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mw-first-heading"><span class="mw-page-title-main">Aktivität (Physik)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Zu einem Artikel in einer anderen Sprache gehen. Verfügbar in 15 Sprachen" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-15" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">15 Spraaken</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D1%81%D1%86%D1%8C_%D1%80%D0%B0%D0%B4%D1%8B%D0%B5%D0%B0%D0%BA%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D0%B9_%D0%BA%D1%80%D1%8B%D0%BD%D1%96%D1%86%D1%8B" title="Актыўнасць радыеактыўнай крыніцы – Wittruss’sch" lang="be" hreflang="be" data-title="Актыўнасць радыеактыўнай крыніцы" data-language-autonym="Беларуская" data-language-local-name="Wittruss’sch" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82_%D0%BD%D0%B0_%D1%80%D0%B0%D0%B4%D0%B8%D0%BE%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D0%B5%D0%BD_%D0%B8%D0%B7%D1%82%D0%BE%D1%87%D0%BD%D0%B8%D0%BA" title="Активност на радиоактивен източник – Bulgaarsch" lang="bg" hreflang="bg" data-title="Активност на радиоактивен източник" data-language-autonym="Български" data-language-local-name="Bulgaarsch" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Aktivit%C3%A4t_(Physik)" title="Aktivität (Physik) – Düütsch" lang="de" hreflang="de" data-title="Aktivität (Physik)" data-language-autonym="Deutsch" data-language-local-name="Düütsch" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Total_activity" title="Total activity – Engelsch" lang="en" hreflang="en" data-title="Total activity" data-language-autonym="English" data-language-local-name="Engelsch" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Radioaktiivse_aine_aktiivsus" title="Radioaktiivse aine aktiivsus – Eestnisch" lang="et" hreflang="et" data-title="Radioaktiivse aine aktiivsus" data-language-autonym="Eesti" data-language-local-name="Eestnisch" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Activit%C3%A9_(physique)" title="Activité (physique) – Franzöösch" lang="fr" hreflang="fr" data-title="Activité (physique)" data-language-autonym="Français" data-language-local-name="Franzöösch" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Aktivit%C3%A1s" title="Aktivitás – Ungaarsch" lang="hu" hreflang="hu" data-title="Aktivitás" data-language-autonym="Magyar" data-language-local-name="Ungaarsch" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%A1%D5%A4%D5%AB%D5%B8%D5%A1%D5%AF%D5%BF%D5%AB%D5%BE_%D5%A1%D5%B2%D5%A2%D5%B5%D5%B8%D6%82%D6%80%D5%AB_%D5%A1%D5%AF%D5%BF%D5%AB%D5%BE%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Ռադիոակտիվ աղբյուրի ակտիվություն – Armeensch" lang="hy" hreflang="hy" data-title="Ռադիոակտիվ աղբյուրի ակտիվություն" data-language-autonym="Հայերեն" data-language-local-name="Armeensch" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it badge-Q70893996 mw-list-item" title=""><a href="https://it.wikipedia.org/wiki/Attivit%C3%A0_(fisica)" title="Attività (fisica) – Italieensch" lang="it" hreflang="it" data-title="Attività (fisica)" data-language-autonym="Italiano" data-language-local-name="Italieensch" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D0%BE%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D1%82%D1%96_%D1%81%D3%99%D1%83%D0%BB%D0%B5%D0%BB%D0%B5%D0%BD%D1%83_%D0%BA%D3%A9%D0%B7%D1%96%D0%BD%D1%96%D2%A3_%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D1%82%D1%96%D0%BB%D1%96%D0%B3%D1%96" title="Радиоактивті сәулелену көзінің активтілігі – Kasach’sch" lang="kk" hreflang="kk" data-title="Радиоактивті сәулелену көзінің активтілігі" data-language-autonym="Қазақша" data-language-local-name="Kasach’sch" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Aktywno%C5%9B%C4%87_promieniotw%C3%B3rcza" title="Aktywność promieniotwórcza – Poolsch" lang="pl" hreflang="pl" data-title="Aktywność promieniotwórcza" data-language-autonym="Polski" data-language-local-name="Poolsch" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D1%81%D1%82%D1%8C_%D1%80%D0%B0%D0%B4%D0%B8%D0%BE%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D0%B3%D0%BE_%D0%B8%D1%81%D1%82%D0%BE%D1%87%D0%BD%D0%B8%D0%BA%D0%B0" title="Активность радиоактивного источника – Russ’sch" lang="ru" hreflang="ru" data-title="Активность радиоактивного источника" data-language-autonym="Русский" data-language-local-name="Russ’sch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Aktivnost" title="Aktivnost – Sloweensch" lang="sl" hreflang="sl" data-title="Aktivnost" data-language-autonym="Slovenščina" data-language-local-name="Sloweensch" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D1%96%D1%81%D1%82%D1%8C_%D1%80%D0%B0%D0%B4%D1%96%D0%BE%D0%B0%D0%BA%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D0%B3%D0%BE_%D0%B4%D0%B6%D0%B5%D1%80%D0%B5%D0%BB%D0%B0" title="Активність радіоактивного джерела – Ukrainsch" lang="uk" hreflang="uk" data-title="Активність радіоактивного джерела" data-language-autonym="Українська" data-language-local-name="Ukrainsch" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%94%BE%E5%B0%84%E6%80%A7%E6%B4%BB%E5%BA%A6" title="放射性活度 – Chineesch" lang="zh" hreflang="zh" data-title="放射性活度" data-language-autonym="中文" data-language-local-name="Chineesch" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q317949#sitelinks-wikipedia" title="Interspraaklenken ännern" class="wbc-editpage">Linken ännern</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Naamrüüm"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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dir="ltr"><p>De <b>Aktivität</b> vun en <a href="/wiki/Radioaktivit%C3%A4t" title="Radioaktivität">radioaktiven</a> Stoffmengde beschrifft in de <a href="/wiki/Physik" title="Physik">Physik</a> de Tall vun <a href="/wiki/Karnverfall" class="mw-redirect" title="Karnverfall">Verfallsvörgäng</a> betogen op en Tieteenheit. Se is dormit en <a href="/wiki/Physikaalsch_Gr%C3%B6tt" title="Physikaalsch Grött">physikaalsch Grött</a>. Ehr <a href="/wiki/Formelteken" title="Formelteken">Formelteken</a> is <i>A</i> oder ok <i>R</i>. </p><p>De Aktivität warrt in’t <a href="/wiki/Internatschonal_Eenheitensystem" title="Internatschonal Eenheitensystem">SI-System</a> mit de Eenheit <a href="/wiki/Becquerel_(Eenheit)" title="Becquerel (Eenheit)">Becquerel</a> (Bq) angeven, wobi 1 Bq een Karnverfall in een Sekunn bedüüdt. En öllere Maateenheit, de vundaag nich mehr bruukt warrt, is dat <a href="/wiki/Curie_(Eenheit)" title="Curie (Eenheit)">Curie</a> (Ci). För’t Ümreken gellt: 1 Ci = 3,7 · 10<sup>10</sup> Bq. </p><p>Betütt man de Aktivität op de Masse vun de Proov, seggt man dorto <i>spezifische Aktivität</i>, de denn in Bq/kg angeven warrt. Bi de spezifischen Aktivität mutt aver dorbi angeven warrn, op wovun Masse sik de Angaav betütt. Dat kann op de Masse vun’t reine <a href="/w/index.php?title=Radionuklid&action=edit&redlink=1" class="new" title="Radionuklid (Siet noch nich vörhannen)">Radionuklid</a> betogen wesen, op dat <a href="/wiki/Cheemsch_Element" title="Cheemsch Element">cheemsche Element</a> mit all sien <a href="/wiki/Isotop" title="Isotop">Isotopen</a>, op en <a href="/wiki/Cheemsch_Verbinnen" title="Cheemsch Verbinnen">cheemsche Verbinnen</a> oder op de Samtmasse vun en Proov, de ok en Stoffmischen wesen kann. </p><p>In de <a href="/w/index.php?title=Nuklearmedizin&action=edit&redlink=1" class="new" title="Nuklearmedizin (Siet noch nich vörhannen)">Nuklearmedizin</a> warrt de Aktivität vun en Präparat vör’t Anwennen in en <a href="/w/index.php?title=Aktivimeter&action=edit&redlink=1" class="new" title="Aktivimeter (Siet noch nich vörhannen)">Aktivimeter</a> bestimmt. </p> <div class="mw-heading mw-heading2"><h2 id="Aktivität_un_Verfallskunstant"><span id="Aktivit.C3.A4t_un_Verfallskunstant"></span>Aktivität un Verfallskunstant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aktivit%C3%A4t_(Physik)&veaction=edit&section=1" title="Ännere Afsnitt: Aktivität un Verfallskunstant" class="mw-editsection-visualeditor"><span>ännern</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aktivit%C3%A4t_(Physik)&action=edit&section=1" title="Quellcode des Abschnitts bearbeiten: Aktivität un Verfallskunstant"><span>Bornkood ännern</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jeed <a href="/w/index.php?title=Radionuklid&action=edit&redlink=1" class="new" title="Radionuklid (Siet noch nich vörhannen)">Radionuklid</a> hett en <a href="/w/index.php?title=Verfallskunstant&action=edit&redlink=1" class="new" title="Verfallskunstant (Siet noch nich vörhannen)">Verfallskunstant</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> (lambda), de beschrifft, wo „gau“ der Verfall aflöpt. Dat warrt in de <a