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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1740296</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2025.1740296</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>The study of radiation contamination in roodepoort gold mine tailings using HPGe gamma spectroscopy</article-title>
<alt-title alt-title-type="left-running-head">Mvelase et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphy.2025.1740296">10.3389/fphy.2025.1740296</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Mvelase</surname>
<given-names>Mashinga J.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2410799"/>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing - original draft</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &#x26; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/">Writing - review and editing</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ntshangase</surname>
<given-names>Sifiso S.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Funding acquisition" vocab-term-identifier="https://credit.niso.org/contributor-roles/funding-acquisition/">Funding acquisition</role>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Majola</surname>
<given-names>Siyabonga N. T.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Funding acquisition" vocab-term-identifier="https://credit.niso.org/contributor-roles/funding-acquisition/">Funding acquisition</role>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Kheswa</surname>
<given-names>Bonginkosi V.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Supervision" vocab-term-identifier="https://credit.niso.org/contributor-roles/supervision/">Supervision</role>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Masiteng</surname>
<given-names>Paulus L.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Supervision" vocab-term-identifier="https://credit.niso.org/contributor-roles/supervision/">Supervision</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &#x26; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/">Writing - review and editing</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Maleka</surname>
<given-names>Peane P.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Supervision" vocab-term-identifier="https://credit.niso.org/contributor-roles/supervision/">Supervision</role>
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</contrib-group>
<aff id="aff1">
<label>1</label>
<institution>Department of Physics, University of Zululand</institution>, <city>KwaDlangezwa</city>, <country country="ZA">South Africa</country>
</aff>
<aff id="aff2">
<label>2</label>
<institution>Department of Physics, University of Johannesburg</institution>, <city>Doornfontein</city>, <country country="ZA">South Africa</country>
</aff>
<aff id="aff3">
<label>3</label>
<institution>SSC Laboratory, iThemba Laboratory for Accelerator Based Sciences</institution>, <city>Somerset West</city>, <country country="ZA">South Africa</country>
</aff>
<aff id="aff4">
<label>4</label>
<institution>University of the Western Cape</institution>, <city>Bellville</city>, <country country="ZA">South Africa</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: Mashinga J. Mvelase, <email xlink:href="mailto:emjay.mvelase@gmail.com">emjay.mvelase@gmail.com</email>
</corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-01-15">
<day>15</day>
<month>01</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1740296</elocation-id>
<history>
<date date-type="received">
<day>05</day>
<month>11</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>16</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>18</day>
<month>12</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Mvelase, Ntshangase, Majola, Kheswa, Masiteng and Maleka.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Mvelase, Ntshangase, Majola, Kheswa, Masiteng and Maleka</copyright-holder>
<license>
<ali:license_ref start_date="2026-01-15">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>In this study, a coaxial HPGe high-resolution <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-detector was used to measure the <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-signals in soil samples collected from the Roodepoort Gold Tailings. There have been complaints about dust from the gold tailings, and the study aims to determine the level of contamination. The activity concentration of <sup>238</sup>U ranged from 132.88 <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.68 to 1,421.46 <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.38, with a mean of 464.96 <inline-formula id="inf5">
<mml:math id="m5">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 2.08 Bq/kg. The activity concentration of <sup>226</sup>Ra ranged from 130.19 <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.48 to 1,359.27 <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.83, with a mean of 425.28 <inline-formula id="inf8">
<mml:math id="m8">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.02 Bq/kg. The range of <sup>232</sup>Th was from 5.27 <inline-formula id="inf9">
<mml:math id="m9">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.67 to 19.37 <inline-formula id="inf10">
<mml:math id="m10">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.98, with a mean of 11.20 <inline-formula id="inf11">
<mml:math id="m11">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.03 Bq/kg, and <sup>40</sup>K activity ranged from 65.23 <inline-formula id="inf12">
<mml:math id="m12">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.29 to 264.11 <inline-formula id="inf13">
<mml:math id="m13">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 25.66, with a mean of 127.50 <inline-formula id="inf14">
<mml:math id="m14">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 21.85 Bq/kg. The findings showed that <sup>238</sup>U and <sup>226</sup>Ra activities exceeded the global average of 35 Bq/kg, while <sup>232</sup>Th and <sup>40</sup>K were below their respective limits. The radiological hazard indices exceeded recommended limits, making the tailings soil completely unsuitable for use as building materials, as this may have deleterious health effects on residents in the future.</p>
</abstract>
<kwd-group>
<kwd>AEDE</kwd>
<kwd>ELCR</kwd>
<kwd>HPGe &#x3b3; - spectroscopy</kwd>
<kwd>radioactivity</kwd>
<kwd>radiological health hazards</kwd>
</kwd-group>
<funding-group>
<award-group id="gs1">
<funding-source id="sp1">
<institution-wrap>
<institution>National Research Foundation</institution>
<institution-id institution-id-type="doi" vocab="open-funder-registry" vocab-identifier="10.13039/open_funder_registry">10.13039/501100001321</institution-id>
</institution-wrap>
</funding-source>
</award-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This research was funded by the National Research Foundation (NRF) of South Africa under grant number CPRR23040388976.</funding-statement>
</funding-group>
<counts>
<fig-count count="11"/>
<table-count count="4"/>
<equation-count count="15"/>
<ref-count count="75"/>
<page-count count="00"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Radiation Detectors and Imaging</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>Since the formation of the Earth, natural background ionizing radiation has always emanated from the decays of <sup>238</sup>U, <sup>232</sup>Th, and <sup>40</sup>K, which are present in the environment [<xref ref-type="bibr" rid="B1">1</xref>, <xref ref-type="bibr" rid="B2">2</xref>]. Two isotopes make up most of the natural uranium found in Earth&#x2019;s crust: <sup>238</sup>U, which accounts for 99.3 <inline-formula id="inf15">
<mml:math id="m15">
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <sup>235</sup>U, which accounts for approximately 0.7<inline-formula id="inf16">
<mml:math id="m16">
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> [<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B4">4</xref>]. Radioactivity is significant in the mining and processing of ores other than uranium. These activities result in exposure to naturally occurring radioactive materials (NORM). Radiological exposures associated with radioactivity, such as absorbed dose rate, annual effective dose rate, and annual gonadal dose rate, should be evaluated. Most background ionising radiation originates from the decay of the <sup>238</sup>U decay series, the <sup>232</sup>Th decay series, and the non-series <sup>40</sup>K [<xref ref-type="bibr" rid="B4">4</xref>&#x2013;<xref ref-type="bibr" rid="B6">6</xref>]. In Soweto, environmental radioactivity originates from mining tailings, and radiation is transported as dust by the wind to distant locations, so no one is spared from radiation contamination.</p>
<p>Radiation affects the human body externally through <inline-formula id="inf17">
<mml:math id="m17">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-radiation and internally through <inline-formula id="inf18">
<mml:math id="m18">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-radiation, which arises from inhaling dust and radon (<sup>222</sup>Rn) gas. Radon gas is the parent nucleus of both <sup>218</sup>Po and <sup>214</sup>Po, which are alpha emitters. Alpha particles can damage DNA by imparting a high density of ionizations due to their high linear energy transfer [<xref ref-type="bibr" rid="B7">7</xref>]. High linear energy transfer (LET) single hits can generate highly reactive oxygen species capable of inducing cellular damage by direct reaction with biological molecules [<xref ref-type="bibr" rid="B8">8</xref>], as well as nitrogen radicals, which may cause significant DNA damage. High LET radiation is more effective than low LET radiation at inducing cell death, apoptosis, mutation, transformation, carcinogenesis, chromosomal abnormalities, and chromosomal instability [<xref ref-type="bibr" rid="B9">9</xref>]. The highly reactive oxygen species (ROS) produced by high LET radiation consequently damage various cell components, such as lipids, proteins, and nucleic acids, resulting in several chronic and degenerative conditions, including ageing, dementia, kidney, cardiovascular and neurodegenerative diseases, cancer, respiratory disorders, rheumatoid arthritis, and other metabolic disorders [<xref ref-type="bibr" rid="B10">10</xref>]. Nuclear decays inside the body emit <inline-formula id="inf19">
<mml:math id="m19">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-, <inline-formula id="inf20">
<mml:math id="m20">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-, and <inline-formula id="inf21">
<mml:math id="m21">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-radiation [<xref ref-type="bibr" rid="B11">11</xref>, <xref ref-type="bibr" rid="B12">12</xref>], which can damage DNA through cell ionizations. Alpha particles impart a high density of ionizations along their short path, as they have a high linear energy transfer, leading to DNA damage in human cells and potentially resulting in radiation-induced carcinogenesis [<xref ref-type="bibr" rid="B13">13</xref>]. Previous studies have reported that the gold mine tailings in the Witwatersrand Basin have a uranium concentration of 100 mg/kg <inline-formula id="inf22">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>U</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>O</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, which is comparable to or higher than the concentrations of uranium mine tailings in Namibia, ranging from 45.9 <inline-formula id="inf23">
<mml:math id="m23">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 3.0 to 1752.1 <inline-formula id="inf24">
<mml:math id="m24">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.5 Bq/kg for <sup>238</sup>U [<xref ref-type="bibr" rid="B14">14</xref>, <xref ref-type="bibr" rid="B15">15</xref>].</p>
<p>The mining sector has had both positive and negative effects on the South African economy and gross domestic product (GDP) [<xref ref-type="bibr" rid="B16">16</xref>]. South Africa is endowed with numerous mineral resources, particularly metals, coal, and gold, with exploration beginning in the late 1800s [<xref ref-type="bibr" rid="B4">4</xref>] and mining commencing in 1886 [<xref ref-type="bibr" rid="B17">17</xref>]. Extensive mining activity has occurred, bringing soils and rocks that would otherwise have remained underground to the surface. These activities have left behind mountains of pollution known as mining tailings. Gold tailings are a source of dust, especially during the dry and windy season, due to their proximity to residential areas, affecting thousands of impoverished township residents and causing numerous health issues [<xref ref-type="bibr" rid="B18">18</xref>&#x2013;<xref ref-type="bibr" rid="B20">20</xref>]. Inhaling toxic metals trapped in radioactive dust particles can cause various lung diseases [<xref ref-type="bibr" rid="B16">16</xref>]. In the context of climate change, gold tailings are even more hazardous due to unpredictable weather patterns and heavy rains that may cause overflow, allowing pollution to reach human settlements. Toxic metals such as As, Cr, and Ni, and radioactive metals such as <sup>238</sup>U, <sup>232</sup>Th, and <sup>40</sup>K in tailings pose a synergistic health risk to residents [<xref ref-type="bibr" rid="B4">4</xref>]. Knowledge of the distribution of geogenic and anthropogenic radionuclides is recommended for assessing and managing public health risks and should inform any environmental interventions [<xref ref-type="bibr" rid="B21">21</xref>].</p>
