactivity in all rocks and soils. The 226Ra, 232Th, and 40K naturally occurring radioisotopes are the most prevalent on Earth’s surface observing several research on radioisotope amounts in different kinds of rocks [5,6,7,8]. The distribution of naturally occurring radionuclides, such as 226Ra, 232Th, and 40K, as well as other radioactive elements, is contingent upon the origin of the rocks and the processes that lead to their concentration [9]. Any location’s radioactivity level is determined by the kind of soil and the intake of minerals [10]. Natural environmental radioactivity is influenced by the local geology [11, 12]. Building materials include rocks like limestone, gneisses, tuffs, and granite [13]. In order to determine the current amounts of radioactive pollutants released into the environment or in living things, studies of radionuclide distribution and naturally occurring radioactivity levels are typically conducted. These studies are crucial for determining the effects of radiation exposure on humans [14]. In the study, natural radioactivity and radiation were assessed using rock samples from the Kolar area in Karnataka. Using a multivariate statistical method, this evaluation was carried out to provide comprehensive findings on the natural radioactivity and associated radiation hazards in the rock samples. This presumably involved the examination of several factors and data sets. This approach provides significant insights into the study’s objectives and results by enabling a more complete and comprehensive understanding of the radioactivity data and its implications.

Methodology

Study area

The Kolar district’s ten sites provided the rock samples. The easternmost district of the state is Kolar, which is situated in southern Karnataka. The sampling sites were selected at random. Sites were chosen without taking radioactivity into account. The latitude and longitude of the sampling site are mentioned in the fig. 1 and Table 1 below. The locations of the gathered rock samples begin in Kolar and conclude close to Kondarajanahalli.

Fig. 1
figure 1

Sampling Location Map

Full size image
Table 1 Geographical information of sampling points
Full size table

Sample collection

A hammer was used to break the rocks and the pieces were collected from a particular spot. A master sample register contained comprehensive records that included the location date and sample description. Fragments were mixed separately and composited into a representative sample that weighed roughly two kilograms. Following preparation 200-milliliter plastic containers were used to store the samples for a predetermined 30 day period. Throughout this waiting period the progenitor radionuclides (226Ra) to decompose into their offspring substances (222Rn) until the point of equilibrium was reached. The samples were put through gamma ray spectroscopy following the storage time. Different radionuclides including 226Ra, 232Th and 40K were measured for their activity concentrations using gamma ray spectroscopy. The natural radioactivity levels were evaluated and related radiation parameters were computed using the gamma ray spectroscopy results.

Gamma-ray spectroscopy

The TMCA32 programme is used to analyse the spectrum. The measurement was based on the natural radioactivity amounts of three naturally occurring long-live elements: 226Ra, 232Th, and 40K. These elements are thought to be the photopeaks in the natural γ-ray spectra at 1764, 2614, and 1460 keV, respectively [15]. It was determined how well the detection system’s calibration worked and this effort has made use of the outcomes. The following relation was used to compute the activity for the naturally occurring 226Ra, 232Th, and 40K radionuclides [16, 17].

$$ {\text{A}} = \frac{N}{{{\upvarepsilon } \cdot {\upgamma } \cdot {\text{t}} \cdot {\text{m}}}} $$
(1)

where A (Bq kg-1) is the activity concentration of radionuclides, N is the net peak area under the most prominent photo peaks determined by subtracting the corresponding count rate from the background spectrum acquired for the same counting time and Bq kg-1 is the radionuclide activity. The background-subtracted area of the most prominent gamma-ray peaks is used to calculate the measurements net count rate. ε is the detector efficiency of the gamma-ray, γ the absolute transition probability of gamma decay, t the counting time (s) and m the mass of the sample (kg).