href="/wiki/Halfweertstiet" title="Halfweertstiet">Halfweertstiet</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{1/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{1/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/734a923f08f57b747853e98b73963ad657d99e8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:4.056ex; height:3.009ex;" alt="{\displaystyle T_{1/2}}"></span> utdrückt. Twüschen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> un <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{1/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{1/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/734a923f08f57b747853e98b73963ad657d99e8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:4.056ex; height:3.009ex;" alt="{\displaystyle T_{1/2}}"></span> besteiht en eenfachen Tosamenhang: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda ={\frac {\ln 2}{T_{1/2}}}={\frac {0,693...}{T_{1/2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mn>2</mn> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0</mn> <mo>,</mo> <mn>693...</mn> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda ={\frac {\ln 2}{T_{1/2}}}={\frac {0,693...}{T_{1/2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa64ab4ef2d255a05defd47c7e4db6cb3f24ffd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:20.904ex; height:6.176ex;" alt="{\displaystyle \lambda ={\frac {\ln 2}{T_{1/2}}}={\frac {0,693...}{T_{1/2}}}}"></span> .</dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> is de Wohrschienlichkeit för den Verfall vun en enkelten Atomkarn in een Tieteenheit. De Aktivität vun en Proov mit <i>N</i> Atomen to de Tiet <i>t</i> lett sik dorüm utdrücken as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(t)=-{\frac {dN}{dt}}(t)=\lambda \cdot N(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>N</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>λ</mi> <mo>⋅</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(t)=-{\frac {dN}{dt}}(t)=\lambda \cdot N(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e294cc352dc02d5de31ba1b2c0b79a3d91b77e75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.908ex; height:5.509ex;" alt="{\displaystyle A(t)=-{\frac {dN}{dt}}(t)=\lambda \cdot N(t)}"></span> .</dd></dl> <p>Wenn een dat <a href="/w/index.php?title=Verfallsgsett&action=edit&redlink=1" class="new" title="Verfallsgsett (Siet noch nich vörhannen)">Verfallsgsett</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N(t)=N_{0}\cdot e^{-\lambda t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>λ</mi> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N(t)=N_{0}\cdot e^{-\lambda t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bae1d3ac280e8478683d9e90639a9ec2f546bd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.557ex; height:3.176ex;" alt="{\displaystyle N(t)=N_{0}\cdot e^{-\lambda t}}"></span></dd></dl> <p>(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b6328fbe0cded37216c90735c89ee188be26a30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.92ex; height:2.509ex;" alt="{\displaystyle N_{0}}"></span> is de Tall vun Atomen to de Tiet <i>t</i> = 0) mit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span>, berekent sik de Aktivität vun de Proov to en sünnere Tiet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> ut </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A(t)=N(t)\cdot \lambda =N_{0}\cdot e^{-\lambda t}\cdot \lambda =A_{0}\cdot e^{-\lambda t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>λ</mi> <mo>=</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>λ</mi> <mi>t</mi> </mrow> </msup> <mo>⋅</mo> <mi>λ</mi> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>⋅</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>λ</mi> <mi>t</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A(t)=N(t)\cdot \lambda =N_{0}\cdot e^{-\lambda t}\cdot \lambda =A_{0}\cdot e^{-\lambda t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf5bf3803796a10d16ba33a29c5f0b2d00984552" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.837ex; height:3.176ex;" alt="{\displaystyle A(t)=N(t)\cdot \lambda =N_{0}\cdot e^{-\lambda t}\cdot \lambda =A_{0}\cdot e^{-\lambda t}}"></span>.