<p>Most written reports are based primarily on the work of community activists and community-based non-governmental organizations (NGOs) campaigning against mining companies that have left pollution unaddressed. This study aims to measure radioactivity in gold mine tailings, which has been less frequently reported, providing valuable information on radioactivity concentrations. Based on the results, the corresponding probabilistic health risk will be calculated.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<label>2</label>
<title>Materials and methods</title>
<sec id="s2-1">
<label>2.1</label>
<title>Geology and climate of the study area</title>
<p>The study site has a subtropical highland climate with a warm, wet summer [<xref ref-type="bibr" rid="B22">22</xref>]. These tailings are from abandoned old gold mines. The research area&#x2019;s land is mostly utilized for residential development, with very little employed for gold mining [<xref ref-type="bibr" rid="B22">22</xref>, <xref ref-type="bibr" rid="B23">23</xref>]. The gold-bearing conglomerates in the sedimentary layers of the West Rand mining area consist of 10&#x2013;30 <inline-formula id="inf25">
<mml:math id="m25">
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> phyllosilicates and 70&#x2013;90 <inline-formula id="inf26">
<mml:math id="m26">
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> quartz <inline-formula id="inf27">
<mml:math id="m27">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Uraninite <inline-formula id="inf28">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>UO</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, brannerite <inline-formula id="inf29">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>UO</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>Ti</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>O</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, arsenopyrite (FeAsS), cobaltite (CoAsS), galena (PbS), pyrrhotite (FeS), gersdorfite (NiAsS), and chromite <inline-formula id="inf30">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>FeCr</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>O</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, sericite, <inline-formula id="inf31">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>KAl</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
<inline-formula id="inf306">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>AlSi</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>O</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>(OH)<sub>2</sub>, and minor minerals such as rutile <inline-formula id="inf32">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>TiO</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, pyrite <inline-formula id="inf33">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>FeS</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, chromite <inline-formula id="inf34">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>FeCr</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>O</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and uraninite <inline-formula id="inf35">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>UO</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> make up the bulk of the phyllosilicates [<xref ref-type="bibr" rid="B24">24</xref>, <xref ref-type="bibr" rid="B25">25</xref>]. The West Rand Group, mainly composed of quartzite and shale, forms the sedimentary base. The Central Rand Group is characterized by quartzite and conglomerate, particularly gold-bearing conglomerates in its lower section, which are associated with basin-wide unconformities [<xref ref-type="bibr" rid="B26">26</xref>]. The highlands have long, hot summers that generally last from October to March and short, cold winters that last from June to August. Most of the annual rainfall, which ranges from 600 to 732 mm, falls during the summer months. Strong storms are frequent from October to March, and the average annual temperature is 16 <inline-formula id="inf36">
<mml:math id="m37">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>C [<xref ref-type="bibr" rid="B25">25</xref>].</p>
</sec>
<sec id="s2-2">
<label>2.2</label>
<title>Sample collection and preparation</title>
<p>Soil samples were collected from the gold mine tailings in Roodepoort, located at 26<inline-formula id="inf37">
<mml:math id="m38">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>10&#x2032;46&#x2033;S 27<inline-formula id="inf38">
<mml:math id="m39">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>52&#x2032;03&#x2033;E, and stored in plastic zipper bags labelled RDP. The study site has residential areas, businesses, and additional mine tailings in its vicinity, as shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. The samples were placed in polypropylene Marinelli beakers of known weight after being oven-dried at 105 <inline-formula id="inf39">
<mml:math id="m40">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>C, crushed, pulverized, and sieved to remove uncrushed stones and organic matter.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The Roodepoort Google Map shows the gold tailings sampling location.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g001.tif">
<alt-text content-type="machine-generated">A satellite map view of an area showing locations such as Durban Deep, a quarry, and Durban Deep Rifle Club. Roads include Nick Toomey Boulevard, Hail Road, and Cemetery Road. Nearby places include ZCC Bramficher and JV's Corner Lounge. The map is labeled with Google Maps branding.</alt-text>
</graphic>
</fig>
<p>To achieve secular equilibrium between the gamma emitters in the <sup>238</sup>U series (primarily <sup>226</sup>Ra, <sup>214</sup>Bi, and <sup>214</sup>Pb) and the <sup>232</sup>Th series (<sup>228</sup>Ra measured by <sup>228</sup>Ac, and <sup>228</sup>Th measured by <sup>208</sup>Tl), white silicone was applied between the lid and brim of Marinelli beakers to prevent radon leakage, and the beakers were hermetically sealed for 42 days before <inline-formula id="inf40">
<mml:math id="m41">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> - spectroscopic analysis, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. The gross weights were measured, and the difference between the empty and gross weights gave the sample weights. Most of these sample weights averaged approximately 0.250 kg. The prepared gold tailings soil samples are now in Marinelli beakers, where they are kept until they reach secular equilibrium. They will then remain sealed and analysed at a later stage, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The prepared gold tailings soil samples in Marinelli beakers.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g002.tif">
<alt-text content-type="machine-generated">Containers labeled RDP 1 to RDP 16 are arranged on a tray. Each container has a different sample inside, with varying shades of color.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2-3">
<label>2.3</label>
<title>Analysis of soil samples</title>
<p>Gamma spectroscopic analysis of the natural radioactivity (<sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K) in soil was carried out at the Environmental Radiation Laboratory (ERL) at NRF iThemba LABS. The radioactivity was measured using a p-type coaxial Canberra gamma-ray spectrometer detector, optimised for detecting gamma rays at low energies up to 2000 keV, Model No. BE2820 SN 8794, with 45<inline-formula id="inf41">
<mml:math id="m42">
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> relative efficiency and a resolution of <inline-formula id="inf42">
<mml:math id="m43">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>2.00 keV (FWHM) at the 1.33 MeV <inline-formula id="inf43">
<mml:math id="m44">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-ray line of <sup>60</sup>Co. An electronic data acquisition system (Canberra DSA-1000 digital signal processing (DSP) system), interfaced with a Multichannel Analyzer (MCA) and Canberra Genie 2000 software (version 2.0), was used to acquire a spectrum.</p>
<p>The gamma spectrometry system was calibrated for energy and efficiency using a mixed radionuclide standard covering a wide range of gamma-ray energies (0.060&#x2013;2.00 MeV) in a 500 ml Marinelli beaker. Both the samples and the background were counted for 25,200 s, and the background count was subtracted from the sample count to give the net count rate. For quality control, calibration for energy and efficiency was performed to maintain measurement quality. After the samples were hermetically sealed for 42 days in their respective Marinelli beakers, secular equilibrium was assumed to have been reached. The 186.22 keV <inline-formula id="inf44">
<mml:math id="m45">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-signal was used to quantify <sup>226</sup>Ra. The 295.22 keV and 351.93 keV <inline-formula id="inf45">
<mml:math id="m46">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-signals for <sup>214</sup>Pb and the 609.32 keV, 1,120.29 keV, and 1764.49 keV <inline-formula id="inf46">
<mml:math id="m47">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-signals for <sup>214</sup>Bi were used to assess the activity concentration of <sup>238</sup>U [<xref ref-type="bibr" rid="B27">27</xref>&#x2013;<xref ref-type="bibr" rid="B31">31</xref>], while 911.21 keV for <sup>228</sup>Ac and 583.1 keV for <sup>208</sup>Tl were used for <sup>232</sup>Th. The single 1,460 keV <inline-formula id="inf47">
<mml:math id="m48">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> - signal was used to quantify <sup>40</sup>K concentration. The specific <inline-formula id="inf48">
<mml:math id="m49">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> - signals listed in <xref ref-type="table" rid="T1">Table 1</xref> were tracked to measure each radionuclide in the soil samples. The information in the table was sourced from the literature [<xref ref-type="bibr" rid="B32">32</xref>, <xref ref-type="bibr" rid="B33">33</xref>].</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>The data on NORM decay modes showing their specific <inline-formula id="inf49">
<mml:math id="m50">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> - signals and intensity.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Parent nuclide</th>
<th align="left">Daughter</th>
<th align="left">Nuclear</th>
<th align="center">Decay mode</th>
<th align="center">
<inline-formula id="inf50">
<mml:math id="m51">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-ray energy</th>
<th align="center">
<inline-formula id="inf51">
<mml:math id="m52">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-intensity</th>
</tr>
<tr>
<th align="left">(NORM)</th>
<th align="left">Nuclide</th>
<th align="left">Half-life</th>
<th align="center">
<inline-formula id="inf52">
<mml:math id="m53">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th align="center">(keV)</th>
<th align="center">Yield <inline-formula id="inf53">
<mml:math id="m54">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>%</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="3" align="left">
<sup>226</sup>Ra</td>
<td align="left">Ra-226</td>
<td align="left">1,602 years</td>
<td align="center">
<inline-formula id="inf54">
<mml:math id="m55">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (94), <inline-formula id="inf55">
<mml:math id="m56">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (6)</td>
<td align="center">186</td>
<td align="center">3.55</td>
</tr>
<tr>
<td align="left">Pb-214</td>
<td align="left">26.80 min</td>
<td align="center">
<inline-formula id="inf56">
<mml:math id="m57">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (100)</td>
<td align="center">295</td>
<td align="center">19.3</td>
</tr>
<tr>
<td align="left">Pb-214</td>
<td align="left">26.80 min</td>
<td align="center">
<inline-formula id="inf57">
<mml:math id="m58">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (100)</td>
<td align="center">352</td>
<td align="center">37.6</td>
</tr>
<tr>
<td rowspan="3" align="left">
<sup>238</sup>U</td>
<td align="left">Bi-214</td>