Radiological parameters

Radium equivalent (Ra-eq)

The amount that corresponds to the sand’s external γ radiation dosage is known as the radium equivalent concentration. To evaluate the distinct activity of sand with varying concentrations of 226Ra, 232Th, and 40K, the radium equivalent activity Ra-eq is employed, as denoted by the subsequent expression UNSCEAR [14].

$$ {\text{Ra}}_{{ - {\text{eq}}}} = {\text{A}}_{{{\text{Ra}}}} + { 1}.{\text{43 A}}_{{{\text{Th}}}} + \, 0.0{\text{77 A}}_{{\text{K}}} $$
(2)

The activity concentrations of 226Ra, 232Th and 40K are represented by the letters ARa, ATh and AK respectively. The basis for this is that the same gamma-ray dose equivalent is produced by 370 Bq kg-1 of 226Ra, 259 Bq kg-1 of 232Th and 4810 Bq kg-1 of 40K.

Absorbed dose rate (DR)

One of the key factors influencing the natural background radiation is the concentration of radionuclide activity in rock sediments. According to UNSCEAR guidelines, all exposure rates are derived from radioactive sources in the rock sediment, and the activity concentration matches the total absorbed dose rate in the air at one metre above ground. This type of equation is typically used to estimate the gamma dose rate in indoor environments due to the presence of naturally occurring radioactive materials in building materials. DR (nGy h-1) [14, 18, 19].

$$ {\text{D}}_{{{\text{in}}}} = \, 0.{\text{92 C}}_{{{\text{Ra}}}} + { 1}.{\text{1 C}}_{{{\text{Th}}}} + \, 0. \, 0{\text{8 C}}_{{\text{K}}} $$
(3)
$$ {\text{D}}_{{{\text{out}}}} = \, 0.{\text{462 C}}_{{{\text{Ra}}}} + \, 0.{\text{621 C}}_{{{\text{Th}}}} + \, 0.0{\text{417 C}}_{{\text{K}}} $$
(4)

where CRa, CTh and CK are the average activity concentrations of 226Ra, 232Th and 40K in Bq kg-1, respectively.

Annual effective dose (mSv y-1)

The annual effective dose (AED) is estimated by multiplying the dose rate received in the air by an adult by the indoor occupancy factor of 80 % and the conversion factor of 0.7 Sv Gy-1 [20]. The annual effective dose, expressed in mSv y-1, was calculated considering the dose rate in air due to gamma radiation from naturally occurring radionuclides 226Ra, 232Th, and 40K measured at one meter above the ground. The calculation follows the guidelines set forth in RP 112, with the annual effective dose limit set at 1 mSv y-1 [18].

$$ {\rm{AE}}{{\rm{D}}_{{\rm{in}}~}} = {\rm{ }}{{\rm{D}}_{{\rm{in}}}}{\rm{ }} \times {\rm{ 876}}0{\rm{h }} \times {\rm{ }}0.{\rm{8 }} \times {\rm{ }}0.{\rm{7 }} \times {\rm{ 1}}{0^{ - {\rm{6}}}}{\rm{mSv }}{{\rm{y}}^{ - {\rm{1}}}} $$
(5)

The (AEDout) is estimated from the outdoor external dose rate (Dout), time of stay in the outdoor or occupancy factor (20%) of 8760 h in a year and the conversion factor ( 0.7 Sv Gy-1 ) to convert the absorbed dose in air to effective dose. During the present study, the (AEDout) was calculated using the following equations as per [21].

$$ {\rm{AE}}{{\rm{D}}_{{\rm{out}}}} = {\rm{ }}{{\rm{D}}_{{\rm{out}}}}{\rm{ }} \times {\rm{ 876}}0{\rm{h }} \times {\rm{ }}0.{\rm{2 }} \times {\rm{ }}0.{\rm{7 }} \times {\rm{ 1}}{0^{ - {\rm{6}}}}{\rm{mSv }}{{\rm{y}}^{ - {\rm{1}}}} $$
(6)

Hazard index

The index of external hazards an indicator that is frequently used to assess the radioactive danger of construction materials is called Hex. This is how it is computed.

