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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.4" xml:lang="en">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Oalib</journal-id>
      <journal-title-group>
        <journal-title>Open Access Library Journal</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2333-9721</issn>
      <issn pub-type="ppub">2333-9705</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/oalib.1114863</article-id>
      <article-id pub-id-type="publisher-id">Oalib-149323</article-id>
      <article-categories>
        <subj-group>
          <subject>Article</subject>
        </subj-group>
        <subj-group>
          <subject>Biomedical</subject>
          <subject>Life Sciences</subject>
          <subject>Business</subject>
          <subject>Economics</subject>
          <subject>Chemistry</subject>
          <subject>Materials Science</subject>
          <subject>Computer Science</subject>
          <subject>Communications</subject>
          <subject>Earth</subject>
          <subject>Environmental Sciences</subject>
          <subject>Engineering</subject>
          <subject>Medicine</subject>
          <subject>Healthcare</subject>
          <subject>Physics</subject>
          <subject>Mathematics</subject>
          <subject>Social Sciences</subject>
          <subject>Humanities</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Radiological Assessment Due to Natural Radioactivity in Rocks and Associated Health Impacts in Chetambe Hills, Kenya</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Wanyama</surname>
            <given-names>Mukanda Kere</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Waswa</surname>
            <given-names>Michael Nakitare</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Wanjala</surname>
            <given-names>Felix Omonya</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Hashim</surname>
            <given-names>Nadir Omar</given-names>
          </name>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
      </contrib-group>
      <aff id="aff1"><label>1</label> Department of Science, Technology &amp; Engineering, Kibabii University, Bungoma, Kenya </aff>
      <aff id="aff2"><label>2</label> IAEA, Vienna, Austria </aff>
      <aff id="aff3"><label>3</label> Department of Physics, Kenyatta University, Nairobi, Kenya </aff>
      <author-notes>
        <fn fn-type="conflict" id="fn-conflict">
          <p>The authors declare no conflict of interest</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub">
        <day>02</day>
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="collection">
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <volume>13</volume>
      <issue>02</issue>
      <fpage>1</fpage>
      <lpage>15</lpage>
      <history>
        <date date-type="received">
          <day>11</day>
          <month>01</month>
          <year>2026</year>
        </date>
        <date date-type="accepted">
          <day>30</day>
          <month>01</month>
          <year>2026</year>
        </date>
        <date date-type="published">
          <day>02</day>
          <month>02</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© 2026 by the authors and Scientific Research Publishing Inc.</copyright-statement>
        <copyright-year>2026</copyright-year>
        <license license-type="open-access">
          <license-p> This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link> ). </license-p>
        </license>
      </permissions>
      <self-uri content-type="doi" xlink:href="https://doi.org/10.4236/oalib.1114863">https://doi.org/10.4236/oalib.1114863</self-uri>
      <abstract>
        <p>A radiological assessment due to natural radioactivity in rocks and associated health impacts in Chetambe hills, Kenya has been done using NaI (TI) detector employing gamma ray spectrometry technique. The activity concentrations of <sup>238</sup>U in the rock samples ranged from a minimum of 33 ± 1.65 Bq/Kg to a maximum of 119 ± 5.97 Bq/Kg with an average of 68 ± 3.23 Bq/Kg. The activity concentrations of <sup>232</sup>Th varied from a minimum 15 ± 0.75 Bq/Kg to a maximum of 167 ± 8.39 Bq/Kg with an average of 72 ± 3.48 Bq/Kg while the activity concentrations of <sup>40</sup>K varied from a minimum of 50 ± 2.5 Bq/Kg to a maximum of 2042 ± 6.43 Bq/Kg with an average of 866 ± 5.78 Bq/Kg. The averages for the three radionuclides all exceeded 33 Bq/Kg, 45 Bq/Kg and 420 Bq/Kg for <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K respectively. The absorbed dose rate (D<sub>r</sub>) ranged from a minimum of 33 ± 1.67 nGy/h to a maximum of 230 ± 11.53 nGy/h with an average of 111 ± 7.32 nGy. The AEDR<sub>in</sub> ranged from a minimum of 0.1 ± 0 mSv/y to a maximum of 0.8 ± 0.04 mSv/y with an average of 0.4 ± 0.02 mSv/y. AEDR<sub>out</sub> ranged from a minimum of 0.2 ± 0.01 mSv/y to a maximum of 0.5 ± 0.02 mSv/y with a mean of 0.2 ± 0.01 mSv/y. The radium equivalent for the study area varied from a minimum of 74 ± 3.74 Bq/kg to a maximum of 492 ± 24.61 Bq/kg with a mean value of 238 ± 6.34 Bq/kg which was below the world average value of 370 Bq/kg. The internal hazard indices varied from a minimum of 0.2 ± 0.01 mSv/y to a maximum of 1.3 ± 0.06 mSv/y with mean of 0.6 ± 0.02 mSv/y while external hazard indices varied from a minimum of 0.3 ± 0.01 mSv/y to a maximum of 1.6 ± 0.08 mSv/y with an average of 0.8 ± 0.03 mSv/y. The mean values of H<sub>in</sub> and H<sub>ex</sub> were both below the unity. The ELCR<sub>out</sub> values varied from 0.2 ± 0.09 to 1.9 ± 0.08 with a mean of 0.9 ± 0.06 that was below the acceptable limit of 2.9 × 10<sup>−</sup><sup>4</sup>. The values for ELCR<sub>in</sub> ranged from 0.4 ± 0.03 to 2.9 ± 0.07 with a mean value of 1.4 ± 0.05 which was equally lower than the world average of 2.9 × 10<sup>−</sup><sup>4</sup>. Thus radiation exposure from the rocks does not pose a health risk to the general public.</p>
      </abstract>
      <kwd-group kwd-group-type="author-generated" xml:lang="en">
        <kwd>Natural Radioactivity</kwd>
        <kwd>Health Impact</kwd>
        <kwd>Chetambe Hills</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>1. Introduction</title>
      <p>The existence of naturally occurring radionuclides dates back to the formation of the earth [<xref ref-type="bibr" rid="B1">1</xref>]. Exposure to ionizing radiations of primordial origin by human population can be a result of terrestrial radiations. Continuous exposure to ionizing radiation may lead to the damage of germ cells that may result in birth defects and limb deformations [<xref ref-type="bibr" rid="B2">2</xref>]. Natural radioactivity in rocks emanates from the daughter radionuclides of <sup>238</sup>U, <sup>232</sup>Th and singly occurring <sup>40</sup>K [<xref ref-type="bibr" rid="B3">3</xref>] that are significantly found in the environment. The levels of radionuclides of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K vary from place to place depending on the geological and geographical location [<xref ref-type="bibr" rid="B4">4</xref>]. The three radionuclides have very long half-lives; 4.468 × 10<sup>9</sup> years, 1.405 × 10<sup>10</sup> years and 1.22 × 10<sup>9</sup> years for <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K respectively [<xref ref-type="bibr" rid="B5">5</xref>]. According to [<xref ref-type="bibr" rid="B6">6</xref>], assessment and quantification of natural radioactivity levels in the environment are important in determining the safety standards in the utilization of rocks, soils and water. According to [<xref ref-type="bibr" rid="B7">7</xref>], individuals exposed to excess <sup>232</sup>Th have an increased risk of bone cancer while ingestion of high concentration of <sup>238</sup>U can cause lung cancer and kidney damage. Rocks from Chetambe hills are used as construction materials in Bungoma County and the neighboring counties of Tranzoia and Kakamega [<xref ref-type="bibr" rid="B8">8</xref>]. This research was prompted by the outcry of the residents of the study area whose cancer cases have escalated. They were quoted by the star newspaper of 2/11/2023 complaining of the burden of moving long distances seeking for medication. Therefore, there was a need for an assessment of the study area since it is dominated by rocks of granitic nature according to the geological mapping by [<xref ref-type="bibr" rid="B9">9</xref>]. Granitic rocks are associated with high concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K [<xref ref-type="bibr" rid="B10">10</xref>].</p>