<td align="left">19.90 min</td>
<td align="center">
<inline-formula id="inf58">
<mml:math id="m59">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (0.021)</td>
<td align="center">609</td>
<td align="center">46.1</td>
</tr>
<tr>
<td align="left">Bi-214</td>
<td align="left">19.90 min</td>
<td align="center">
<inline-formula id="inf59">
<mml:math id="m60">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (99.98)</td>
<td align="center">1,120</td>
<td align="center">15.4</td>
</tr>
<tr>
<td align="left">Bi-214</td>
<td align="left">19.90 min</td>
<td align="center">
<inline-formula id="inf60">
<mml:math id="m61">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (99.98)</td>
<td align="center">1764</td>
<td align="center">15.4</td>
</tr>
<tr>
<td rowspan="2" align="left">
<sup>232</sup>Th</td>
<td align="left">Ac-228</td>
<td align="left">6.15 h</td>
<td align="center">
<inline-formula id="inf61">
<mml:math id="m62">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (100)</td>
<td align="center">911</td>
<td align="center">26.0</td>
</tr>
<tr>
<td align="left">Tl-208</td>
<td align="left">3.05 min</td>
<td align="center">
<inline-formula id="inf62">
<mml:math id="m63">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (100)</td>
<td align="center">583</td>
<td align="center">86.0</td>
</tr>
<tr>
<td align="left">
<sup>40</sup>K</td>
<td align="left">Ar-40</td>
<td align="left">
<inline-formula id="inf63">
<mml:math id="m64">
<mml:mrow>
<mml:mn>1.284</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>9</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> years</td>
<td align="center">EC (10.7)</td>
<td align="center">1,461</td>
<td align="center">10.7</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>The efficiency and energy calibration curves</title>
<p>When analyzing unknown samples, we rely on gamma spectroscopy; however, before we can use it effectively, we must calibrate the energy scale. To do this, we used several well-known radioactive sources that emit gamma rays at specific energies. These include <sup>210</sup>Pb at 45.54 keV, <sup>241</sup>Am at 59.5 keV, <sup>109</sup>Cd at 88 keV, and <sup>57</sup>Co at 122.1 keV, among others. We also use higher-energy sources such as <sup>137</sup>Cs (661.65 keV), <sup>60</sup>Co (which emits at both 1,173.2 and 1,332.4 keV), and <sup>88</sup>Y (1836.1 keV). The emission probabilities for these radionuclides were obtained from previous research papers [<xref ref-type="bibr" rid="B34">34</xref>]. The efficiency equation depends on energy, as shown in <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, and has been used in work published by the following authors [<xref ref-type="bibr" rid="B35">35</xref>&#x2013;<xref ref-type="bibr" rid="B37">37</xref>]:<disp-formula id="e1">
<mml:math id="m65">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>8</mml:mn>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
<mml:msub>
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>ln</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>In this equation, <inline-formula id="inf64">
<mml:math id="m66">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (keV) represents the peak energy of a particular radioisotope of interest, and <inline-formula id="inf65">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> keV [<xref ref-type="bibr" rid="B38">38</xref>]. The efficiency calibration curve for the HPGe detector was obtained using standard sources at NRF iThemba LABS, Gauteng. As there is a direct relationship between channel number and energy, we can convert our channel readings into energy measurements. The results of both the efficiency and energy calibration curves are shown in <xref ref-type="fig" rid="F3">Figure 3</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Detector efficiency (left) and energy calibration for <inline-formula id="inf66">
<mml:math id="m68">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-ray energies (right).</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g003.tif">
<alt-text content-type="machine-generated">Two graphs are shown. The left graph displays efficiency versus energy with data points and a curve showing decreasing efficiency as energy increases up to 2000 keV. The right graph illustrates energy plotted against channel number, with a linear fit indicated by a line, and the equation \(E_y &#x3d; 0.1281C &#x2b; 37.015\) with \(R^2 &#x3d; 0.9997\), where \(E_y\) is energy.</alt-text>
</graphic>
</fig>
<sec id="s3-1">
<label>3.1</label>
<title>Minimum detectable activity and error calculations</title>
<p>The background count was conducted using the same geometry as the samples. An empty Marinelli beaker was placed on the detector, as with the sample measurements, and counted for periods similar to those used for the sample counts. The peaks generated from this procedure were subtracted from the corresponding peaks of the samples. In this way, the background count rate was manually subtracted from the measured samples. After determining the background radiation for the radionuclides of interest, the minimum detectable activity (MDA) was calculated using the following <xref ref-type="disp-formula" rid="e2">Equation 2</xref>:<disp-formula id="e2">
<mml:math id="m69">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>A</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mi>q</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>k</mml:mi>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2.71</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>4.66</mml:mn>
<mml:msqrt>
<mml:mrow>
<mml:mi>B</mml:mi>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>T</mml:mi>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>Where MDA (Bq/kg) is the specific activity in a sample, B is the background activity of the sample, <inline-formula id="inf67">
<mml:math id="m70">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the absolute detector efficiency of the specific <inline-formula id="inf68">
<mml:math id="m71">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-ray, T is the accumulation time, and m is the mass of the sample in kilograms. <inline-formula id="inf69">
<mml:math id="m72">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the emission probability of a specific energy photopeak. Using the background activities, the average MDA for <sup>226</sup>Ra is 6.68 Bq/kg at 186.2 keV, 26.1 Bq/kg for <sup>40</sup>K at 1,460 keV, and 1.68 Bq/kg for <sup>214</sup>Pb at 352 keV.</p>
<p>For specific activity concentration, the error was calculated by taking the square root of the sum of the background and sample readings, then dividing by T, <inline-formula id="inf70">
<mml:math id="m73">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf71">
<mml:math id="m74">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and mass m. The resulting value was then multiplied by two, as 2<inline-formula id="inf72">
<mml:math id="m75">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> was used for our measurements. For the other radiological indices, error propagation was applied.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Calculations of risk assessment of radionuclides</title>
<p>After calculating the detector efficiency and energy calibration, the samples were subjected to gamma spectroscopic analysis which resulted to the measurement of specific activity concentration. Radiological indices, including Radium Equivalent <inline-formula id="inf73">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>Ra</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Eq</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, Absorbed Dose Rate (ADR), Annual Effective Dose Equivalent (AEDE), Excess Lifetime Cancer Risk (ELCR), Internal Hazard Index <inline-formula id="inf74">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
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<mml:mtext>In</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, External Hazard Index <inline-formula id="inf75">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Ex</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, Annual Gonadal Dose Equivalent (AGDE), Alpha Index <inline-formula id="inf76">
<mml:math id="m79">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and Radioactivity Index <inline-formula id="inf77">
<mml:math id="m80">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, were estimated using their respective models from the literature.</p>
<sec id="s4-1">
<label>4.1</label>
<title>Calculation of activity concentration in soil samples</title>
<p>All measurements were taken with the samples in contact with the detector housing for 25,200 s, and spectral analysis was performed using Genie 2000 software. The activity concentrations in the measured samples were calculated using <xref ref-type="disp-formula" rid="e3">Equation 3</xref> [<xref ref-type="bibr" rid="B34">34</xref>, <xref ref-type="bibr" rid="B39">39</xref>]:<disp-formula id="e3">
<mml:math id="m81">
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>B</mml:mi>
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<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
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<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>T</mml:mi>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>Where A (Bq/kg) is the specific activity in a sample, <inline-formula id="inf78">
<mml:math id="m82">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the activity of the sample with the background activity subtracted.</p>
</sec>
<sec id="s4-2">
<label>4.2</label>
<title>The radium equivalent activity Ra<sub>Eq</sub>
</title>
<p>The radium equivalent activity is an index introduced to represent the specific activities of <sup>226</sup>Ra, <sup>232</sup>Th, and <sup>40</sup>K by a single quantity that accounts for the radiation hazards associated with them. The radium equivalent activity was estimated using <xref ref-type="disp-formula" rid="e4">Equation 4</xref> [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B39">39</xref>&#x2013;<xref ref-type="bibr" rid="B41">41</xref>]:<disp-formula id="e4">
<mml:math id="m84">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mi>q</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>k</mml:mi>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1.43</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.077</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>This radiation index uses baseline measurements of 370 Bq/kg for <sup>226</sup>Ra, 259 Bq/kg for <sup>232</sup>Th, and 4,810 Bq/kg for <sup>40</sup>K, as these levels produce equivalent gamma radiation doses [<xref ref-type="bibr" rid="B5">5</xref>]. To keep radiation exposure within safe limits, experts recommend that the index should not exceed 370 Bq/kg in soil [<xref ref-type="bibr" rid="B42">42</xref>]. This helps to assess how gamma radiation may affect living organisms and allows evaluation of potential health risks in different locations.</p>
</sec>
<sec id="s4-3">
<label>4.3</label>
<title>The absorbed dose rate in air (ADR)</title>
<p>The absorbed gamma dose rate measures the rate at which ionizing radiation from gamma rays is deposited at a specific location, providing insight into the potential biological effects of gamma radiation. The total absorbed dose rate due to naturally occurring radioactive materials (NORM) in air 1 m above the ground is calculated using the following equations. Absorbed dose rates are estimated using <xref ref-type="disp-formula" rid="e5">Equations 5</xref>, <xref ref-type="disp-formula" rid="e6">6</xref> [<xref ref-type="bibr" rid="B40">40</xref>, <xref ref-type="bibr" rid="B43">43</xref>&#x2013;<xref ref-type="bibr" rid="B45">45</xref>]:<disp-formula id="e5">
<mml:math id="m85">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Ind</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
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<mml:mi>y</mml:mi>
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<mml:mi>h</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.920</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1.100</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.0810</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
<disp-formula id="e6">
<mml:math id="m86">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
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<mml:mfenced open="(" close=")">
<mml:mrow>
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<mml:mi>h</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.462</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.604</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.0417</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>Where 0.462, 0.604, 0.0417, 0.92, 1.1, and 0.081 are dose conversion factors in nGy/h per Bq/kg, and <inline-formula id="inf80">