$$ {\text{H}}_{{{\text{ex}}}} = \frac{{A_{Ra} }}{370} + \frac{{A_{Th} }}{259} + { }\frac{{A_{K} }}{4810}{ } \le 1 $$
(7)

where ARa, ATh and AK stand for the same activities in the building material or surroundings as before representing 226Ra, 232Th and 40K (Bq kg−1). A material that has an external gamma dose of 1.5 mSv y−1 is associated with a Hex index of unity. Radium equivalent activity (Raeq) principles are applied by the Hex. According to the estimate 370 Bq kg−1 for 226Ra, 259 Bq kg−1 for 232Th and 4810 Bq kg−1 for 40K produce an equivalent gamma-ray dose rate [22, 23]. The index of internal danger (Hin) The internal hazard index factor should be determined in order to evaluate the radiation hazard risk posed by radon and its short-lived daughter products, which are dangerous to respiratory organs [24]. The internal hazard index (Hin), which is determined by the following equation, measures the internal exposure to radon and its daughter products.

$$ {\text{H}}_{{{\text{in}}}} = \frac{{A_{Ra} }}{185} + \frac{{A_{Th} }}{259} + { }\frac{{A_{K} }}{4810}{ } \le 1 $$
(8)

Gamma index

The gamma index (Iγ) is a useful tool for assessing the potential health risks associated with naturally occurring radioactivity in materials such as rocks, soil and building materials. The formula for the gamma index is. It is computed using the activity concentrations of three radionuclides that are frequently found in natural materials: potassium-40, radium-226 and thorium-232. [25].

$$ {\text{I}}_{\gamma } = \frac{{A_{Ra} }}{300} + \frac{{A_{Th} }}{200} + { }\frac{{A_{K} }}{3000}{ } \le 1 $$
(9)

where ARa, ATh, and AK are the activity concentrations (Bq kg−1) of radium (226Ra), thorium (232Th), and potassium (40K), respectively.

Activity utilization index (AUI)

AUI is a metric that is used to evaluate the radioactivity of radioactive materials in rocks or building materials in order to determine whether or not they can be used. In order to do this the external gamma dose rate must be calculated at a reference distance (like one meter) from the material and compared to any applicable regulatory or guideline limits. AUI determines whether a material satisfies safety standards for radiation exposure by integrating the activity concentration of radionuclides and the corresponding dose rates.

$$\text{I}=\frac{{\text{A}}_{\text{Ra}}}{50}{\text{f}}_{\text{Ra}}+\frac{{\text{A}}_{\text{Th}}}{50}{\text{f}}_{\text{Th}}+ \frac{{\text{A}}_{\text{K}}}{500}{\text{f}}_{\text{K}}\le 2$$
(10)

The fractional contributions of gamma radiation from the actual concentrations of these radionuclides fTh (0. 604), fRa (0. 462) and fK (0. 041) to the total dose rate in air are taken into consideration [26, 27].

Excess lifetime cancer risk (ELCR)

The excess lifetime cancer risk (ELCR) was calculated using the equation:

$$ {\text{ELCR}}_{{{\text{Out}}}} = {\text{ AEDE}}_{{{\text{out}}}} *{\text{ DL}}*{\text{ RF}} $$
(11)
$$ {\text{ELCR}}_{{{\text{In}}}} = {\text{ AEDE}}_{{{\text{in}}}} *{\text{ DL}}*{\text{ RF }} $$
(12)

In this case RF represents the risk factor (Sv−1) or the fatal cancer risk per sievert and DL stands for average lifespan (70 years). ICRP 103 recommended a public exposure level of 0. 05 to account for stochastic effects from low dose background radiation [28].

Annual gonad dose equivalent

According to UNSCEAR (1988) [29], the active bone marrow and the bone surface cells are the organs of interest. Since 226Ra, 232Th, and 40K are particular activities found in building materials, the annual gonad dose equivalent (AGDE) (µSv y−1) for individuals residing within a structure is determined using the formula below.

$$ {\text{AGDE }} = { 3}.0{9 } \times {\text{ A}}_{{{\text{Ra}}}} + { 418 } \times {\text{ A}}_{{{\text{Th}}}} + \, 0.0{317 } \times {\text{A}}_{{\text{K}}} $$
(13)

Elemental concentration

Naturally ocuuring radioactivity levels are commonly expressed in one of two ways: parts per million (ppm) indicates the concentration of a specific radioisotope in the material while becquerels per kilogram (or gram) indicates the level of radioactivity generally or due to a particular isotope. CTh (1 ppm) in rock is equivalent to 4.06 Bq kg−1, CRa (1 ppm) in rock is equivalent to 12.35 Bq kg−1 and CK 1(%) in rock is equivalent to 313 Bq kg−1 according to the IAEA [30, 31].

