vendredi 28 juin 2013

Activité et défaut de masse illustrés par Gilg Jürgen


Le listing :

\documentclass[dvipsnames]{article}
\usepackage{amsmath}
\usepackage{pst-grad,pst-slpe,multido}
\SpecialCoor
\def\Kernradius{7.5pt}
\def\KernabstandHe{7.5pt}
\def\KernabstandA{7.5pt}
\def\KernabstandB{7.7pt}
\def\KernabstandCB{11.8pt}
\def\KernabstandCD{12.3pt}
\def\KernabstandC{12.5pt}
\def\KernabstandD{13.0pt}
\def\KernabstandE{20.5pt}
\def\KernabstandBaE{19.8pt}
\def\KernabstandEA{20.0pt}
\def\KernabstandF{24.0pt}
\def\KernabstandG{23.4pt}
\def\ColorProton{red}
\def\ColorNeutron{gray!20}

\newpsstyle{proton}{linecolor={[rgb]{0.72 0 0}},slopebegin=red!50,sloperadius=0.15,linewidth=0.1pt,slopecenter=0.65 0.6,linestyle=solid}
\newpsstyle{neutron}{linecolor=gray!50,slopebegin=white,sloperadius=0.11,linewidth=0.1pt,slopecenter=0.65 0.6,linestyle=solid}
\def\Proton{\psBall[style=proton](0,0){\ColorProton}{\Kernradius}}
\def\Neutron{\psBall[style=neutron](0,0){\ColorNeutron}{\Kernradius}}

\def\AtomKernU{%
%---------- 0. Ebene -------------------
\rput(\KernabstandG;108){\Neutron}%
\rput(\KernabstandG;144){\Neutron}%
\rput(\KernabstandG;180){\Proton}%
\rput(\KernabstandG;216){\Neutron}%
\rput(\KernabstandG;252){\Neutron}%
\rput(\KernabstandG;288){\Proton}%
\rput(\KernabstandG;324){\Neutron}%
\rput(\KernabstandG;0){\Proton}%
\rput(\KernabstandG;36){\Proton}%
\rput(\KernabstandG;72){\Proton}%
%---------- 1. Ebene -------------------
\rput(\KernabstandF;90){\Neutron}%
\rput(\KernabstandF;126){\Proton}%
\rput(\KernabstandF;162){\Neutron}%
\rput(\KernabstandF;198){\Proton}%
\rput(\KernabstandF;234){\Proton}%
\rput(\KernabstandF;270){\Neutron}%
\rput(\KernabstandF;306){\Neutron}%
\rput(\KernabstandF;342){\Neutron}%
\rput(\KernabstandF;18){\Neutron}%
\rput(\KernabstandF;54){\Neutron}%
%------------ 2. Ebene ------------------
\rput(\KernabstandE;73){\Proton}%
\rput(\KernabstandE;145){\Proton}%
\rput(\KernabstandE;107){\Neutron}%
\rput(\KernabstandE;180){\Neutron}%
\rput(\KernabstandE;215){\Neutron}%
\rput(\KernabstandE;290){\Neutron}%
\rput(\KernabstandE;253){\Neutron}%
\rput(\KernabstandE;36){\Neutron}%
\rput(\KernabstandE;1){\Neutron}%
\rput(\KernabstandE;325){\Proton}%
%------------ 3. Ebene ------------------
\rput(\KernabstandD;225){\Proton}%
\rput(\KernabstandC;282){\Neutron}%
\rput(\KernabstandC;327){\Neutron}%
\rput(\KernabstandC;171){\Neutron}%
\rput(\KernabstandC;104){\Neutron}%
\rput(\KernabstandC;36){\Proton}%
\rput(0;0){\Neutron}%
}%