    </sec>
    <sec id="sec2">
      <title>2. Study Area</title>
      <p>The study area is located in Bungoma County. The Hills rise steeply to a height of 1685 m above sea level. Chetambe Hills area was previously called the Broderick falls area bounded by latitudes 0<sup>°</sup>30"N and 1<sup>°</sup>00"N and by longitudes 34<sup>°</sup>30"E and 35<sup>°</sup>00"E. The area of study is characterized by biotite gneisses, migmatites, granitic and granodioritic intrusives [<xref ref-type="bibr" rid="B9">9</xref>] that are highly rich in <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K. Bungoma East sub County where the study area is located has a population of 114, 548 persons [<xref ref-type="bibr" rid="B11">11</xref>]. Bungoma County has an estimated size of 2207 km<sup>2</sup> of which Chetambe Hills covers approximately 58 km<sup>2</sup> [<xref ref-type="bibr" rid="B8">8</xref>]. (See <xref ref-type="fig" rid="fig1">Figure 1</xref><xref ref-type="fig" rid="fig1">Figure 1</xref>)</p>
      <fig id="fig1">
        <label>Figure 1</label>
        <graphic xlink:href="https://html.scirp.org/file/1114863-rId13.jpeg?20260202022727" />
      </fig>
      <p><xref ref-type="fig" rid="fig1">Figure 1</xref><bold>.</bold> Location of Chetambe hills area (Survey of Kenya, 1969).</p>
      <p><bold>Rock Sample Collection</bold><bold>and Preparation</bold></p>
      <p>According to [<xref ref-type="bibr" rid="B12">12</xref>], proper contamination analysis of a specific place depends on proper sample collection, preparation and good storage methods so that the results obtained are credible and reliable. A total of 20 rock samples were collected at different locations of the study area. The sampling points were recorded using a hand held Global Positioning System (GPS) model. The samples were collected and put in containers and labelled according to its location to avoid mix up. The samples were then dried in the oven for 24 hours at 110˚C and then ground to a fine powder, then sieved through a 2.00 mm sieve. 500 g of each of the rock samples were put in airtight containers and be kept for a minimum of 30 days to allow for secular equilibrium between <sup>238</sup>U, <sup>232</sup>Th and <sup>222</sup>Rn and their progeny [<xref ref-type="bibr" rid="B13">13</xref>]. The NaI (Ti) detector was used in the analysis of the levels of natural radioactivity.</p>
    </sec>
    <sec id="sec3">
      <title>3. Experimental Techniques</title>
      <sec id="sec3dot1">
        <title>3.1. Efficiency Calibration of NaI (Ti) Detector</title>
        <p>The efficiency calibration of the detector is a crucial process because it helps in ascertaining the quality and reliability of the results obtained. In this research calibration of the detector was done using the standard reference materials supplied by IAEA with known activity concentrations using Equation (1) [<xref ref-type="bibr" rid="B14">14</xref>].</p>
        <disp-formula id="FD1">
          <label>(1)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>ℰ</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mi>N</mml:mi>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>P</mml:mi>
                    <mml:mi>y</mml:mi>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:mi>M</mml:mi>
                  <mml:mo>×</mml:mo>
                  <mml:mi>T</mml:mi>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math display="inline"><mml:mi> ℰ </mml:mi></mml:math></inline-formula> is the efficiency of the detector, <italic>N</italic> is the net area under the photo peak, T, <italic>P</italic><italic><sub>y</sub></italic> is the emission probability, m is the mass of the sample in Kg, <italic>T</italic> is the counting time and <italic>A</italic> is the activity concentration.</p>
      </sec>
      <sec id="sec3dot2">
        <title>3.2. Energy Calibration of NaI (Ti) Detector</title>
        <p>The energy calibration of NaI (Ti) detector was done by relating the channel number with photo energy using the gamma line of <sup>214</sup>Pb, <sup>214</sup>Bi, <sup>228</sup>Ac, <sup>40</sup>K with energies 351 KeV, 609 KeV, 911 KeV, 1765 KeV and 1460 KeV using Equation (2) [<xref ref-type="bibr" rid="B15">15</xref>].</p>
        <disp-formula id="FD2">
          <label>(2)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>E</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:mi>a</mml:mi>
              <mml:mo>×</mml:mo>
              <mml:mi>c</mml:mi>
              <mml:mi>h</mml:mi>
              <mml:mo>+</mml:mo>
              <mml:mi>b</mml:mi>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <italic>E</italic> is the energy, <italic>a</italic> and <italic>b</italic> are constants and <italic>ch</italic> is the channel number. The activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K in the soil and rock samples were determined using the counts 351 KeV (<sup>214</sup>Pb) and 609 KeV (<sup>214</sup>Bi), 911 KeV (<sup>228</sup>Ac) for <sup>232</sup>Th and 1460 Kev for (<sup>40</sup>K).</p>
        <p><bold>Radiological Risk Measurements in Rock Samples using</bold><bold>NaI</bold><bold>(TI) detector</bold></p>
      </sec>
      <sec id="sec3dot3">
        <title>3.3. Activity Concentrations in the Rocks</title>
        <p>The activity concentrations of the samples in Bq/Kg were determined using Equation (3) [<xref ref-type="bibr" rid="B13">13</xref>].</p>
        <disp-formula id="FD3">
          <label>(3)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mi>i</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>Bq</mml:mtext>
                  <mml:mo>⋅</mml:mo>
                  <mml:msup>
                    <mml:mrow>
                      <mml:mtext>kg</mml:mtext>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mo>−</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                  </mml:msup>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>N</mml:mi>
                    <mml:mrow>
                      <mml:mi>c</mml:mi>
                      <mml:mi>i</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>ε</mml:mi>
                  <mml:mo>×</mml:mo>
                  <mml:msub>
                    <mml:mi>ϒ</mml:mi>
                    <mml:mi>i</mml:mi>
                  </mml:msub>
                  <mml:mo>×</mml:mo>
                  <mml:mi>m</mml:mi>
                  <mml:mo>×</mml:mo>