<mml:math id="m87">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf81">
<mml:math id="m88">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf82">
<mml:math id="m89">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the radionuclide concentrations for <sup>226</sup>Ra, <sup>232</sup>Th, and <sup>40</sup>K, respectively [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B41">41</xref>, <xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B47">47</xref>].</p>
</sec>
<sec id="s4-4">
<label>4.4</label>
<title>The annual effective dose rate (AEDE)</title>
<p>The air absorbed dose rates found above are multiplied by a conversion factor F with a value of 0.7<inline-formula id="inf83">
<mml:math id="m90">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
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<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> Sv/y [<xref ref-type="bibr" rid="B5">5</xref>] to convert to the effective dose received by adults and 0.2 and 0.8 for the outdoor and indoor occupancy factors, respectively [<xref ref-type="bibr" rid="B46">46</xref>]. The effective dose rate per year should be less than a unity [<xref ref-type="bibr" rid="B48">48</xref>]. The indoor and outdoor annual effective dose equivalent is estimated using <xref ref-type="disp-formula" rid="e7">Equations 7</xref>, <xref ref-type="disp-formula" rid="e8">8</xref> [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B49">49</xref>]:<disp-formula id="e7">
<mml:math id="m91">
<mml:mrow>
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<mml:mi>D</mml:mi>
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<mml:mrow>
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<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
<disp-formula id="e8">
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<mml:mi>v</mml:mi>
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<mml:mo>&#x3d;</mml:mo>
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<mml:mi>D</mml:mi>
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</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
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<mml:mo>&#xd7;</mml:mo>
<mml:mn>0.2</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>Where T is hours in a year (365<inline-formula id="inf84">
<mml:math id="m93">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>24 h &#x3d; 8,760 h), and F is the conversion factor with a value of 0.7<inline-formula id="inf85">
<mml:math id="m94">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>6</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> Sv/y.</p>
</sec>
<sec id="s4-5">
<label>4.5</label>
<title>The excess lifetime cancer risk (ELCR)</title>
<p>Excess lifetime cancer risk (ELCR) is a term used in radiation protection to estimate the potential increase in a person&#x2019;s cancer risk due to exposure to ionizing radiation that exceeds the baseline risk of cancer exposure without radiation exposure. The indoor and outdoor ELCR values should, on average, be less than or equal to the global average of 1.16<inline-formula id="inf86">
<mml:math id="m95">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf87">
<mml:math id="m96">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and 0.29<inline-formula id="inf88">
<mml:math id="m97">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf89">
<mml:math id="m98">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>, respectively. The excess lifetime cancer risk <inline-formula id="inf90">
<mml:math id="m99">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>ELCR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Ind</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the indoor environment was calculated using <xref ref-type="disp-formula" rid="e9">Equation 9</xref> [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B50">50</xref>&#x2013;<xref ref-type="bibr" rid="B52">52</xref>]:<disp-formula id="e9">
<mml:math id="m100">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>C</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Ind</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>D</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Ind</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
<mml:mi>L</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
</p>
<p>The outdoor excess lifetime cancer risk <inline-formula id="inf91">
<mml:math id="m101">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>ELCR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Out</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> was calculated using <xref ref-type="disp-formula" rid="e10">Equation 10</xref> [<xref ref-type="bibr" rid="B51">51</xref>, <xref ref-type="bibr" rid="B52">52</xref>]:<disp-formula id="e10">
<mml:math id="m102">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>C</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Out</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>D</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Out</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
<mml:mi>L</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<p>Where DL is the life expectancy, which is about 70 years, and RF is the risk factor, which is given as 0.05 <inline-formula id="inf92">
<mml:math id="m103">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mtext>Sv</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>. The indoor and outdoor ELCR values should, on average, be less than or equal to the global averages of 1.16<inline-formula id="inf93">
<mml:math id="m104">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and 0.29<inline-formula id="inf94">
<mml:math id="m105">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>, respectively.</p>
</sec>
<sec id="s4-6">
<label>4.6</label>
<title>The internal hazard index H<sub>
<italic>In</italic>
</sub>
</title>
<p>The internal hazard index is a crucial concept in radiation protection and safety, assessing potential radiation exposure and hazards linked with radioactive material intake. It establishes tolerable intake limits for radioactive materials and assesses the need for extra precautions like radiation protection or medical follow-up. Inhaling radon and thoron gases can be hazardous to the respiratory organs [<xref ref-type="bibr" rid="B53">53</xref>] as these particles undergo alpha decay, thus releasing alpha particles, which can tear the epithelial cells of the lungs, and <xref ref-type="disp-formula" rid="e11">Equation 11</xref> is used to calculate the hazard index [<xref ref-type="bibr" rid="B40">40</xref>, <xref ref-type="bibr" rid="B54">54</xref>&#x2013;<xref ref-type="bibr" rid="B56">56</xref>]:<disp-formula id="e11">
<mml:math id="m107">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>185</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>259</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>4810</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
</p>
<p>For the safe use of building materials in shelter construction, the index should be less than one.</p>
</sec>
<sec id="s4-7">
<label>4.7</label>
<title>The external hazard index H<sub>
<italic>Ex</italic>
</sub>
</title>
<p>External gamma radiation dose refers to the amount of ionising radiation a person is exposed to from gamma rays emitted by an external source, typically associated with radionuclides of concern. To limit this dose, an external hazard index <inline-formula id="inf97">
<mml:math id="m109">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is calcutaled using <xref ref-type="disp-formula" rid="e12">Equation 12</xref> [<xref ref-type="bibr" rid="B40">40</xref>, <xref ref-type="bibr" rid="B54">54</xref>&#x2013;<xref ref-type="bibr" rid="B57">57</xref>]:<disp-formula id="e12">
<mml:math id="m110">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>370</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>259</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>4810</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
<p>For the safety of individuals outdoors, the index should be less than unity.</p>
</sec>
<sec id="s4-8">
<label>4.8</label>
<title>The annual gonadal dose equivalent (AGDE)</title>
<p>The annual gonadal dose equivalent (AGDE) is a measure used in radiation protection to estimate the potential dose to the reproductive organs (gonads) from a person&#x2019;s exposure to ionising radiation over a year. The AGDE resulting from the specific activities of <sup>226</sup>Ra, <sup>232</sup>Th, and <sup>40</sup>K was calculated using <xref ref-type="disp-formula" rid="e13">Equation 13</xref> [<xref ref-type="bibr" rid="B40">40</xref>, <xref ref-type="bibr" rid="B58">58</xref>]:<disp-formula id="e13">
<mml:math id="m111">
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mi>G</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>E</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mtext>Sv/y</mml:mtext>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>3.09</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>4.18</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>0.314</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>The AGDE considers the type of radiation, the amount of radiation exposure, and the sensitivity of the gonads to radiation-induced damage.</p>
</sec>
<sec id="s4-9">
<label>4.9</label>
<title>The alpha hazard index I<sub>&#x3b1;</sub>
</title>
<p>The index estimates the risk of internal exposure to alpha radiation from a mixture of <inline-formula id="inf99">
<mml:math id="m113">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-emitting radionuclides and expresses the total hazard in a single numerical value. Excess alpha radiation from inhalation of radon from building materials is estimated using <xref ref-type="disp-formula" rid="e14">Equation 14</xref> [<xref ref-type="bibr" rid="B12">12</xref>, <xref ref-type="bibr" rid="B59">59</xref>]:<disp-formula id="e14">
<mml:math id="m114">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>200</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>
</p>
<p>The alpha index, <inline-formula id="inf100">
<mml:math id="m115">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>1 is equivalent to 200 Bq/kg of radium. Construction material with <sup>226</sup>Ra exceeding 200 Bq/kg should be avoided in building because this may lead to 200 Bq/m<sup>3</sup> of radon, exposing occupants to internal radiation. In the above equations, <sup>226</sup>Ra, <sup>232</sup>Th, and <sup>40</sup>K represent the radionuclide concentrations.</p>
</sec>
<sec id="s4-10">
<label>4.10</label>
<title>The radioactivity index I<sub>&#x3b3;</sub>
</title>
<p>This study examines the possibility of radiation exposure to human settlements near gold mine tailings dams, especially informal settlements. The plastering sand-like soil can easily be excavated for building purposes, and unaware of its toxicity, people may make bricks and use it as building sand, which will, in turn, expose the inhabitants to gamma radiation. The gamma radiations emitted by certain natural radionuclides in building materials are linked to this index by <xref ref-type="disp-formula" rid="e15">Equation 15</xref> [<xref ref-type="bibr" rid="B50">50</xref>, <xref ref-type="bibr" rid="B51">51</xref>, <xref ref-type="bibr" rid="B60">60</xref>]:<disp-formula id="e15">
<mml:math id="m117">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>150</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>100</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1500</mml:mn>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>
</p>
<p>An increase in the gamma index beyond the worldwide acceptable limit may result in radiation risk, leading to the deformation of human cells, thereby causing cancer. <inline-formula id="inf102">
<mml:math id="m118">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; 1 as an upper limit, <inline-formula id="inf103">
<mml:math id="m119">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mspace width="0.3333em"/>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>1 corresponds to 0.3 mSv/y, and <inline-formula id="inf104">
<mml:math id="m120">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mspace width="0.3333em"/>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>3 corresponds to 1 mSv/y. For materials used in bulk like bricks, the ranges of <inline-formula id="inf105">
<mml:math id="m121">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are: 0.5 <inline-formula id="inf106">
<mml:math id="m122">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf107">
<mml:math id="m123">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>1 [<xref ref-type="bibr" rid="B61">61</xref>].</p>
</sec>
</sec>
<sec sec-type="results|discussion" id="s5">
<label>5</label>
<title>Results and discussion</title>
<sec id="s5-1">