</dd></dl> <p>Dorna entwickelt sik de Aktivität na dat glieke exponentielle Verfallsgesett, as de Tall vun de radioaktiven Atomen in de Proov. </p> <div class="mw-heading mw-heading3"><h3 id="Rekenbispeel">Rekenbispeel</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aktivit%C3%A4t_(Physik)&veaction=edit&section=2" title="Ännere Afsnitt: Rekenbispeel" class="mw-editsection-visualeditor"><span>ännern</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aktivit%C3%A4t_(Physik)&action=edit&section=2" title="Quellcode des Abschnitts bearbeiten: Rekenbispeel"><span>Bornkood ännern</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Polonium" title="Polonium">Polonium</a>-210 hett en Halfweertstiet vun 138 Daag. In en <a href="/wiki/Mol_(Eenheit)" title="Mol (Eenheit)">Mol</a>, also 209,98 g, sünd ruchweg <a href="/w/index.php?title=Avogadro-Tall&action=edit&redlink=1" class="new" title="Avogadro-Tall (Siet noch nich vörhannen)"><i>N</i><sub>A</sub></a> = 6,022·10<sup>23</sup> Atomen. 1 g frisch <sup>210</sup>Po hett dormit de Aktivität: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {\ln(2)}{T_{1/2}}}{\frac {N_{\mathrm {A} }}{209,98}}\,=1{,}7\cdot 10^{14}\,\mathrm {Bq} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mrow> <mn>209</mn> <mo>,</mo> <mn>98</mn> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>7</mn> <mo>⋅</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>14</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {\ln(2)}{T_{1/2}}}{\frac {N_{\mathrm {A} }}{209,98}}\,=1{,}7\cdot 10^{14}\,\mathrm {Bq} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a77460c804cd06f13a8bd2e8f717fed16dee7cb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:33.885ex; height:6.509ex;" alt="{\displaystyle A={\frac {\ln(2)}{T_{1/2}}}{\frac {N_{\mathrm {A} }}{209,98}}\,=1{,}7\cdot 10^{14}\,\mathrm {Bq} }"></span> .</dd></dl> <p>De Mengde is mit 1 Gramm annahmen worrn, also is de spezifische Aktivität in dissen Fall: 1,7 · 10<sup>14</sup> Bq/g. </p> <div class="mw-heading mw-heading3"><h3 id="Utwählte_Bispelen_för_spezifische_Aktivitäten"><span id="Utw.C3.A4hlte_Bispelen_f.C3.B6r_spezifische_Aktivit.C3.A4ten"></span>Utwählte Bispelen för spezifische Aktivitäten</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Aktivit%C3%A4t_(Physik)&veaction=edit&section=3" title="Ännere Afsnitt: Utwählte Bispelen för spezifische Aktivitäten" class="mw-editsection-visualeditor"><span>ännern</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Aktivit%C3%A4t_(Physik)&action=edit&section=3" title="Quellcode des Abschnitts bearbeiten: Utwählte Bispelen för spezifische Aktivitäten"><span>Bornkood ännern</span></a><span class="mw-editsection-bracket">]</span></span></div> <table cellpadding="10"> <tbody><tr> <td align="center"> <table class="Tabell" style="width: 25em;"> <tbody><tr> <th>Element (natürliche Isotopenmischen)</th> <th>Spezifische Aktivität </th></tr> <tr> <td><a href="/wiki/Kalium" title="Kalium">Kalium</a></td> <td align="right">31.200 Bq/kg </td></tr> <tr> <td><a href="/wiki/Tellur" title="Tellur">Tellur</a></td> <td align="right">100 Bq/kg </td></tr> <tr> <td><a href="/wiki/Osmium" title="Osmium">Osmium</a></td> <td align="right">0,055 Bq/kg </td></tr> <tr> <td><a href="/wiki/Platin" title="Platin">Platin</a></td> <td align="right">10 Bq/kg </td></tr> <tr> <td><a href="/wiki/Wismut" title="Wismut">Wismut</a></td> <td align="right">0,0033 Bq/kg </td></tr> <tr> <td><a href="/wiki/Thorium" title="Thorium">Thorium</a></td> <td align="right">4.040.000 Bq/kg </td></tr> <tr> <td><a href="/wiki/Uran" title="Uran">Uran</a></td> <td align="right">12.870.000 Bq/kg </td></tr></tbody></table> </td> <td> <table class="wikitable" style="width: 25em;"> <tbody><tr> <th>Radionuklid</th> <th>Spezifische Aktivität </th></tr> <tr> <td><a href="/wiki/Iod" class="mw-redirect" title="Iod">I</a>-131</td> <td align="right">4,6 <a href="/wiki/Exa" title="Exa">E</a>Bq/kg </td></tr> <tr> <td><a href="/wiki/Plutonium" title="Plutonium">Pu</a>-239</td> <td align="right">2,3 <a href="/wiki/Tera" title="Tera">T</a>Bq/kg </td></tr> <tr> <td><a href="/wiki/Thorium" title="Thorium">Th</a>-232</td> <td align="right">4,06 <a href="/wiki/Mega" title="Mega">M</a>Bq/kg </td></tr> <tr> <td><a href="/wiki/Uran" title="Uran">U</a>-235</td> <td align="right">80 <a href="/wiki/Mega" title="Mega">M</a>Bq/kg </td></tr> <tr> <td><a href="/wiki/Uran" title="Uran">U</a>-238</td> <td align="right">12 <a href="/wiki/Mega" title="Mega">M</a>Bq/kg </td></tr></tbody></table> </td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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