Radiogenic heat production

Rock heat may be calculated using estimates of 40K, 226Ra, and 232Th concentrations from gamma ray spectroscopy. Thermal energy is released when naturally occurring radionuclides in the ground disintegrate; the majority of this energy is created by the decay of 40K, 226Ra, and 232Th. The density of rock, ρ (kg/m3), the concentration of radioelements CK (%), CRa (ppm), and CTh (ppm), and the heat production (HP) of rocks are connected by [29].

$$ {\text{HP}} = ({3}.{\text{48 C}}_{{\text{K}}} + { 9}.{\text{52 C}}_{{{\text{Ra}}}} + { 2}.{\text{56 C}}_{{{\text{Th}}}} ){1}0 -^{{5}} \left( {\mu {\text{W m}}^{{ - {3}}} } \right) $$
(14)

Result and discussion

The radionuclide (226Ra, 232Th and 40K) activity concentration of rock samples were shown in table 2. The activity concentration of 226Ra, 232Th and 40K were found to be ranged from 5.05 to 171.43 Bq kg−1, 5.04–274.64 Bq kg−1, 287.23 to 2603.45 Bq kg−1 and the mean value of 226Ra, 232Th, 40K is 21.40 Bq kg−1, 141.03 Bq kg−1, 1297.92 Bq kg−1. For bellow detectable limit the value of 5.05 Bq kg−1 for 226Ra and 5.04 Bq kg−1 for 232Th limit of detector is used. So it gives uncertainty and bias into subsequent calculations of radiological parameters. The highest value radium found to be Kolar 171.43 Bq kg−1, for thorium Bettani 274.64 Bq kg−1 and for potassium Kondarajanahalli 2603.45 Bq kg−1. The lowest value for 226Ra found to be Kendatti Gollahali, Madivala, Arabikothanur, Kaparasiddanahalli, Kondarajanahalli, Vibhuthipura, Kandripura, Near Kondarajanahalli (5.05); for 232Th Kolar (5.04); and 40K Kolar (287.23 Bq kg−1). The 232Th/226Ra ratio shows how abundant 232Th is in comparison to 226Ra in the rock samples. 0.03 to 52.66 are the range of values and average value: 23.14; 40K/226Ra ratio shows how abundant 40K is in the samples in comparison to 226Ra. 1.68 to 515.53 are the range of values and average value 223.09; 40K/232Th ratio shows how abundant 40K is in the samples in comparison to 232Th, range from 3.01 to 101.00 and average value is 25.42. In particular the 40K/226Ra ratio exhibits a broad range ranging from very high values exceeding (KR7) to relatively low values around (KR1).

Table 2 Activity Concentration (Bq kg-1) and ratio of activities.
Full size table
Table 3 Elemental concentration ppm and Radiogenic heat production µW/m3 in the rock samples from Karnataka
Full size table

In Table 3 elemental concentration radium range is from 0.41 to 13.88 ppm, thorium range is from 1.24 to 67.65 ppm and potassium range is from 0.92 to 8.32% with the mean value of radium, thorium and potassium is 1.73 ppm, 34.74 ppm and 4.15%. Radiogenic Heat Production (RHP µW/m3) range is from 0.6 to 6.39 µW/m3 with mean value of 3.41 µW/m3 (Fig. 2).