<label>5.1</label>
<title>Specific activity concentrations of natural radionuclides in samples</title>
<p>Samples from four different gold tailings were collected and analyzed at iThemba LABS. The activity concentration of <sup>238</sup>U ranged from 132.88 <inline-formula id="inf108">
<mml:math id="m124">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.68 to 1,421.46 <inline-formula id="inf109">
<mml:math id="m125">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.38 with a mean of 464.96 <inline-formula id="inf110">
<mml:math id="m126">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 2.08 Bq/kg. The activity concentration of <sup>226</sup>Ra ranged from 112.02 <inline-formula id="inf111">
<mml:math id="m127">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.09 to 1,195.80 <inline-formula id="inf112">
<mml:math id="m128">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 30.63 with a mean of 407.42 <inline-formula id="inf113">
<mml:math id="m129">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.23 Bq/kg, which is 12 the 35 Bq/kg recommended value by [<xref ref-type="bibr" rid="B5">5</xref>]. The range of <sup>232</sup>Th was from 5.27 <inline-formula id="inf114">
<mml:math id="m130">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.67 to 19.37 <inline-formula id="inf115">
<mml:math id="m131">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.98 with a mean of 11.20 <inline-formula id="inf116">
<mml:math id="m132">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.03 Bq/kg, and <sup>40</sup>K activity ranged from 65.23 <inline-formula id="inf117">
<mml:math id="m133">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.29 to 264.11 <inline-formula id="inf118">
<mml:math id="m134">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 25.66 with a mean of 127.50 <inline-formula id="inf119">
<mml:math id="m135">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 21.85 Bq/kg as presented in <xref ref-type="table" rid="T2">Table 2</xref>. The <sup>238</sup>U was calculated from the concentrations of <sup>214</sup>Pb and <sup>214</sup>Bi, while radium was calculated from its signal of 186.20 keV. The findings showed that <sup>238</sup>U and <sup>226</sup>Ra activity exceeded the global average of 30 and 35 Bq/kg, respectively, while <sup>232</sup>Th and <sup>40</sup>K were below their respective limits [<xref ref-type="bibr" rid="B5">5</xref>].</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The specific activity concentrations of <sup>238</sup>U, <sup>226</sup>Ra, <sup>232</sup>Th and <sup>40</sup>K in the tailings.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Gold tailings</th>
<th rowspan="2" align="left">Sample ID</th>
<th colspan="4" align="center">Specific activity concentration in roodepoort samples (Bq/kg)</th>
</tr>
<tr>
<th align="left">
<sup>238</sup>U</th>
<th align="left">
<sup>226</sup>Ra</th>
<th align="left">
<sup>232</sup>Th</th>
<th align="left">
<sup>40</sup>K</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="17" align="left">Roodepoort</td>
<td align="left">RDP 01</td>
<td align="left">444.81 <inline-formula id="inf120">
<mml:math id="m136">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.20</td>
<td align="left">397.67 <inline-formula id="inf121">
<mml:math id="m137">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 16.6</td>
<td align="left">10.66 <inline-formula id="inf122">
<mml:math id="m138">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.97</td>
<td align="left">119.52 <inline-formula id="inf123">
<mml:math id="m139">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 18.18</td>
</tr>
<tr>
<td align="left">RDP 02</td>
<td align="left">584.28 <inline-formula id="inf124">
<mml:math id="m140">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 10.23</td>
<td align="left">470.98 <inline-formula id="inf125">
<mml:math id="m141">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 18.73</td>
<td align="left">12.76 <inline-formula id="inf126">
<mml:math id="m142">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.12</td>
<td align="left">163.42 <inline-formula id="inf127">
<mml:math id="m143">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 20.92</td>
</tr>
<tr>
<td align="left">RDP 03</td>
<td align="left">483.32 <inline-formula id="inf128">
<mml:math id="m144">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.08</td>
<td align="left">413.61 <inline-formula id="inf129">
<mml:math id="m145">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 16.26</td>
<td align="left">8.96 <inline-formula id="inf130">
<mml:math id="m146">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.84</td>
<td align="left">128.92 <inline-formula id="inf131">
<mml:math id="m147">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.53</td>
</tr>
<tr>
<td align="left">RDP 04</td>
<td align="left">480.67 <inline-formula id="inf132">
<mml:math id="m148">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 7.95</td>
<td align="left">393.29 <inline-formula id="inf133">
<mml:math id="m149">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.04</td>
<td align="left">12.60 <inline-formula id="inf134">
<mml:math id="m150">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.13</td>
<td align="left">135.19 <inline-formula id="inf135">
<mml:math id="m151">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 19.61</td>
</tr>
<tr>
<td align="left">RDP 05</td>
<td align="left">441.44 <inline-formula id="inf136">
<mml:math id="m152">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.21</td>
<td align="left">367.66 <inline-formula id="inf137">
<mml:math id="m153">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 16.82</td>
<td align="left">11.84 <inline-formula id="inf138">
<mml:math id="m154">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.12</td>
<td align="left">122.94 <inline-formula id="inf139">
<mml:math id="m155">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 19.64</td>
</tr>
<tr>
<td align="left">RDP 06</td>
<td align="left">279.51 <inline-formula id="inf140">
<mml:math id="m156">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 6.72</td>
<td align="left">347.55 <inline-formula id="inf141">
<mml:math id="m157">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.788</td>
<td align="left">10.12 <inline-formula id="inf142">
<mml:math id="m158">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.99</td>
<td align="left">87.83 <inline-formula id="inf143">
<mml:math id="m159">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.17</td>
</tr>
<tr>
<td align="left">RDP 07</td>
<td align="left">247.96 <inline-formula id="inf144">
<mml:math id="m160">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 6,67</td>
<td align="left">296.721 <inline-formula id="inf145">
<mml:math id="m161">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 14.26</td>
<td align="left">8.73 <inline-formula id="inf146">
<mml:math id="m162">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.87</td>
<td align="left">106.15 <inline-formula id="inf147">
<mml:math id="m163">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.28</td>
</tr>
<tr>
<td align="left">RDP 08</td>
<td align="left">362.03 <inline-formula id="inf148">
<mml:math id="m164">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.03</td>
<td align="left">276.40 <inline-formula id="inf149">
<mml:math id="m165">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.06</td>
<td align="left">8.64 <inline-formula id="inf150">
<mml:math id="m166">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.83</td>
<td align="left">91.18 <inline-formula id="inf151">
<mml:math id="m167">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.40</td>
</tr>
<tr>
<td align="left">RDP 09</td>
<td align="left">499.35 <inline-formula id="inf152">
<mml:math id="m168">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.69</td>
<td align="left">472.04 <inline-formula id="inf153">
<mml:math id="m169">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 20.27</td>
<td align="left">19.36 <inline-formula id="inf154">
<mml:math id="m170">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.48</td>
<td align="left">177.19 <inline-formula id="inf155">
<mml:math id="m171">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 23.81</td>
</tr>
<tr>
<td align="left">RDP 10</td>
<td align="left">1,421.46 <inline-formula id="inf156">
<mml:math id="m172">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.38</td>
<td align="left">1,195.80 <inline-formula id="inf157">
<mml:math id="m173">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 30.63</td>
<td align="left">18.81 <inline-formula id="inf158">
<mml:math id="m174">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.42</td>
<td align="left">264.11 <inline-formula id="inf159">
<mml:math id="m175">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 25.66</td>
</tr>
<tr>
<td align="left">RDP 11</td>
<td align="left">456.98 <inline-formula id="inf160">
<mml:math id="m176">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 7.95</td>
<td align="left">417.81 <inline-formula id="inf161">
<mml:math id="m177">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 18.55</td>
<td align="left">14.71 <inline-formula id="inf162">
<mml:math id="m178">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.23</td>
<td align="left">125.11 <inline-formula id="inf163">
<mml:math id="m179">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 20.81</td>
</tr>
<tr>
<td align="left">RDP 12</td>
<td align="left">437.17 <inline-formula id="inf164">
<mml:math id="m180">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.28</td>
<td align="left">356.985 <inline-formula id="inf165">
<mml:math id="m181">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.54</td>
<td align="left">10.86 <inline-formula id="inf166">
<mml:math id="m182">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.97</td>
<td align="left">111.84 <inline-formula id="inf167">
<mml:math id="m183">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.48</td>
</tr>
<tr>
<td align="left">RDP 13</td>
<td align="left">547.86 <inline-formula id="inf168">
<mml:math id="m184">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 10.16</td>
<td align="left">457.89 <inline-formula id="inf169">
<mml:math id="m185">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 18.85</td>
<td align="left">10.49 <inline-formula id="inf170">
<mml:math id="m186">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.05</td>
<td align="left">147.52 <inline-formula id="inf171">
<mml:math id="m187">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 20.89</td>
</tr>
<tr>
<td align="left">RDP 14</td>
<td align="left">373.40 <inline-formula id="inf172">
<mml:math id="m188">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.26</td>
<td align="left">308.16 <inline-formula id="inf173">
<mml:math id="m189">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 14.29</td>
<td align="left">8.02 <inline-formula id="inf174">
<mml:math id="m190">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.80</td>
<td align="left">98.05 <inline-formula id="inf175">
<mml:math id="m191">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 16.56</td>
</tr>
<tr>
<td align="left">RDP 15</td>
<td align="left">132.88 <inline-formula id="inf176">
<mml:math id="m192">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.68</td>
<td align="left">12.02 <inline-formula id="inf177">
<mml:math id="m193">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.09</td>
<td align="left">5.27 <inline-formula id="inf178">
<mml:math id="m194">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.67</td>
<td align="left">65.23 <inline-formula id="inf179">
<mml:math id="m195">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.29</td>
</tr>
<tr>
<td align="left">RDP 16</td>
<td align="left">237.16 <inline-formula id="inf180">
<mml:math id="m196">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 6.20</td>
<td align="left">248.18 <inline-formula id="inf181">
<mml:math id="m197">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.70</td>
<td align="left">6.82 <inline-formula id="inf182">
<mml:math id="m198">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.79</td>
<td align="left">85.01 <inline-formula id="inf183">
<mml:math id="m199">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.46</td>
</tr>
<tr>
<td align="left">RDP 17</td>
<td align="left">474.11 <inline-formula id="inf184">
<mml:math id="m200">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.48</td>
<td align="left">393.29 <inline-formula id="inf185">
<mml:math id="m201">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 18.04</td>
<td align="left">11.82 <inline-formula id="inf186">
<mml:math id="m202">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.19</td>
<td align="left">138.32 <inline-formula id="inf187">
<mml:math id="m203">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 21.36</td>