\def\AtomKernRn{%
%---------- 0. Ebene -------------------
\rput(\KernabstandG;108){\Proton}%
\rput(\KernabstandG;144){\Neutron}%
\rput(\KernabstandG;180){\Proton}%
\rput(\KernabstandG;216){\Neutron}%
\rput(\KernabstandG;252){\Neutron}%
\rput(\KernabstandG;288){\Proton}%
\rput(\KernabstandG;324){\Neutron}%
\rput(\KernabstandG;0){\Proton}%
\rput(\KernabstandG;36){\Proton}%
\rput(\KernabstandG;72){\Neutron}%
%---------- 1. Ebene -------------------
\rput(\KernabstandF;90){\Neutron}%
\rput(\KernabstandF;126){\Neutron}%
\rput(\KernabstandF;162){\Neutron}%
\rput(\KernabstandF;198){\Proton}%
\rput(\KernabstandF;234){\Proton}%
\rput(\KernabstandF;270){\Proton}%
\rput(\KernabstandF;306){\Neutron}%
\rput(\KernabstandF;342){\Neutron}%
\rput(\KernabstandF;18){\Neutron}%
\rput(\KernabstandF;54){\Neutron}%
%------------ 2. Ebene ------------------
\rput(\KernabstandE;73){\Proton}%
\rput(\KernabstandE;145){\Proton}%
\rput(\KernabstandE;107){\Neutron}%
\rput(\KernabstandE;180){\Neutron}%
\rput(\KernabstandE;215){\Neutron}%
\rput(\KernabstandE;290){\Neutron}%
\rput(\KernabstandE;253){\Neutron}%
\rput(\KernabstandE;36){\Neutron}%
\rput(\KernabstandE;1){\Neutron}%
\rput(\KernabstandE;325){\Proton}%
%------------ 3. Ebene ------------------
\rput(\KernabstandD;225){\Proton}%
\rput(\KernabstandC;282){\Neutron}%
\rput(\KernabstandC;327){\Neutron}%
\rput(\KernabstandC;171){\Neutron}%
\rput(\KernabstandC;104){\Neutron}%
\rput(\KernabstandC;36){\Neutron}%
\rput(0;0){\Proton}%
}%

\def\AtomKernHe{%
\multido{\iAngle=40+180}{2}{%
\rput(\KernabstandHe;\iAngle){\Proton}%
}%
\multido{\iAngle=130+180}{2}{%
\rput(\KernabstandHe;\iAngle){\Neutron}%
}%
}%


\definecolor{TextA}{rgb}{0.2,0.402,0.333}% Pfeile Medium Aquamarine


\begin{document}


\section*{Activit\'{e}}

\begin{center}
\begin{pspicture}(-6,-3)(5,4)
\def\stoppuhr{%
\psframe[fillstyle=solid,fillcolor=black](-0.3,1.7)(0.3,1.85)
\psframe[fillstyle=solid,fillcolor=black](-0.1,1.8)(0.1,2)
\psellipse[fillstyle=gradient,gradend=lightgray!70,gradbegin=lightgray!30,gradmidpoint=0.25,gradangle=0,linewidth=0.5pt](0,2.1)(0.25,0.1)
\psline[linewidth=0.5\pslinewidth](0,2.2)(0,2.1)
\psline[linewidth=0.5\pslinewidth](-0.05,2.195)(-0.075,2.1)
\psline[linewidth=0.5\pslinewidth](0.05,2.195)(0.075,2.1)
\psline[linewidth=0.5\pslinewidth](-0.1,2.185)(-0.135,2.1)
\psline[linewidth=0.5\pslinewidth](0.1,2.185)(0.135,2.1)
\pscircle[fillstyle=gradient,gradend=OliveGreen!70,gradbegin=OliveGreen!30,gradmidpoint=0.75,gradangle=90,linewidth=0.5pt](0,0){1.75}
\pscircle[fillstyle=gradient,gradend=NavyBlue!20,gradbegin=NavyBlue!5,gradmidpoint=0.75,gradangle=90,linewidth=0.5pt](0,0){1.5}
\multido{\rA=-6+12}{30}{%
\rput(1.4;\rA){\pscircle*[linecolor=black](0,0){0.05}}
}
\multido{\rB=30+60}{6}{%
\psline[linewidth=3pt](1.45;\rB)(1.2;\rB)
}
\pswedge[fillstyle=solid,fillcolor=Goldenrod,linecolor=Goldenrod,opacity=0.85](0,0){1.175}{42}{90}
\psdot(0,0)
\psline(0,0)(1;42)
\uput{0.7cm}[90](0,0){\small 30}
\uput{0.7cm}[150](0,0){\small 25}
\uput{0.7cm}[210](0,0){\small 20}
\uput{0.7cm}[270](0,0){\small 15}
\uput{0.7cm}[330](0,0){\small 10}
\uput{0.7cm}[30](0,0){\small 5}
}