Fig. 2
figure 2

Elemental concentration ppm and Radiogenic heat production µW/m3

Full size image

Radiological parameters

The radiological parameters assessed in the study show a range of values for different metrics. The Radium Equivalent Activity (Raeq) ranges from 107.47 to 549.22 Bq kg−1, with a mean value of 318.68 Bq kg−1, indicating moderate to high radioactivity in the samples. The indoor and outdoor dose rates range from 115.26 to 471.47 nGy h−1 and 60.57 to 258.09 nGy h−1, respectively, averaging at 282.92 nGy h−1 (indoor) and 153.77 nGy h−1 (outdoor). Annual Effective Dose (AED) values are higher indoors 0.57 to 2.31 mSv y−1, average 1.39 mSv y−1 compared to outdoors 0.07 to 0.32 mSv y−1, average 0.19 mSv y−1. Hazard indices (Hex and Hin) vary from 0.31 to 1.51 and 0.33 to 1.63, respectively, with average values suggesting potential risks in some samples (Table 4). The Gamma Index (GI) ranges from 0.48 to 2.06, with an average of 1.23, indicating varying levels of gamma radiation hazard. The Excess Lifetime Cancer Risk (ELCR) is significantly higher indoors, ranging from 1.98 to 8.09, compared to 0.26 to 1.11 outdoors. The Activity Utilization Index (AUI) and Annual Gonad Dose Equivalent (AGEDE) also show some variation, with values suggesting moderate risk levels. When compared to the UNSCEAR 2000 guidelines, the results indicate that parameters like Raeq, indoor dose rate, indoor AED, and ELCR are slightly elevated, suggesting a higher potential health risk, while other parameters remain within normal limits.

Table 4 Radiological Parameters for Karnataka rock samples
Full size table
Table 5 Average value for activity concentration in other states of Karnataka
Full size table

In Table 5 some significant differences and contributions can be seen when comparing the radionuclide activity concentrations from the present study in Kolar Taluk with those from earlier studies in Karnataka: the present study reports 226Ra activity concentration of 25.44 Bq kg−1, 232Th of 141.53 Bq kg−1 and 40K of 1297.92 Bq kg−1. 238U was recorded as 47.05 Bq kg−1 in the earlier studies conducted in Gadag which is substantially higher than in Kolar Taluk. This study contributes to the spatial diversity of data available for Karnataka by providing data specific to Kolar Taluk. A number of other districts including Ramanagara District, Tumkur District, Coorg District, Gadag, Gulbarga, Kottur and Kaiga environment have been the subject of earlier research all of which demonstrate variations in radionuclide levels based on geological and environmental factors. The current study in Kolar Taluk makes a contribution by completing geographical gaps in Karnataka radionuclide data. It offers current concentrations that are useful for risk assessment regulatory compliance and environmental monitoring. This study in Kolar Taluk adds to the body of knowledge about environmental radioactivity studies in Karnataka India by providing unique data on radionuclide activity concentrations and highlighting regional variability. The importance of localized studies in improving our comprehension of the distribution of natural radioactivity and its implications is highlighted by this comparative analysis.

Correlation analysis

Correlation coefficient R suggests that moderate level of connection between two variables. In correlation connection shows strength of the relation is weak or strong or fall somewhere in between. Positive correlation indicates that variable tends to move in same direction as one increases and other one also increases. Negative correlation indicates that variable tends to move in opposite direction as one increases other decreases.

The table 6 presents the Pearson correlation coefficients and corresponding p values for the relationships between three features (40K, 232Th and 226Ra). The correlation between 40K and 226Ra is −0.52 with a p value of 0.11, suggesting a moderate negative correlation that is not statistically significant at the 0.05 level. The correlation between 226Ra and 232Th is −0.34 with a p value of 0.32, indicating a weak negative correlation, which is also not statistically significant. The correlation between 40K and 232Th is 0.15 with a p value of 0.66, showing a very weak positive correlation that is not statistically significant. Overall, none of the correlations are statistically significant, indicating that there is no strong evidence of a meaningful linear relationship between these pairs of features. Correlations suggests that these radionuclides may not be directly related in this dataset, or that any relationship is too weak to be detected with the current sample size

Table 6 Correlation for activity concentration (Bq kg-1)
Full size table

Statistical analysis

Skewness and kurtosis

In probability skewness is a measure of the asymmetry of distribution. A distribution is asymmetry when its left and right side are not mirror images. A distribution can have left as negative, right as positive and zero as skewness. Kurtosis in statistics describes the distribution of the data set points of a particular differ from the data of a normal distribution. It may use to determine whether a distribution contain extreme values.