</tr>
<tr>
<td rowspan="5" align="left">Activity statistics</td>
<td align="left">Min</td>
<td align="left">132.88 <inline-formula id="inf188">
<mml:math id="m204">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 6.20</td>
<td align="left">112.02 <inline-formula id="inf189">
<mml:math id="m205">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.09</td>
<td align="left">5.27 <inline-formula id="inf190">
<mml:math id="m206">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.67</td>
<td align="left">65.23 <inline-formula id="inf191">
<mml:math id="m207">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.29</td>
</tr>
<tr>
<td align="left">Max</td>
<td align="left">1,421.46 <inline-formula id="inf192">
<mml:math id="m208">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 13.38</td>
<td align="left">1,195.80 <inline-formula id="inf193">
<mml:math id="m209">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 30.63</td>
<td align="left">19.37 <inline-formula id="inf194">
<mml:math id="m210">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.48</td>
<td align="left">264.11 <inline-formula id="inf195">
<mml:math id="m211">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 25.66</td>
</tr>
<tr>
<td align="left">Mean</td>
<td align="left">464.96 <inline-formula id="inf196">
<mml:math id="m212">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 2.08</td>
<td align="left">407.41 <inline-formula id="inf197">
<mml:math id="m213">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.23</td>
<td align="left">11.20 <inline-formula id="inf198">
<mml:math id="m214">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.03</td>
<td align="left">127.50 <inline-formula id="inf199">
<mml:math id="m215">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 21.85</td>
</tr>
<tr>
<td align="left">STDev</td>
<td align="left">274.12</td>
<td align="left">222.56</td>
<td align="left">3.76</td>
<td align="left">45.58</td>
</tr>
<tr>
<td align="left">Median</td>
<td align="left">444.81 <inline-formula id="inf200">
<mml:math id="m216">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.20</td>
<td align="left">393.29 <inline-formula id="inf201">
<mml:math id="m217">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.04</td>
<td align="left">10.66 <inline-formula id="inf202">
<mml:math id="m218">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.97</td>
<td align="left">122.94 <inline-formula id="inf203">
<mml:math id="m219">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 19.64</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The concentration of <sup>40</sup>K ranged from <inline-formula id="inf204">
<mml:math id="m220">
<mml:mrow>
<mml:mn>113.34</mml:mn>
<mml:mspace width="0.2em"/>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 20.80 Bq/kg to 145.79 <inline-formula id="inf205">
<mml:math id="m221">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 22.51 Bq/kg with a mean of 126.15 <inline-formula id="inf206">
<mml:math id="m222">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 10.90 Bq/kg, which is 11 times the concentration of <sup>232</sup>Th. The level of <sup>40</sup>K is below the permissible limit of 400 Bq/kg, and <sup>232</sup>Th ranged from 8.25 <inline-formula id="inf207">
<mml:math id="m223">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.31 to 11.20 <inline-formula id="inf208">
<mml:math id="m224">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 1.03 Bq/kg with a mean of 10.06 <inline-formula id="inf209">
<mml:math id="m225">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.68 Bq/kg. The mean concentration of <sup>226</sup>Ra is 40.3 times that of <sup>232</sup>Th, whereas it is 3.5 times the level of <sup>40</sup>K in the samples, and in decreasing order they are: <sup>238</sup>U<inline-formula id="inf210">
<mml:math id="m226">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo>&#x3e;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>226</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>Ra<inline-formula id="inf211">
<mml:math id="m227">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo>&#x3e;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>40</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>K<inline-formula id="inf212">
<mml:math id="m228">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo>&#x3e;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>232</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>Th.</p>
<p>In this analysis, <sup>214</sup>Bi and <sup>214</sup>Pb were used to estimate <sup>238</sup>U, assuming secular equilibrium [<xref ref-type="bibr" rid="B29">29</xref>, <xref ref-type="bibr" rid="B30">30</xref>], and radium was estimated directly from its 186 keV signal, as there were very few significant responses from <sup>235</sup>U signals to indicate its presence. Both <sup>214</sup>Bi and <sup>214</sup>Pb are short-lived decay products of textsuperscript222Rn gas and are strong gamma-ray emitters. Their characteristic gamma rays&#x2014;295 and 351.9 keV for <sup>214</sup>Pb, and 609.3, 1,120.3, and 1764.5 keV for <sup>214</sup>Bi&#x2013;are easily detected by <inline-formula id="inf213">
<mml:math id="m229">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-ray spectrometry.</p>
<p>The use of these daughter products to determine the parent uranium concentration relies on the concept of secular equilibrium, which states that the activity of each intermediate product is proportional to the amount of uranium present because its rate of decay equals its rate of production. The activities of <sup>226</sup>Ra and <sup>214</sup>Pb were correlated to see if the analysis was indeed carried out at radioactive secular equilibrium samples for Roodepoort tailings. There was a good positive correlation between the activities of <sup>226</sup>Ra and <sup>238</sup>U in the samples, indicating the system was indeed at radioactive secular equilibrium for the Roodepoort tailings samples after 42 days.</p>
<p>The activity concentration of <sup>232</sup>Th was detected, but it was within the background levels. The activity concentration of <sup>40</sup>K was present at an intermediate level but below the permissible limit of 400 Bq/kg [<xref ref-type="bibr" rid="B5">5</xref>]. The specific activity concentration of <sup>238</sup>U and <sup>226</sup>Ra dominated all NORM activities in the soil samples from Roodepoort tailings, as shown in <xref ref-type="fig" rid="F4">Figure 4</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>The mean specific activity concentration.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g004.tif">
<alt-text content-type="machine-generated">Bar graph showing the specific activity of radionuclides in soil. Uranium has the highest activity at four hundred sixty-four point ninety-six becquerels per kilogram, followed by radium at four hundred fifty-two point twenty-eight, potassium at one hundred twenty-seven point fifty, and thorium at eleven point twenty.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="table" rid="T3">Table 3</xref> compares radium in this study, in the region, and globally in tailings of different mined resources. The high radium activity concentrations, compared with activities in other tailings except for gold from various countries, are presented in <xref ref-type="table" rid="T3">Table 3</xref>. The mean radium concentration in the CMR gold tailings is 451 <inline-formula id="inf214">
<mml:math id="m230">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.00 Bq/kg, which is lower than the 662 Bq/kg found in New Zealand&#x2019;s phosphate rock ore [<xref ref-type="bibr" rid="B62">62</xref>], but higher than the 253.6 Bq/kg in Saudi Arabia&#x2019;s phosphate ore [<xref ref-type="bibr" rid="B63">63</xref>]. Compared to phosphate tailings in Tanzania, which exceed 2,939.0 and 5,591.2 Bq/kg [<xref ref-type="bibr" rid="B64">64</xref>], the CMR concentration is significantly lower. However, it is higher than the concentration of 54 <inline-formula id="inf215">
<mml:math id="m231">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 3 Bq/kg around the Geita Gold Mine in Tanzania [<xref ref-type="bibr" rid="B65">65</xref>], and higher than 200.42 and 306.67 Bq/kg in silver mining areas of Brazil [<xref ref-type="bibr" rid="B66">66</xref>]. It is notable that phosphate rock waste have high radium and uranium activities. This is because the fertilizer processing focuses solely on extracting phosphates, leaving uranium concentrated in the waste.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>The comparison of radium activity concentration in tailings of different mining wastes.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Tailings type</th>
<th align="left">Min</th>
<th align="left">Max</th>
<th align="left">Mean</th>
<th align="left">References</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Phosphate rock Ore</td>
<td align="left">107</td>
<td align="left">1,649</td>
<td align="left">662</td>
<td align="left">[<xref ref-type="bibr" rid="B62">62</xref>]</td>
</tr>
<tr>
<td align="left">Phosphate Ore</td>
<td align="left">62.3</td>
<td align="left">333.5</td>
<td align="left">253.6</td>
<td align="left">[<xref ref-type="bibr" rid="B63">63</xref>]</td>
</tr>
<tr>
<td align="left">Phosphate tailings 1</td>
<td align="left">311.0</td>
<td align="left">3,945.8</td>
<td align="left">2,939.0</td>
<td align="left">[<xref ref-type="bibr" rid="B64">64</xref>]</td>
</tr>
<tr>
<td align="left">Phosphate tailings 2</td>
<td align="left">3,759.8</td>
<td align="left">7,606.3</td>
<td align="left">5,591.2</td>
<td align="left">[<xref ref-type="bibr" rid="B64">64</xref>]</td>
</tr>
<tr>
<td align="left">Geita gold mine</td>
<td align="left">13 <inline-formula id="inf216">
<mml:math id="m232">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9</td>
<td align="left">99 <inline-formula id="inf217">
<mml:math id="m233">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4</td>
<td align="left">54 <inline-formula id="inf218">
<mml:math id="m234">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 3</td>
<td align="left">[<xref ref-type="bibr" rid="B65">65</xref>]</td>
</tr>
<tr>
<td align="left">Silver mining, zone A</td>
<td align="left">124.26</td>
<td align="left">303.45</td>
<td align="left">200.42</td>
<td align="left">[<xref ref-type="bibr" rid="B66">66</xref>]</td>
</tr>
<tr>
<td align="left">Silver mining, zone B</td>
<td align="left">105.76</td>
<td align="left">596.26</td>
<td align="left">306.67</td>
<td align="left">[<xref ref-type="bibr" rid="B66">66</xref>]</td>
</tr>
<tr>
<td align="left">West rand</td>
<td align="left">12.35</td>
<td align="left">941.07</td>
<td align="left">53.09</td>
<td align="left">[<xref ref-type="bibr" rid="B23">23</xref>]</td>
</tr>
<tr>
<td align="left">Roodepoort</td>
<td align="left">112.02 <inline-formula id="inf219">
<mml:math id="m235">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.09</td>
<td align="left">1,195.80 <inline-formula id="inf220">
<mml:math id="m236">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 30.63</td>
<td align="left">407.41 <inline-formula id="inf221">
<mml:math id="m237">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 4.23</td>
<td align="left">This study</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s5-2">
<label>5.2</label>
<title>Radiological hazard assessment in soil samples</title>
<p>For RDP samples shown in <xref ref-type="table" rid="T4">Table 4</xref>, the <inline-formula id="inf222">
<mml:math id="m238">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>Ra</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Eq</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> has a mean of 433.28 <inline-formula id="inf223">
<mml:math id="m239">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.06 Bq/kg, a value 1.2 times the permissible limit of 370 Bq/kg [<xref ref-type="bibr" rid="B42">42</xref>]. The indoor and outdoor air absorbed dose rates have average values which exceeded their recommended values of 84 and 59 nGy/h, respectively. The indoor and outdoor AEDE are above their recommended values of 0.41 and 0.07 mSv/y, respectively [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B67">67</xref>]. The values of the AEDE are higher than 0.23 <inline-formula id="inf224">
<mml:math id="m240">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 10.07 mSv/y for outdoor and 0.92 <inline-formula id="inf225">
<mml:math id="m241">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 10.29 mSv/y for indoor, as reported in a study in Cameroon [<xref ref-type="bibr" rid="B68">68</xref>]. Both the cancer risks (ELCR) are higher than their recommended values of 1.16<inline-formula id="inf226">
<mml:math id="m242">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and 0.29<inline-formula id="inf227">