                  <mml:mi>t</mml:mi>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <italic>A</italic><italic><sub>i</sub></italic> is the activity concentrations of the <italic>i</italic><sup>th</sup> radio nuclide in Bq·kg<sup>−</sup><sup>1</sup>, <italic>ε</italic> is the efficiency of the detector at the energy of the <italic>i</italic><sup>th</sup> radionuclide, <italic>N</italic><italic><sub>ci</sub></italic> is the net counts of the <italic>i</italic><sup>th</sup> radionuclide in the corresponding photo peak after background subtraction, ϒ<italic><sub>i</sub></italic> is the emission probability of the <italic>i</italic><sup>th</sup> radionuclide, <italic>m</italic> is the mass of the sample in kg and <italic>t</italic>is the counting time. </p>
      </sec>
      <sec id="sec3dot4">
        <title>
          3.4. Absorbed Dose Rate (
          <italic>D</italic>
          <italic>
            <sub>r</sub>
          </italic>
          )
        </title>
        <p>The absorbed dose rate was determined using Equation (4) [<xref ref-type="bibr" rid="B10">10</xref>] by applying the conversion factors of 0.462, 0.604 and 0.0147 for <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K respectively.</p>
        <disp-formula id="FD4">
          <label>(4)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mi>r</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mn>0.462</mml:mn>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mi>u</mml:mi>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mn>0.604</mml:mn>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>h</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mn>0.0417</mml:mn>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mi>k</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> u </mml:mi></mml:msub><mml:mo> , </mml:mo><mml:msub><mml:mi> A </mml:mi><mml:mrow><mml:mi> T </mml:mi><mml:mi> h </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> k </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K in Bq·kg<sup>−</sup><sup>1</sup> respectively.</p>
      </sec>
      <sec id="sec3dot5">
        <title>3.5. Annual Effective Dose Rate (AEDR)</title>
        <p>In assessing both AEDR (in) and AEDR (out) to individuals, the occupancy factor was put into consideration [<xref ref-type="bibr" rid="B16">16</xref>]. According to [<xref ref-type="bibr" rid="B10">10</xref>] recommendations, the occupancy factors of 0.2 and 0.8 for outdoor and indoor occupancy factors were used. The values imply that a person on average spends 4.8 hours outdoors and 19.2 indoors. AEDR (in) and AEDR (out) were computed using Equations (5a) and (5b) respectively [<xref ref-type="bibr" rid="B17">17</xref>].</p>
        <disp-formula id="FD5">
          <label>(5a)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mtext>AEDR</mml:mtext>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>in</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mi>r</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:mn>8760</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mn>0.8</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mn>0.7</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:msup>
                <mml:mrow>
                  <mml:mn>10</mml:mn>
                </mml:mrow>
                <mml:mrow>
                  <mml:mo>−</mml:mo>
                  <mml:mn>6</mml:mn>
                </mml:mrow>
              </mml:msup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <disp-formula id="FD6">
          <label>(5b)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mtext>AEDR</mml:mtext>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>out</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>D</mml:mi>
                <mml:mi>r</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:mn>8760</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mn>0.2</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mn>0.7</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:msup>
                <mml:mrow>
                  <mml:mn>10</mml:mn>
                </mml:mrow>
                <mml:mrow>
                  <mml:mo>−</mml:mo>
                  <mml:mn>6</mml:mn>
                </mml:mrow>
              </mml:msup>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where AEDR (in) and AEDR (out) are Annual Effective Doses for indoor and outdoor environments respectively, <italic>D</italic><italic><sub>r</sub></italic> is the absorbed dose rate in air in nGy/h, 0.7 (Sv/Gy) is the conversion factor for absorbed dose rate in air to an effective dose, 0.8 is the indoor occupancy factor while 0.2 is the outdoor occupancy factor.</p>
      </sec>
      <sec id="sec3dot6">
        <title>
          3.6. Radium Equivalent (
          <italic>Ra</italic>
          <italic>
            <sub>eq</sub>
          </italic>
          )
        </title>
        <p>Radium equivalent refers to the weighted sum of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K. Radium equivalent was used to estimate the uniform activity and radiation exposure rates and was determined following Equation (6) [<xref ref-type="bibr" rid="B18">18</xref>].</p>
        <disp-formula id="FD7">
          <label>(6)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:mi>R</mml:mi>
              <mml:msub>
                <mml:mi>a</mml:mi>
                <mml:mrow>
                  <mml:mi>e</mml:mi>
                  <mml:mi>q</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mi>u</mml:mi>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mn>1.43</mml:mn>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>h</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>+</mml:mo>
              <mml:mn>0.077</mml:mn>
              <mml:msub>
                <mml:mi>A</mml:mi>
                <mml:mi>k</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> u </mml:mi></mml:msub><mml:mo> , </mml:mo><mml:msub><mml:mi> A </mml:mi><mml:mrow><mml:mi> T </mml:mi><mml:mi> h </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> k </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K in Bq·kg<sup>−</sup><sup>1</sup> respectively</p>
        <p>While 1.43 and 0.077 are conversion factors.</p>
      </sec>
      <sec id="sec3dot7">
        <title>
          3.7. Internal and External Hazard Indices (
          <italic>H</italic>
          <italic>
            <sub>in</sub>
          </italic>
          and
          <italic>H</italic>
          <italic>
            <sub>ex</sub>
          </italic>
          )
        </title>
        <p>The internal hazard is due to inhalation of the radionuclides and their short lived progenies. The internal hazard index will be evaluated using Equation (7) [<xref ref-type="bibr" rid="B19">19</xref>]. </p>
        <disp-formula id="FD8">
          <label>(7)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>H</mml:mi>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mi>n</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>A</mml:mi>
                    <mml:mi>u</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mn>185</mml:mn>
                </mml:mrow>
              </mml:mfrac>
              <mml:mo>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>A</mml:mi>
                    <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>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>A</mml:mi>
                    <mml:mi>k</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mn>4810</mml:mn>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> u </mml:mi></mml:msub><mml:mo> , </mml:mo><mml:msub><mml:mi> A </mml:mi><mml:mrow><mml:mi> T </mml:mi><mml:mi> h </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> k </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K in Bq·kg<sup>−</sup><sup>1</sup> respectively</p>