The table 7 includes data for three radioactive isotopes 226Ra, 232Th, and 40K. The highest observed values for each isotope are 171.43 for 226Ra, 274.64 for 232Th, and 2603.45 for 40K (Figs. 3, 4 and 5). This indicates the maximum concentration of these isotopes in the sample set. The lowest observed values for each isotope are zero for both 226Ra and 232Th, and 287.23 for 40K. A minimum value of zero suggests that some samples had no detectable levels of 226Ra and 232Th. The average concentration of each isotope across all samples is 21.4 for 226Ra, 141 for 232Th, and 1298 for 40K. These values give a central tendency of the isotope concentrations. The middle value when the data are ordered from least to greatest is zero for 226Ra, 134.44 for 232Th, and 1250.99 for 40K. A median of 0 for 226Ra suggests that more than half of the samples had no detectable 226Ra. This measures the asymmetry of the data distribution. 226Ra has a skewness of 2.86, indicating a highly positively skewed distribution. 232Th has a skewness of  − 0.01, indicating a slightly negatively skewed distribution. 40K has a skewness of 0.60, indicating a moderately positively skewed distribution. This measures the tailedness of the data distribution. 226Ra has a kurtosis of 8.35, indicating a highly peaked distribution with heavy tails. 232Th has a kurtosis of − 1.74, suggesting a flatter distribution than a normal distribution. 40K has a kurtosis of 1.95, indicating a slightly peaked distribution. The standard deviation, which measures the dispersion or spread of the data, is 54.38 for 226Ra, 104.70 for 232Th, and 616 for 40K. These values indicate the variability of each isotope’s concentration. The number of samples analyzed for each isotope is 10, which means all statistical measures are based on 10 data points for each isotope. The frequency distribution is described as Normal for 226Ra, meaning the data is approximately normally distributed. For 232Th and 40K, the distribution is described as Peaked, indicating that these data sets have a higher peak than a normal distribution. It provides an overall estimate of the total amount of these constituents that are present. Finally these statistics offer a thorough summary of the datasets 226Ra, 232Th, and 40K distribution variability and central tendency. To comprehend their environmental or geological significance and possible impacts they draw attention to variations in their means spreads (standard deviations) shapes (kurtosis) and skewness. Both descriptive statistics and correlation analysis provides a comprehensive understanding of the data, indicating that while there are observed relationships, they are not statistically significant.

Table 7 Activity Concentration (Bq kg-1) Statistical Analysis
Full size table
Fig. 3
figure 3

Frequency distribution for 226Ra

Full size image
Fig. 4
figure 4

Frequency distribution for 232Th

Full size image
Fig. 5
figure 5

Frequency distribution for 40K

Full size image

Conclusion

In summary important results are obtained from the analysis of radionuclide activity concentrations in rock samples from Kolar Taluk. Mean values of 21.40 Bq kg−1, 141.03 Bq kg−1, 1297.92 Bq kg−1 respectively, indicate the wide variation in 226Ra, 232Th and 40K concentrations across the samples. These elements relative abundance in the samples can be understood by examining the ratios of 232Th/226Ra, 40K/226Ra and 40K/232Th which show different relationships between them. The elemental composition of potassium, thorium and radium is further explained by their respective elemental concentrations which have mean values of 1.73 ppm, 34.74 ppm and 4.15%. With the exception of slightly higher levels of radiological parameters in comparison to UNESCAR 2000 standards, radiological parameters such as annual effective doses, activity utilization index and hazard indices show values within acceptable limits. The study fills in geographic data gaps and provides crucial information for risk assessment and environmental monitoring by highlighting the regional variability in natural radioactivity levels within Karnataka. Additionally the datasets statistical analysis highlights the distributional features of 226Ra, 232Th and 40K emphasizing their asymmetries variability and central tendencies. These results highlight the value of localized studies in comprehending the consequences of natural radioactivity in the environment in addition to adding to the body of knowledge already available about environmental radioactivity in Karnataka.