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\begin{enumerate}
    \item Vervollst\"{a}ndige die Zerfallsreihe unter Verwendung des unten stehenden Auszugs aus einer Nuklidkarte in der angegebenen Weise:

          $${}^{232}_{\ 90}\mathrm{Th} \overset{\alpha}{\rightarrow} {}^{228}_{\ 88}\mathrm{Ra}\qquad\ldots\qquad {}^{212}_{\ 84}\mathrm{Po}\overset{\alpha}{\rightarrow}{}^{208}_{\ 82}\mathrm{Pb}$$
\end{enumerate}

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           {\mbox{$7{,}6\mathrm{m}$}}
           {\mbox{}}
           {\mbox{}}
           {cyan}
           {132}
           {83}
    \mykern{Bi 216}
           {\mbox{}}
           {\mbox{}}
           {\mbox{}}
           {cyan}
           {133}
           {83}
    \mykern{Bi 217}
           {\mbox{}}
           {\mbox{}}
           {\mbox{}}
           {cyan}
           {134}
           {83}
    \mykern{Bi 218}
           {\mbox{}}
           {\mbox{}}
           {\mbox{}}
           {cyan}
           {135}
           {83}
	\end{pspicture}
\end{center}

\bigskip
\begin{enumerate}
    \item Welche spezielle Eigenschaft haben die Massenzahlen aller Elemente dieser Zerfallsreihe?
    \item Beim $\alpha$--Zerfall von Th--232 zu Ra--228 finden wir im Feld f\"{u}r Th--232, dass
          die Energie der $\alpha$--Teilchen $4{,}1\,\mathrm{MeV}$ betr\"{a}gt.
          Best\"{a}tige durch Rechnung, dass dieser Wert korrekt ist. F\"{u}hre diese Rechnung
          auch f\"{u}r den Zerfall von Bi--212 durch und vergleiche dein Ergebnis mit dem in dem
          Auszug aus der Nuklidkarte angegebenen Wert.

          Ben\"{o}tigte Kernmassen: He--4: $4{,}001\,506\,5\,\mathrm{u}$, Bi-212: $211{,}946\,667\,2\mathrm{u}$,
          Po--212: $211{,}943\,700\,0\,\mathrm{u}$, \\ Ra--228: $227{,}983\,777\,6\,\mathrm{u}$,
          Th--232: $231{,}989\,682\,1\,\mathrm{u}$.
          Masse des Elektrons: $5{,}48580\cdot10^{-4}\,\mathrm{u}$
\end{enumerate}
}
\LSG{
\begin{enumerate}
  \item ${}^{232}_{\ 90}\mathrm{Th} \overset{\alpha}{\rightarrow}
         {}^{228}_{\ 88}\mathrm{Ra} \overset{\beta^{-}}{\rightarrow}
         {}^{228}_{\ 89}\mathrm{Ac} \overset{\beta^{-}}{\rightarrow}
         {}^{228}_{\ 90}\mathrm{Th} \overset{\alpha}{\rightarrow}
         {}^{224}_{\ 88}\mathrm{Ra} \overset{\alpha}{\rightarrow}
         {}^{220}_{\ 86}\mathrm{Rn} \overset{\alpha}{\rightarrow}
         {}^{216}_{\ 84}\mathrm{Po} \overset{\alpha}{\rightarrow}
         {}^{212}_{\ 82}\mathrm{Pb} \overset{\beta^{-}}{\rightarrow}
         {}^{212}_{\ 83}\mathrm{Bi} \overset{\beta^{-}}{\rightarrow}
         {}^{212}_{\ 84}\mathrm{Po} \overset{\alpha}{\rightarrow}
         {}^{208}_{\ 82}\mathrm{Pb}$
  \item Alle Massenzahlen der Zerfallsreihe sind Vielfache von 4.
  \item $\left(231{,}989\,682\,1-227{,}983\,777\,6-4{,}001\,506\,5\right)\,\mathrm{u}\mathrm{c}^2=4{,}1\,\mathrm{MeV}$

        $\left(211{,}946\,667\,2-211{,}943\,700\,0-5{,}48580\cdot10^{-4}\right)\,\mathrm{u}\mathrm{c}^2=2{,}2\,\mathrm{MeV}$
\end{enumerate}
}