        <p>The external exposure results from direct radiation. To account for the exposure in the samples H<sub>ex</sub> was determined using Equation (8) [<xref ref-type="bibr" rid="B19">19</xref>]. </p>
        <disp-formula id="FD9">
          <label>(8)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mi>H</mml:mi>
                <mml:mrow>
                  <mml:mi>e</mml:mi>
                  <mml:mi>x</mml:mi>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>A</mml:mi>
                    <mml:mi>u</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mn>370</mml:mn>
                </mml:mrow>
              </mml:mfrac>
              <mml:mo>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>A</mml:mi>
                    <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>+</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>A</mml:mi>
                    <mml:mi>k</mml:mi>
                  </mml:msub>
                </mml:mrow>
                <mml:mrow>
                  <mml:mn>4810</mml:mn>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> u </mml:mi></mml:msub><mml:mo> , </mml:mo><mml:msub><mml:mi> A </mml:mi><mml:mrow><mml:mi> T </mml:mi><mml:mi> h </mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi> A </mml:mi><mml:mi> k </mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K in Bq·kg<sup>−</sup><sup>1</sup> respectively.</p>
        <p>The external hazard index should be less than unity for the radiation hazard to be negligible.</p>
      </sec>
      <sec id="sec3dot8">
        <title>3.8. Excess Life Time Cancer Risk (ELCR)</title>
        <p>The excess life time cancer risk due to exposure to the radiation was determined using Equation (9a) and (9b) [<xref ref-type="bibr" rid="B20">20</xref>].</p>
        <disp-formula id="FD10">
          <label>(9a)</label>
          <mml:math display="inline">
            <mml:mrow>
              <mml:msub>
                <mml:mrow>
                  <mml:mtext>ELCR</mml:mtext>
                </mml:mrow>
                <mml:mrow>
                  <mml:mtext>in</mml:mtext>
                </mml:mrow>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:msub>
                <mml:mrow>
                  <mml:mtext>AEDR</mml:mtext>
                </mml:mrow>
                <mml:mrow>
                  <mml:mtext>in</mml:mtext>
                </mml:mrow>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>L</mml:mi>
                <mml:mi>f</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>f</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <disp-formula id="FD11">
          <label>(9b)</label>
          <mml:math display="inline">
            <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:mo>=</mml:mo>
              <mml:msub>
                <mml:mrow>
                  <mml:mtext>AEDR</mml:mtext>
                </mml:mrow>
                <mml:mrow>
                  <mml:mtext>out</mml:mtext>
                </mml:mrow>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>L</mml:mi>
                <mml:mi>f</mml:mi>
              </mml:msub>
              <mml:mo>×</mml:mo>
              <mml:msub>
                <mml:mi>R</mml:mi>
                <mml:mi>f</mml:mi>
              </mml:msub>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where ELCR is the excess life time cancer risk, AEDR is the annual effective dose rate, <italic>L</italic><italic><sub>f</sub></italic> is the average life expectancy (70 years in Kenya), <italic>R</italic><italic><sub>f</sub></italic> is the associated risk factor which is 0.05 [<xref ref-type="bibr" rid="B21">21</xref>].</p>
      </sec>
    </sec>
    <sec id="sec4">
      <title>4. Results and Discussions</title>
      <sec id="sec4dot1">
        <title>4.1. Activity Concentrations of Rock Samples</title>
        <p>The rock samples were labelled R<sub>1</sub> to R<sub>20</sub> with their corresponding coordinates for longitude and latitude including the activity taking place at the sampled point. The activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K of all the rock samples were calculated using Equation (1) and their results summarized as shown in <bold>Table 1</bold>.</p>
        <p><bold>Table 1</bold><bold>.</bold> Activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K of the samples in this work.</p>
        <table-wrap id="tbl1">
          <label>Table 1</label>
          <table>
            <tbody>
              <tr>
                <td rowspan="2">Sample</td>
                <td rowspan="2">Sample point activity</td>
                <td rowspan="2">Long (E)</td>
                <td rowspan="2">Lat (N)</td>
                <td colspan="3">Activity concentration (Bq/kg)</td>
              </tr>
              <tr>
                <td>
                  <sup>238</sup>
                  U
                </td>
                <td>
                  <sup>232</sup>
                  Th
                </td>
                <td>
                  <sup>40</sup>
                  K
                </td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>1</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>58 ± 2.92</td>
                <td>62 ± 3.11</td>
                <td>830 ± 4.19</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>2</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  49'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>76 ± 3.81</td>
                <td>69 ± 3.48</td>
                <td>1028 ± 1.42</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>3</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  31'
                </td>
                <td>109 ± 5.46</td>
                <td>84 ± 4.24</td>
                <td>2042 ± 3.43</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>4</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  47'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>119 ± 5.97</td>
                <td>113 ± 5.65</td>
                <td>1102 ± 5.13</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>5</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>116 ± 5.84</td>
                <td>167 ± 8.39</td>
                <td>1774 ± 4.73</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>6</sub>
                </td>
                <td>Falls view H</td>
                <td>
                  34
                  <sup>°</sup>
                  52'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>63 ± 3.17</td>
                <td>167 ± 8.39</td>
                <td>883 ± 3.19</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>7</sub>
                </td>
                <td>Road construction</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  29'
                </td>
                <td>38 ± 1.92</td>
                <td>124 ± 6.22</td>
                <td>1271 ± 3.55</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>8</sub>
                </td>
                <td>Maize/bean growing</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>66 ± 3.31</td>
                <td>60 ± 3.01</td>
                <td>1410 ± 2.53</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>9</sub>
                </td>
                <td>Car wash</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>58 ± 2.92</td>
                <td>113 ± 5.65</td>
                <td>1405 ± 2.28</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>10</sub>
                </td>
                <td>Church (SA)</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>45 ± 2.28</td>
                <td>18 ± 0.94</td>