<mml:math id="m243">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>, respectively [<xref ref-type="bibr" rid="B67">67</xref>].</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Comparison of radiological health indices with their globally recommended upper limits.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Site</th>
<th align="left">Radiological indices</th>
<th align="left">Minimum</th>
<th align="left">Maximum</th>
<th align="left">Mean</th>
<th align="center">Upper limit</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="12" align="left">RDP</td>
<td align="left">
<inline-formula id="inf228">
<mml:math id="m244">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>Ra</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (Bq/kg)</td>
<td align="left">142.74 <inline-formula id="inf229">
<mml:math id="m245">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 9.24</td>
<td align="left">1,242.98 <inline-formula id="inf230">
<mml:math id="m246">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 30.78</td>
<td align="left">433.28 <inline-formula id="inf231">
<mml:math id="m247">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 17.06</td>
<td align="center">370</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf232">
<mml:math id="m248">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>ADR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Ind</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (nGy/h)</td>
<td align="left">114.15 <inline-formula id="inf233">
<mml:math id="m249">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 8.51</td>
<td align="left">1,142.21 <inline-formula id="inf234">
<mml:math id="m250">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 28.32</td>
<td align="left">397.42 <inline-formula id="inf235">
<mml:math id="m251">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 15.17</td>
<td align="center">84</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf236">
<mml:math id="m252">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>ADR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Out</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (nGy/h)</td>
<td align="left">57.68 <inline-formula id="inf237">
<mml:math id="m253">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 6.40</td>
<td align="left">574.91 <inline-formula id="inf238">
<mml:math id="m254">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 14.23</td>
<td align="left">200.35 <inline-formula id="inf239">
<mml:math id="m255">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 7.89</td>
<td align="center">59</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf240">
<mml:math id="m256">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>AEDE</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Ind</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (mSv/y)</td>
<td align="left">0.56 <inline-formula id="inf241">
<mml:math id="m257">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.04</td>
<td align="left">5.60 <inline-formula id="inf242">
<mml:math id="m258">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.14</td>
<td align="left">1.95 <inline-formula id="inf243">
<mml:math id="m259">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.08</td>
<td align="center">0.41</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf244">
<mml:math id="m260">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>AEDE</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Out</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (mSv/y)</td>
<td align="left">0.07 <inline-formula id="inf245">
<mml:math id="m261">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.01</td>
<td align="left">0.71 <inline-formula id="inf246">
<mml:math id="m262">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.02</td>
<td align="left">0.25 <inline-formula id="inf247">
<mml:math id="m263">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.01</td>
<td align="center">0.07</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf248">
<mml:math id="m264">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>ELCR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Ind</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf249">
<mml:math id="m265">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mspace width="-0.2em"/>
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mspace width="-0.2em"/>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">1.96 <inline-formula id="inf250">
<mml:math id="m266">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.15</td>
<td align="left">19.61 <inline-formula id="inf251">
<mml:math id="m267">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.49</td>
<td align="left">6.82 <inline-formula id="inf252">
<mml:math id="m268">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.27</td>
<td align="center">1.16</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf253">
<mml:math id="m269">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>ELCR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">Out</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> <inline-formula id="inf254">
<mml:math id="m270">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mspace width="-0.2em"/>
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mspace width="-0.2em"/>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">0.25 <inline-formula id="inf255">
<mml:math id="m271">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.02</td>
<td align="left">2.47 <inline-formula id="inf256">
<mml:math id="m272">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.06</td>
<td align="left">0.86 <inline-formula id="inf257">
<mml:math id="m273">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.03</td>
<td align="center">0.29</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf258">
<mml:math id="m274">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">0.64 <inline-formula id="inf259">
<mml:math id="m275">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.06</td>
<td align="left">6.59 <inline-formula id="inf260">
<mml:math id="m276">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.18</td>
<td align="left">2.27 <inline-formula id="inf261">
<mml:math id="m277">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.10</td>
<td align="center">
<inline-formula id="inf262">
<mml:math id="m278">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>1</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf263">
<mml:math id="m279">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">0.34 <inline-formula id="inf264">
<mml:math id="m280">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.07</td>
<td align="left">3.36 <inline-formula id="inf265">
<mml:math id="m281">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.12</td>
<td align="left">1.17 <inline-formula id="inf266">
<mml:math id="m282">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.09</td>
<td align="center">
<inline-formula id="inf267">
<mml:math id="m283">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>1</td>
</tr>
<tr>
<td align="left">AGDE <inline-formula id="inf268">
<mml:math id="m284">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mtext>Sv/y</mml:mtext>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">388.68 <inline-formula id="inf269">
<mml:math id="m285">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 28.75</td>
<td align="left">3,856.56 <inline-formula id="inf270">
<mml:math id="m286">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 95.28</td>
<td align="left">1,345.78 <inline-formula id="inf271">
<mml:math id="m287">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 52.90</td>
<td align="center">300</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf272">
<mml:math id="m288">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">0.42 <inline-formula id="inf273">
<mml:math id="m289">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.04</td>
<td align="left">4.71 <inline-formula id="inf274">
<mml:math id="m290">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.12</td>
<td align="left">1.46 <inline-formula id="inf275">
<mml:math id="m291">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.07</td>
<td align="center">
<inline-formula id="inf276">
<mml:math id="m292">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>1</td>
</tr>
<tr>
<td align="left">
<inline-formula id="inf277">
<mml:math id="m293">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="left">0.56 <inline-formula id="inf278">
<mml:math id="m294">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.05</td>
<td align="left">5.98 <inline-formula id="inf279">
<mml:math id="m295">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.15</td>
<td align="left">2.04 <inline-formula id="inf280">
<mml:math id="m296">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 0.08</td>
<td align="center">
<inline-formula id="inf281">
<mml:math id="m297">
<mml:mrow>
<mml:mo>&#x3c;</mml:mo>
<mml:mspace width="-0.2em"/>
</mml:mrow>
</mml:math>
</inline-formula>1</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The internal hazard index is 2.51 times higher than its recommended value, while the external hazard index is 1.3 times higher than its recommended value but is of the same order as the value found in the study in Cameroon [<xref ref-type="bibr" rid="B68">68</xref>] and higher than the value of 0.59 reported in Turkey [<xref ref-type="bibr" rid="B69">69</xref>]. The mean values of AGDE, <inline-formula id="inf282">
<mml:math id="m298">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf283">
<mml:math id="m299">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are 4.5, 2.0, and 1.5 times higher than their recommended values, respectively, and the average <inline-formula id="inf284">
<mml:math id="m300">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is lower than the value of 1.60 reported in Turkey [<xref ref-type="bibr" rid="B69">69</xref>].</p>
<p>In the figure, the radium equivalent activity of the RDP gold tailings samples shows that only 4 out of 17 samples&#x2013;RDP 06, 07, 15, and 16&#x2014;with RDP 15 having the lowest values, fall below the recommended regulatory benchmark of 370 Bq/kg [<xref ref-type="bibr" rid="B42">42</xref>, <xref ref-type="bibr" rid="B70">70</xref>], which corresponds to an external dose rate limit of about 1.5 mSv/y [<xref ref-type="bibr" rid="B70">70</xref>] for shelter occupants. The RDP samples with high radium levels&#x2013;RDP 02, 03, 04, 05, 09, 10, 11, 12, 13, and 17&#x2014;showed high <inline-formula id="inf285">
<mml:math id="m301">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>Ra</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Eq</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> values, with RDP 10 having the highest value, as shown in <xref ref-type="fig" rid="F5">Figure 5</xref>; overall, the values exceeded the recommended limit. The mean radium equivalent was higher than the 189 Bq/kg found in a study of tailings in Tanzania [<xref ref-type="bibr" rid="B65">65</xref>].</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>The radium equivalent activity in samples.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g005.tif">
<alt-text content-type="machine-generated">Bar chart comparing permissible and measured radium equivalent values in Becquerels per kilogram for samples RDP01 to RDP17. Most measured values exceed permissible limits, with RDP10 showing a significant peak.</alt-text>
</graphic>
</fig>
<p>The relationship between the ADR and AEDE in Roodepoort gold tailings samples is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>. The internal and external absorbed dose rates exceeded their recommended limits of 84 and 59.9 nGy/h, respectively [<xref ref-type="bibr" rid="B5">5</xref>]. The indoor ADR is similar to the 413.50 nGy/h reported in the West Rand [<xref ref-type="bibr" rid="B23">23</xref>], but higher than the value found in Cameroon, which was 188.2 <inline-formula id="inf286">
<mml:math id="m302">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 59.4 nGy/h.The outdoor ADR is higher than 49.09 nGy/h and 70.12 nGy/h, which were found in the East Rand and Soweto, respectively [<xref ref-type="bibr" rid="B23">23</xref>]. The total annual effective dose equivalent exceeded the permitted value of 0.48 mSv/y in all samples, and they were higher than the global limit of 1.00 mSv/y [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B71">71</xref>], and they were higher than the values in the East Rand of 0.51 mSv/y [<xref ref-type="bibr" rid="B23">23</xref>]. <xref ref-type="fig" rid="F6">Figure 6</xref> shows that a proportionality exists between the absorbed dose rate and the annual effective dose rate.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The comparison of ADR and AEDE in samples.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g006.tif">