                <td>50 ± 2.52</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>11</sub>
                </td>
                <td>Borehole drilled</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  41'
                </td>
                <td>66 ± 3.33</td>
                <td>60 ± 3.01</td>
                <td>1410 ± 70.53</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>12</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>33 ± 1.65</td>
                <td>20 ± 1.03</td>
                <td>161 ± 8.05</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>13</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  44'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>38 ± 1.92</td>
                <td>15 ± 0.75</td>
                <td>244 ± 12.21</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>14</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  25'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>68 ± 3.42</td>
                <td>41 ± 2.07</td>
                <td>588 ± 29.41</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>15</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  32'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>83 ± 4.19</td>
                <td>16 ± 0.84</td>
                <td>299 ± 14.95</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>16</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>104 ± 5.23</td>
                <td>30 ± 1.57</td>
                <td>94 ± 4.73</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>17</sub>
                </td>
                <td>school</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>68 ± 3.42</td>
                <td>147 ± 7.35</td>
                <td>917 ± 45.86</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>18</sub>
                </td>
                <td>Church (SDA)</td>
                <td>
                  34
                  <sup>°</sup>
                  41'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>43 ± 2.15</td>
                <td>18 ± 0.94</td>
                <td>66 ± 3.32</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>19</sub>
                </td>
                <td>Brick making</td>
                <td>
                  34
                  <sup>°</sup>
                  39'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>76 ± 3.81</td>
                <td>99 ± 4.99</td>
                <td>1551 ± 77.59</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>20</sub>
                </td>
                <td>Quarrying (Misikhu)</td>
                <td>
                  34
                  <sup>°</sup>
                  35'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  27'
                </td>
                <td>35 ± 1.77</td>
                <td>22 ± 1.13</td>
                <td>201 ± 10.05</td>
              </tr>
              <tr>
                <td>AVER</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>68 ± 3.23</td>
                <td>72 ± 3.48</td>
                <td>866 ± 5.78</td>
              </tr>
              <tr>
                <td>MAX</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>119 ± 5.97</td>
                <td>167 ± 8.39</td>
                <td>2042 ± 6.43</td>
              </tr>
              <tr>
                <td>MIN</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>33 ± 1.65</td>
                <td>15 ± 0.75</td>
                <td>50 ± 2.5</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>The results from the study indicate a spatial distribution of the three radionuclides: <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K activity in rock samples from one rock sample to the other with some samples having higher radiation levels than others. The activity concentrations for the three radionuclides were notably high at the quarries, maize growing points and brick making site. The activity concentrations of <sup>238</sup>U varied from a minimum of 33 ± 1.65 Bq/Kg to a maximum of 119 ± 5.97 Bq/Kg with an average of 68 ± 3.23 Bq/Kg. The activity concentrations of <sup>232</sup>Th varied from a minimum 15 ± 0.75 Bq/Kg to a maximum of 167 ± 8.39 Bq/Kg with an average of 72 ± 3.48 Bq/Kg while the activity concentrations of <sup>40</sup>K varied from a minimum of 50 ± 2.5 Bq/Kg to a maximum of 2042 ± 6.43 Bq/Kg with an average of 866 ± 5.78 Bq/Kg. The averages for the three radionuclides all exceeded the world averages of 33 Bq/Kg, 45 Bq/Kg and 420 Bq/Kg for <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K respectively [<xref ref-type="bibr" rid="B10">10</xref>]. but within the world reported range [<xref ref-type="bibr" rid="B2">2</xref>]. </p>
        <p>The high levels of activity concentrations of <sup>238</sup>U can be attributed to geological formation of the study area characterized by granitic rocks that are highly rich in <sup>238</sup>U. In addition, the high levels of <sup>238</sup>U can also be because of the enrichment by phosphate fertilizers (DAP) used for growing of crops at the study area that contains <sup>238</sup>U [<xref ref-type="bibr" rid="B22">22</xref>]. The elevated levels of <sup>232</sup>Th could be due to the presence of granitic rocks at the study area. On the other hand, the higher activity concentrations of <sup>40</sup>K could be attributed to the presence of granites and rhyolites that are rich in potassium bearing minerals or the potassium rich fertilizers used in replenishing the soils [<xref ref-type="bibr" rid="B23">23</xref>]. The results were also represented as shown in <xref ref-type="fig" rid="fig2">Figure 2</xref><xref ref-type="fig" rid="fig2">Figure 2</xref> which shows the concentrations of the radionuclides in the order <sup>238</sup>U &lt; <sup>232</sup>Th &lt; <sup>40</sup>K. </p>
        <fig id="fig2">
          <label>Figure 2</label>
          <graphic xlink:href="https://html.scirp.org/file/1114863-rId54.jpeg?20260202022727" />
        </fig>
        <p><xref ref-type="fig" rid="fig2">Figure 2</xref><bold>.</bold> Activity concentrations of the rock samples in this work.</p>
        <p>For a comprehensive analysis, correlation graphs were also drawn as shown in <xref ref-type="fig" rid="fig3">Figure 3</xref><xref ref-type="fig" rid="fig3">Figures 3(a)-(c)</xref>.</p>
        <fig id="fig3">
          <label>Figure 3</label>
          <graphic xlink:href="https://html.scirp.org/file/1114863-rId55.jpeg?20260202022727" />
        </fig>
        <p>(a)</p>
        <fig id="fig4">
          <label>Figure 4</label>
          <graphic xlink:href="https://html.scirp.org/file/1114863-rId56.jpeg?20260202022727" />
        </fig>
        <p>(b)</p>
        <fig id="fig5">
          <label>Figure 5</label>
          <graphic xlink:href="https://html.scirp.org/file/1114863-rId57.jpeg?20260202022727" />
        </fig>
        <p>(c)</p>
        <p><bold>Figure 3</bold><bold>.</bold> (a) Correlation between <sup>238</sup>U and <sup>232</sup>Th; (b) Correlation between <sup>238</sup>U and <sup>40</sup>K; (c) Correlation between <sup>238</sup>Th and <sup>40</sup>K.</p>
        <p>From <xref ref-type="fig" rid="fig3">Figure 3</xref><xref ref-type="fig" rid="fig3">Figures 3(a)-(c)</xref>, it is clear that there exists a weak relationship between the three radionuclides as seen from the R<sup>2</sup> values.</p>
        <p>The findings from this research are in agreement with those of [<xref ref-type="bibr" rid="B15">15</xref>] in Chiewo hills where the highest average values of the activity concentrations were 3017.8 Bq/kg for <sup>40</sup>K. </p>
      </sec>
      <sec id="sec4dot2">
        <title>
          4.2.
          <italic>D</italic>
          <italic>
            <sub>r</sub>
          </italic>
          , AEDR (in) and AEDR (out)
        </title>
        <p>The <italic>D</italic><italic><sub>r</sub></italic>, AEDR (in) and AEDR (out) were determined using respective equations and finally the results tabulated in <bold>Table 2</bold>.</p>
        <p><bold>Table 2</bold><bold>.</bold><italic>D</italic><italic><sub>r</sub></italic>, AEDR (in) and AEDR (out) for all the rock samples collected and measured in this work.</p>
        <table-wrap id="tbl2">
          <label>Table 2</label>
          <table>
            <tbody>
              <tr>
                <td>Sample</td>
                <td>Sample point activity</td>
                <td>Long (E)</td>
                <td>Lat (N)</td>
                <td>
                  <italic>D</italic>
                  <italic>
                    <sub>r</sub>
                  </italic>
                  (nGy/h)
                </td>
                <td>
                  AEDR
                  <sub>in</sub>
                  (mSv/y)
                </td>
                <td>
                  AEDR
                  <sub>out</sub>
                  (mSv/y)
                </td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>1</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>99 ± 4.96</td>
                <td>0.3 ± 0.01</td>
                <td>0.2 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>2</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  49'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>120 ± 6.32</td>
                <td>0.4 ± 0.02</td>
                <td>0.2 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>3</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  31'
                </td>
                <td>187 ± 9.36</td>
                <td>0.6 ± 0.03</td>
                <td>0.4 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>4</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  47'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>168 ± 8.43</td>
                <td>0.6 ± 0.03</td>
                <td>0.4 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>5</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>230 ± 11.53</td>
                <td>0.8 ± 0.04</td>
                <td>0.5 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>6</sub>
                </td>
                <td>Falls view H</td>
                <td>
                  34
                  <sup>°</sup>
                  52'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>169 ± 8.47</td>
                <td>0.6 ± 0.03</td>
                <td>0.4 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>7</sub>
                </td>
                <td>Road construction</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  29'
                </td>
                <td>148 ± 7.41</td>
                <td>0.5 ± 0.02</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>8</sub>
                </td>
                <td>Maize/bean growing</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>126 ± 6.32</td>
                <td>0.4 ± 0.02</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>9</sub>
                </td>
                <td>Car wash</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>155 ± 7.78</td>
                <td>0.5 ± 0.02</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>10</sub>
                </td>
                <td>Church (SA)</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>33 ± 1.67</td>
                <td>0.1 ± 0</td>
                <td>0 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>11</sub>
                </td>
                <td>Borehole drilled</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  41'
                </td>
                <td>126 ± 6.32</td>
                <td>0.4 ± 0.02</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>12</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>33 ± 1.69</td>
                <td>0.1 ± 0</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>13</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  44'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>36 ± 1.8</td>
                <td>0.1 ± 0</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>14</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  25'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>80 ± 4.01</td>
                <td>0.2 ± 0.01</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>15</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  32'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>59 ± 2.96</td>
                <td>0.2 ± 0.01</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>16</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>67 ± 3.36</td>
                <td>0.2 ± 0.01</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>17</sub>
                </td>
                <td>school</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>160 ± 8.01</td>
                <td>0.5 ± 0.02</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>18</sub>
                </td>
                <td>Church (SDA)</td>
                <td>
                  34
                  <sup>°</sup>
                  41'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>33 ± 1.65</td>
                <td>0.1 ± 0</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>19</sub>
                </td>
                <td>Brick making</td>
                <td>
                  34
                  <sup>°</sup>
                  39'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>161 ± 8.07</td>
                <td>0.5 ± 0.02</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>20</sub>
                </td>
                <td>Quarrying (Misikhu)</td>
                <td>
                  34
                  <sup>°</sup>
                  35'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  27'
                </td>
                <td>37 ± 1.89</td>
                <td>0.1 ± 0</td>
                <td>0.1 ± 0</td>
              </tr>
              <tr>
                <td>AVER</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>111 ± 7.32</td>
                <td>0.4 ± 0.02</td>
                <td>0.2 ± 0.01</td>
              </tr>
              <tr>
                <td>MAX</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>230 ± 11.53</td>
                <td>0.8 ± 0.04</td>
                <td>0.5 ± 0.02</td>
              </tr>
              <tr>
                <td>MIN</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>33 ± 1.69</td>
                <td>0.1 ± 0</td>
                <td>0.2 ± 0.01</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>The Absorbed dose rate (<italic>D</italic><italic><sub>r</sub></italic>) ranged from a minimum of 33 ± 1.67 nGy/h to a maximum of 230 ± 11.53 nGy/h with an average of 111 ± 7.32 nGy/h which was above the 60 nGy/h [<xref ref-type="bibr" rid="B10">10</xref>]. The values are not uniformly distributed owing to the different activity concentrations of the three radionuclides. Since the absorbed dose rate is determined from the activity concentrations with conversion factors, then the sample with the highest activity concentration of the three radionuclides also had a higher absorbed dose rate <italic>i.e.</italic> R<sub>5</sub>. Despite their higher values, they were below the world safety limit of 1500 nGy/h [<xref ref-type="bibr" rid="B24">24</xref>]. The findings from this study are similar to those of [<xref ref-type="bibr" rid="B2">2</xref>] average experimental value of 114 ± 34 nGy/h. </p>
        <p>The results on the activity concentrations and absorbed dose rates of this study were compared with those other areas and represented in <bold>Table 3</bold>.</p>
        <p><bold>Table 3</bold><bold>.</bold> Comparison of activity concentrations and absorbed dose rates in rocks in this study with others. </p>
        <table-wrap id="tbl3">
          <label>Table 3</label>
          <table>
            <tbody>
              <tr>
                <td rowspan="2">Author/Year</td>
                <td rowspan="2">Country/place</td>
                <td colspan="3">Activity concentrations (Bq/Kg)</td>
                <td rowspan="2">Absorbed dose rate (nGy/h)</td>
              </tr>
              <tr>
                <td>
                  <sup>238</sup>
                  U
                </td>
                <td>
                  <sup>232</sup>
                  Th
                </td>
                <td>
                  <sup>40</sup>
                  K
                </td>
              </tr>
              <tr>
                <td>Present study</td>
                <td>Kenya (Chetambe hills)</td>
                <td>68 ± 3.23</td>
                <td>72 ± 3.48</td>
                <td>866 ± 5.78</td>
                <td>111 ± 7.32</td>
              </tr>
              <tr>
                <td>
                  Kebwaro
                  <italic>et al.</italic>
                  , 2011
                </td>
                <td>Kenya (Mrima hills)</td>
                <td>207 ± 11.3</td>
                <td>500.7 ± 20.0</td>
                <td>805.4 ± 20.0</td>
                <td>440.7</td>
              </tr>
              <tr>
                <td>
                  Otuoma
                  <italic>et al.</italic>
                  , 2012
                </td>
                <td>Kenya (Chiewo hills)</td>
                <td>195.3</td>
                <td>915.6</td>
                <td>409.5</td>
                <td>108 - 1596.4</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>From the comparison <bold>Table 3</bold>, it is clear that despite the regional difference, the activity concentrations and absorbed dose rates both from the current study and those other two regions were higher than their world averages except for <sup>40</sup>K in Chiewo hills. </p>