<alt-text content-type="machine-generated">Bar chart comparing indoor and outdoor absorbed dose rates (ADR) in nanograys per hour and annual effective dose equivalent (AEDE) in millisieverts per year across 17 RDP locations. Blue bars represent indoor ADR, yellow bars represent outdoor ADR, black bars represent AEDE total, with limits marked by sky blue, red, and green bars. Peak values are observed at RDP10 for ADR and AEDE.</alt-text>
</graphic>
</fig>
<p>It is evident in <xref ref-type="fig" rid="F6">Figure 6</xref> that all samples follow a similar distribution trend to the absorbed dose rate, as the annual effective dose has a linear relationship with the absorbed dose rate. The relationship between ADR and AEDE in Roodepoort gold tailings samples is illustrated. The annual effective dose equivalent increases with an increase in the air absorbed dose rate; this relationship is confirmed by <xref ref-type="fig" rid="F7">Figure 7</xref>, which shows that a proportionality exists between the absorbed dose rate and the annual effective dose rate.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>The linear plot between ADR and AEDE.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g007.tif">
<alt-text content-type="machine-generated">Graph showing a linear relationship between total annual effective dose equivalent (AEDE_tot in mSv/y) and total ambient dose rate (ADR_tot in nGy/h). Data points form a line with the equation AEDE &#x3d; 0.0037 &#xD7; ADR - 0.001, and R&#xB2; is 1, indicating a perfect fit. Error bars accompany the data points.</alt-text>
</graphic>
</fig>
<p>The radiological health indices in the Roodepoort gold tailings, for which the permissible maximum value should be unity, are shown in <xref ref-type="fig" rid="F8">Figure 8</xref>, with RDP 10 exceeding all others and RDP 15 having the lowest values in <inline-formula id="inf287">
<mml:math id="m303">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>In</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf288">
<mml:math id="m304">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Ex</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf289">
<mml:math id="m305">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf290">
<mml:math id="m306">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. These indicators suggest that, in the long term, people who reside permanently in these areas may face health issues.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>The <inline-formula id="inf291">
<mml:math id="m307">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>In</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf292">
<mml:math id="m308">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Ex</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf293">
<mml:math id="m309">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
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<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf294">
<mml:math id="m310">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>I</mml:mtext>
</mml:mrow>
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<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indices.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g008.tif">
<alt-text content-type="machine-generated">Bar chart showing radiological indices for RDP01 to RDP17. Bars represent HIn (blue), HEx (purple), I&#x3B3; (green), I&#x3B1; (red), with permissible values (black). RDP10 has the highest indices.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F9">Figure 9</xref> shows a comparison of indoor and outdoor excess lifetime cancer risk factors calculated for these samples. For Sample RDP 10, the outdoor ELCR is nine times higher than its acceptable value. Both the indoor and outdoor ELCR exceed their respective limits of <inline-formula id="inf295">
<mml:math id="m311">
<mml:mrow>
<mml:mn>1.16</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf296">
<mml:math id="m312">
<mml:mrow>
<mml:mn>0.29</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
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<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> [<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B67">67</xref>], as shown in the figure below.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>The excess lifetime cancer risks and their limits.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g009.tif">
<alt-text content-type="machine-generated">Bar chart comparing Indoor ELCR, Indoor ELCR Limit, Outdoor ELCR, and Outdoor ELCR Limit for RDP01 to RDP17. Indoor and outdoor ELCR values are depicted as blue and green bars, respectively. Limits are shown as red and yellow bars. Indoor ELCR peaks at RDP10.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F10">Figure 10</xref> shows a plot of the ELCR and AEDE values for the gold tailings soil samples from Roodepoort. This plot indicates a linear relationship between radiation exposure and the likelihood of developing cancer during a human lifetime.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>The linear plot between ELCR and AEDE.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g010.tif">
<alt-text content-type="machine-generated">Scatter plot showing a positive linear relationship between Annual Effective Dose Equivalent (AEDE) in millisieverts per year and Excess Lifetime Cancer Risk (ELCR). The red line represents the linear regression fit with the equation \(y &#x3d; 3.296x &#x2b; 0.568\) and \(R^2 &#x3d; 1\). Blue data points with error bars are plotted along the line.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F11">Figure 11</xref> shows the relationship between the radium equivalent activity and the annual gonadal dose equivalent in the tailings samples from Roodepoort. The graph indicates that the AGDE is proportional to the activity present in the samples. The mean AGDE is 1,345.78 <inline-formula id="inf297">
<mml:math id="m313">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 52.90 <inline-formula id="inf298">
<mml:math id="m314">
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mtext>Sv/y</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, which is 4.5 times the recommended value of 300 <inline-formula id="inf299">
<mml:math id="m315">
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mtext>Sv/y</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> [<xref ref-type="bibr" rid="B72">72</xref>] and is higher than the AGDE value of 678 <inline-formula id="inf300">
<mml:math id="m316">
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mtext>Sv/y</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> found in a study in Tanzania [<xref ref-type="bibr" rid="B65">65</xref>].</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>The AGDE and <inline-formula id="inf301">
<mml:math id="m317">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>Rad</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>Eq</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in Roodepoort samples.</p>
</caption>
<graphic xlink:href="fphy-13-1740296-g011.tif">
<alt-text content-type="machine-generated">Bar chart showing Radium Equivalent (RaEq) in blue and AGDE in black for samples RDP01 to RDP17. RaEq peaks significantly at RDP10. Permissible levels, marked in green, are constant and lower than both Radium Equivalent and AGDE across all samples.</alt-text>
</graphic>
</fig>
<p>Soil samples with high activity tend to release high levels of radiation; therefore, all radiation hazard indices for these samples are high, and the reproductive organs (gonads) of people exposed to such soil are at risk of significant radiation exposure, which can affect future generations. Radiation can cause genetic damage in the gonads, leading to mutations and hereditary diseases, as there is no minimum safe dose of radiation to the gonads [<xref ref-type="bibr" rid="B73">73</xref>]. No amount of ionizing radiation is considered negligible, as it is believed that any exposure may increase the risk of stochastic effects. It is assumed that these effects follow a linear model with no specific threshold; therefore, radiology specialists encourage adherence to the ALARA principle [<xref ref-type="bibr" rid="B74">74</xref>].</p>
<p>As radiation is invisible to the human eye but can be harmful at high levels, it is important to keep exposure as low as possible. The ALARA principle consists of three factors: time, distance, and shielding. If citizens live permanently near radioactive waste, these ALARA factors are continuously disregarded, which also violates the United Nations Sustainable Development Goals (SDGs), such as SDG 3: Good Health and Wellbeing and SDG 11: Sustainable Cities and Communities. If such radiation reaches water bodies, both SDG 14: Life Below Water and SDG 15: Life on Land are also not observed of [<xref ref-type="bibr" rid="B75">75</xref>].</p>
</sec>
</sec>
<sec id="s6">
<label>6</label>
<title>Conclusion and outlook</title>
<p>The Roodepoort gold tailings samples were collected, prepared, and analyzed for radioactivity using a high-energy resolution coaxial HPGe <inline-formula id="inf302">
<mml:math id="m318">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> - detector. In this analysis, both uranium and radium exceeded their recommended global limits, while thorium and potassium were below their recommended limits.</p>
<p>The average radium equivalent was 1.2 times higher than its recommended value of 370 Bq/kg. The average indoor and outdoor absorbed dose rates were 4.7 and 3.3 times higher than their respective recommended values of 84 nGy/h and 59 nGy/h. The average indoor and outdoor annual effective dose equivalents were 4.8 and 3.6 times higher than their recommended values of 0.41 and 0.07 mSv/y, respectively. The average indoor and outdoor excess lifetime cancer risks were 5.9 and 3.0 times higher than their respective recommended values of <inline-formula id="inf303">
<mml:math id="m319">
<mml:mrow>
<mml:mn>1.16</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf304">
<mml:math id="m320">
<mml:mrow>
<mml:mn>0.29</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>1</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>. The averages of internal and external hazard indices were 2.5 and 1.3 times higher than unity. The annual gonadal dose equivalent had a mean value 4.5 times higher than the recommended value of 300 <inline-formula id="inf305">
<mml:math id="m321">
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
<mml:mtext>Sv/y</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>. The mean values of the alpha and gamma hazard indexes were 2.26 and 1.61 times greater than unity, respectively.</p>
<p>Although they originate from background ionising radiation, these findings may, in the long term, have deleterious health effects on residents in the vicinity of the tailings, as the recommended radiological health limits were exceeded. Additional oversight and regulatory control measures are required to ensure the safety of the environment and residents near the tailings. Our study was limited to measuring radioactivity using gamma spectroscopy and did not use alpha spectroscopy, even though radon gas is also an alpha emitter. Future studies may address this aspect.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s8">
<title>Author contributions</title>
<p>MM: Writing &#x2013; original draft, Writing &#x2013; review and editing. SN: Funding acquisition, Supervision, Writing &#x2013; review and editing. SM: Funding acquisition, Supervision, Writing &#x2013; review and editing. BK: Supervision, Writing &#x2013; review and editing. PLM: Supervision, Writing &#x2013; review and editing. PPM: Supervision, Writing &#x2013; review and editing.</p>
</sec>
<ack>
<title>Acknowledgements</title>
<p>The first author thanks the NRF-iThemba LABS for providing access to the facility. Special thanks are extended to Mr. A. Kwelilanga, an applied nuclear and radiation physicist at iThemba LABS, for his knowledge of gamma spectrometric analysis. Most importantly, the Department of Physics, University of Zululand, supported this study.</p>
</ack>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s11">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="s12">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<fn-group>
<fn fn-type="custom" custom-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/975529/overview">Mauro Menichelli</ext-link>, Istituto Nazionale di Fisica Nucleare di Perugia, Italy</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1033009/overview">Belafrites Abdelfettah</ext-link>, University of Jijel, Algeria</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3288762/overview">Gebi Tuku</ext-link>, Mizan Tepi University, Ethiopia</p>
</fn>
</fn-group>
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