        <p>The AEDR<sub>in</sub> ranged from a minimum of 0.1 ± 0 mSv/y to a maximum of 0.8 ± 0.04 mSv/y with an average of 0.4 ± 0.02 mSv/y that was below the permissible limit of 1 mSv/y although above the 0.07 mSv/y [<xref ref-type="bibr" rid="B10">10</xref>]. On the other hand, AEDR<sub>out</sub> ranged from a minimum of 0.2 ± 0.01 mSv/y, a maximum of 0.5 ± 0.02 mSv/y with a mean of 0.2 ± 0.01 mSv/y that was below the permissible limit 1 mSv/y [<xref ref-type="bibr" rid="B25">25</xref>]. These findings disagree with those from the study done by [<xref ref-type="bibr" rid="B26">26</xref>] in which the AED was found to 0.985 mSv/y.</p>
      </sec>
      <sec id="sec4dot3">
        <title>
          4.3. Radium Equivalent (
          <italic>Ra</italic>
          <italic>
            <sub>eq</sub>
          </italic>
          ), Internal (
          <italic>H</italic>
          <italic>
            <sub>in</sub>
          </italic>
          ) and External (
          <italic>H</italic>
          <italic>
            <sub>ex</sub>
          </italic>
          ) Hazard Indices
        </title>
        <p>Radium Equivalent (<italic>Ra</italic><italic><sub>eq</sub></italic>), Internal hazard index (<italic>H</italic><italic><sub>in</sub></italic>) and external (<italic>H</italic><italic><sub>ex</sub></italic>) hazard index (<italic>H</italic><italic><sub>ex</sub></italic>) were determined for all the samples and their values represented in <bold>Table 4</bold>.</p>
        <p><bold>Table 4</bold><bold>.</bold> Radium equivalent (<italic>Ra</italic><italic><sub>eq</sub></italic>), Internal (<italic>H</italic><italic><sub>in</sub></italic>) and External (<italic>H</italic><italic><sub>ex</sub></italic>) hazard indices for all the rock samples collected and measured in this work.</p>
        <table-wrap id="tbl4">
          <label>Table 4</label>
          <table>
            <tbody>
              <tr>
                <td>Sample</td>
                <td>Sample point activity</td>
                <td>Long (E)</td>
                <td>Lat (N)</td>
                <td>
                  <italic>Ra</italic>
                  <italic>
                    <sub>eq</sub>
                  </italic>
                  (Bq/Kg)
                </td>
                <td>
                  <italic>H</italic>
                  <italic>
                    <sub>in</sub>
                  </italic>
                  (mSv/y)
                </td>
                <td>
                  <italic>H</italic>
                  <italic>
                    <sub>ex</sub>
                  </italic>
                  (mSv/y)
                </td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>1</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>210 ± 10.54</td>
                <td>0.5 ± 0.02</td>
                <td>0.7 ± 0.03</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>2</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  49'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>254 ± 12.73</td>
                <td>0.6 ± 0.03</td>
                <td>0.8 ± 0.04</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>3</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  31'
                </td>
                <td>387 ± 19.36</td>
                <td>1 ± 0.05</td>
                <td>1.3 ± 0.06</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>4</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  47'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>365 ± 18.25</td>
                <td>0.9 ± 0.04</td>
                <td>1.3 ± 0.06</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>5</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>492 ± 24.61</td>
                <td>1.3 ± 0.06</td>
                <td>1.6 ± 0.08</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>6</sub>
                </td>
                <td>Falls view H</td>
                <td>
                  34
                  <sup>°</sup>
                  52'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>370 ± 18.52</td>
                <td>1 ± 0.05</td>
                <td>1.1 ± 0.05</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>7</sub>
                </td>
                <td>Road construction</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  29'
                </td>
                <td>313 ± 15.65</td>
                <td>0.8 ± 0.04</td>
                <td>0.9 ± 0.04</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>8</sub>
                </td>
                <td>Maize/bean growing</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>260 ± 13.02</td>
                <td>0.7 ± 0.03</td>
                <td>0.8 ± 0.04</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>9</sub>
                </td>
                <td>Car wash</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>327 ± 16.38</td>
                <td>0.8 ± 0.04</td>
                <td>1 ± 0.05</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>10</sub>
                </td>
                <td>Church (SA)</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>76 ± 3.82</td>
                <td>0.2 ± 0.01</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>11</sub>
                </td>
                <td>Borehole drilled</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  41'
                </td>
                <td>260 ± 13.02</td>
                <td>0.7 ± 0.03</td>
                <td>0.8 ± 0.04</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>12</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>74 ± 3.74</td>
                <td>0.2 ± 0.01</td>
                <td>0.2 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>13</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  44'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>78 ± 3.91</td>
                <td>0.2 ± 0.01</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>14</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  25'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>172 ± 8.64</td>
                <td>0.4 ± 0.02</td>
                <td>0.6 ± 0.03</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>15</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  32'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>131 ± 6.55</td>
                <td>0.3 ± 0.01</td>
                <td>0.5 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>16</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>154 ± 7.71</td>
                <td>0.4 ± 0.02</td>
                <td>0.6 ± 0.03</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>17</sub>
                </td>
                <td>school</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>348 ± 17.42</td>
                <td>0.9 ± 0.04</td>
                <td>1.1 ± 0.05</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>18</sub>
                </td>
                <td>Church (SDA)</td>
                <td>
                  34
                  <sup>°</sup>
                  41'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>75 ± 3.75</td>
                <td>0.2 ± 0.01</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>19</sub>
                </td>
                <td>Brick making</td>
                <td>
                  34
                  <sup>°</sup>
                  39'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>337 ± 16.89</td>
                <td>0.9 ± 0.04</td>
                <td>1.1 ± 0.05</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>20</sub>
                </td>
                <td>Quarrying (Misikhu)</td>
                <td>
                  34
                  <sup>°</sup>
                  35'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  27'
                </td>
                <td>83 ± 4.16</td>
                <td>0.2 ± 0.01</td>
                <td>0.3 ± 0.01</td>
              </tr>
              <tr>
                <td>AVER</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>238 ± 6.34</td>
                <td>0.6 ± 0.02</td>
                <td>0.8 ± 0.03</td>
              </tr>
              <tr>
                <td>MAX</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>492 ± 24.61</td>
                <td>1.3 ± 0.06</td>
                <td>1.6 ± 0.08</td>
              </tr>
              <tr>
                <td>MIN</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>74 ± 3.74</td>
                <td>0.2 ± 0.01</td>
                <td>0.3 ± 0.01</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <p>Samples R<sub>3</sub> and R<sub>5</sub> had the highest radium equivalent values 387 ± 19.36 Bq/kg and 492 ± 24.61 Bq/kg that were as a result of their high values of activity concentrations in the respective radionuclides. They were even higher than the world average of 370 Bq/kg. The radium equivalent for the study area varied from a minimum of 74 ± 3.74 Bq/kg to a maximum of 492 ± 24.61 Bq/kg. The mean value of radium equivalent from this study was 238 ± 6.34 Bq/kg which was below the world average value of 370 Bq/kg. The values of the internal hazard index varied from a minimum of 0.2 ± 0.01 mSv/y to a maximum of 1.3 ± 0.06 mSv/y with mean of 0.6 ± 0.02 mSv/y. The external hazard indices varied from a minimum of 0.3 ± 0.01 mSv/y to a maximum of 1.6 ± 0.08 mSv/y with an average of 0.8 ± 0.03 mSv/y. The external and internal hazard indices from the various samples were different because of the difference in the activity concentrations of the radionuclides in the respective samples. Despite some samples having their internal and external hazard indices higher; they were below the world average level of 1 mSv/y [<xref ref-type="bibr" rid="B10">10</xref>].</p>
      </sec>
      <sec id="sec4dot4">
        <title>
          4.4. ELCR
          <sub>in</sub>
          and ELCR
          <sub>out</sub>
        </title>
        <p>ELCR<sub>in</sub> and ELCR<sub>out</sub> were determined using equations 9a and 9b respectively and their values represented in <bold>Table 5</bold>. </p>
        <p>The ELCR<sub>out</sub> values were in the range of 0.2 ± 0.09 to 1.9 ± 0.08 with a mean value of 0.9 ± 0.06 that was below the acceptable limit of 2.9 × 10<sup>−</sup><sup>4</sup>. The values for ELCR<sub>in</sub> ranged from 0.4 ± 0.03 to 2.9 ± 0.07 with a mean value of 1.4 ± 0.05 which was equally lower than the world average of 2.9 × 10<sup>−</sup><sup>4</sup>. </p>
        <p><bold>Table 5</bold><bold>.</bold> ELCR<sub>in</sub> and ELCR<sub>out</sub> for all the rock samples collected and determined in this study.</p>
        <table-wrap id="tbl5">
          <label>Table 5</label>
          <table>
            <tbody>
              <tr>
                <td>Sample</td>
                <td>Sample point activity</td>
                <td>Long (E)</td>
                <td>Lat (N)</td>
                <td>
                  ELCR
                  <sub>in</sub>
                  10
                  <sup>−</sup>
                  <sup>6</sup>
                </td>
                <td>
                  ELCR
                  <sub>out</sub>
                  10
                  <sup>−</sup>
                  <sup>6</sup>
                </td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>1</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>1.2 ± 0.08</td>
                <td>0.8 ± 0.06</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>2</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  49'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>1.5 ± 0.06</td>
                <td>1.0 ± 0.04</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>3</sub>
                </td>
                <td>Maize growing</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  31'
                </td>
                <td>2.4 ± 0.03</td>
                <td>1.6 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>4</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  47'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>2.1 ± 0.08</td>
                <td>1.4 ± 0.05</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>5</sub>
                </td>
                <td>Quarrying</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>2.9 ± 0.07</td>
                <td>1.9 ± 0.08</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>6</sub>
                </td>
                <td>Falls view H</td>
                <td>
                  34
                  <sup>°</sup>
                  52'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>2.1 ± 0.09</td>
                <td>1.4 ± 0.06</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>7</sub>
                </td>
                <td>Road construction</td>
                <td>
                  34
                  <sup>°</sup>
                  48'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  29'
                </td>
                <td>1.9 ± 0.02</td>
                <td>1.2 ± 0.08</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>8</sub>
                </td>
                <td>Maize/bean growing</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>1.6 ± 0.03</td>
                <td>1.0 ± 0.09</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>9</sub>
                </td>
                <td>Car wash</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  33'
                </td>
                <td>2.0 ± 0.01</td>
                <td>1.3 ± 0.04</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>10</sub>
                </td>
                <td>Church (SA)</td>
                <td>
                  34
                  <sup>°</sup>
                  42'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>0.4 ± 0.02</td>
                <td>0.2 ± 0.09</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>11</sub>
                </td>
                <td>Borehole drilled</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  41'
                </td>
                <td>1.6 ± 0.05</td>
                <td>1.0 ± 0.09</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>12</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  43'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>0.4 ± 0.02</td>
                <td>0.2 ± 0.08</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>13</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  44'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  34'
                </td>
                <td>0.4 ± 0.03</td>
                <td>0.3 ± 0.02</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>14</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  25'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>1.0 ± 0.04</td>
                <td>0.6 ± 0.03</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>15</sub>
                </td>
                <td>Near spring</td>
                <td>
                  34
                  <sup>°</sup>
                  32'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  36'
                </td>
                <td>0.7 ± 0.05</td>
                <td>0.5 ± 0.01</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>16</sub>
                </td>
                <td>Residence</td>
                <td>
                  34
                  <sup>°</sup>
                  45'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  32'
                </td>
                <td>0.8 ± 0.06</td>
                <td>0.5 ± 0.08</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>17</sub>
                </td>
                <td>school</td>
                <td>
                  34
                  <sup>°</sup>
                  46'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  35'
                </td>
                <td>2.0 ± 0.06</td>
                <td>1.3 ± 0.08</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>18</sub>
                </td>
                <td>Church (SDA)</td>
                <td>
                  34
                  <sup>°</sup>
                  41'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  38'
                </td>
                <td>0.4 ± 0.03</td>
                <td>0.2 ± 0.09</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>19</sub>
                </td>
                <td>Brick making</td>
                <td>
                  34
                  <sup>°</sup>
                  39'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  37'
                </td>
                <td>2.0 ± 0.08</td>
                <td>1.3 ± 0.09</td>
              </tr>
              <tr>
                <td>
                  R
                  <sub>20</sub>
                </td>
                <td>Quarrying (Misikhu)</td>
                <td>
                  34
                  <sup>°</sup>
                  35'
                </td>
                <td>
                  0
                  <sup>°</sup>
                  27'
                </td>
                <td>0.4 ± 0.09</td>
                <td>0.3 ± 0.06</td>
              </tr>
              <tr>
                <td>AVER</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>1.4 ± 0.05</td>
                <td>0.9 ± 0.06</td>
              </tr>
              <tr>
                <td>MAX</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>2.9 ± 0.07</td>
                <td>1.9 ± 0.08</td>
              </tr>
              <tr>
                <td>MIN</td>
                <td>
                </td>
                <td>
                </td>
                <td>
                </td>
                <td>0.4 ± 0.03</td>
                <td>0.2 ± 0.09</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
        <fig id="fig6">
          <label>Figure 6</label>
          <graphic xlink:href="https://html.scirp.org/file/1114863-rId58.jpeg?20260202022727" />
        </fig>
        <p><xref ref-type="fig" rid="fig4">Figure 4</xref><bold>.</bold> Graph of ELCR<sub>in</sub> and ELCR<sub>out</sub> of all the samples in this research.</p>
        <p>The ELCR<sub>in</sub> and ELCR<sub>out</sub> values from this research were represented in <xref ref-type="fig" rid="fig4">Figure 4</xref><xref ref-type="fig" rid="fig4">Figure 4</xref>.</p>
        <p>From <xref ref-type="fig" rid="fig4">Figure 4</xref><xref ref-type="fig" rid="fig4">Figure 4</xref>, it can be seen that ELCR<sub>in</sub> was higher than ELCR<sub>out</sub> for all the samples which can be attributed to the higher values of AEDR<sub>in</sub> than AEDR<sub>out</sub></p>
      </sec>
    </sec>
    <sec id="sec5">
      <title>5. Conclusions and Recommendations</title>
      <p>A radiological assessment due to natural radioactivity in rocks and associated health impacts has been done in this research. The average activity concentrations of <sup>238</sup>U, <sup>232</sup>Th and <sup>40</sup>K were all higher than the permissible values. However, the other radiological parameters were within the permissible limits as already discussed. Therefore, escalated cancer cases in the study area may not be a result of radiation exposure from natural radioactivity from the rocks since the radiation exposure from the rocks does not pose a health risk to the general public.</p>
      <p>This study recommends further studies in soils so as to have comprehensive data on natural radioactivity and hence clarity of the possible cause of cancer in the study area.</p>
    </sec>
    <sec id="sec6">
      <title>Acknowledgements</title>
      <p>The authors thank the department of Science, Technology and Engineering for provision of facilities for this research.</p>
    </sec>
    <sec id="sec7">
      <title>Conflicts of Interest</title>
      <p>The authors declare no conflict of interest </p>
    </sec>
  </body>
  <back>
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