\rput(3,0){\stoppuhr}
\def\uran{%
\psscalebox{0.3}{%
\AtomKernU
}}
\def\helium{%
\psscalebox{0.3}{%
\AtomKernHe
}}
\psframe(-6,-3)(1,4)
\rput(-5,-2){\uran}
\rput(-4,-2.5){\helium}
\psline{->}(-4.6,-2.2)(-4.2,-2.4)
\rput(-4,0){\uran}
\rput(-3,0.5){\helium}
\psline{->}(-3.6,0.2)(-3.2,0.4)
\rput(0,1){\uran}
\rput(0,2){\helium}
\psline{->}(0,1.4)(0,1.8)
\psline{->}(-3.6,0.2)(-3.2,0.4)
\rput(-2,2){\uran}
\rput(-3,2.5){\helium}
\psline{->}(-2.4,2.2)(-2.8,2.4)
\rput(-5.2,3.4){\uran}
\rput(-4.5,1.5){\uran}
\rput(-5.4,0.4){\uran}
\rput(-4,3){\uran}
\rput(-1.5,-1){\uran}
\rput(0.5,-2.5){\uran}
\rput(-1.8,0.6){\uran}
\rput(-2.4,3.5){\uran}
\rput(-3,-1.5){\uran}
\rput(-0.25,-0.25){\uran}
\rput(0.2,3.2){\uran}
\rput(-1,-2){\uran}
\end{pspicture}
\end{center}
$\Delta n =4$ d\'{e}sint\'{e}grations en $\Delta t=4\,\mathrm{s}$
\[
A=\dfrac{\Delta n}{\Delta t}=1\,\mathrm{Bq}
\]
\section*{D\'{e}faut de masse}

\begin{center}
\begin{pspicture}(-4.75,-0.25)(4.75,5.5)
\pscustom[fillstyle=solid,fillcolor=gray]{%
\psline(-1.5,0)(1.5,0)
\psline(1.5,0)(1.25,0.5)
\psline(1.25,0.5)(-1.25,0.5)
\closepath
}

\def\waagSchale{%
\psline(-1.4,0.1)(0,3)(1.4,0.1)
\psframe[fillstyle=solid,fillcolor=OliveGreen](-1.5,0)(1.5,0.175)
}

\rput(-3,1.3){\waagSchale}
\rput(3,1.85){\waagSchale}

\rput{5}(0,4.6){%
\pscustom[fillstyle=solid,fillcolor=OliveGreen]{%
\psline(-3.5,0)(3.5,0)
\psline(3.5,0)(3.5,0.1)
\psline(3.5,0.1)(0,0.55)
\psline(0,0.55)(-3.5,0.1)
\closepath
}
}
\pscustom[fillstyle=solid,fillcolor=OliveGreen]{%
\psline(-0.35,0.5)(0.35,0.5)
\psline(0.35,0.5)(0.35,5)
\psarc(0,5){0.35}{0}{180}
\closepath
}
\rput(0,5){%
\pscustom[fillstyle=solid,fillcolor=yellow]{%
\psarc(0,0){3.5}{250}{290}
\psline(3.5;290)(3;290)
\psarcn(0,0){3}{290}{250}
\closepath
}
\multido{\rA=250+2.5}{17}{%
\psline(3;\rA)(3.3;\rA)
}
\psdot(0,0)
\psline[linewidth=2.5pt]{->}(0,0)(3.25;275)
}
\rput(-3.9,1.78){\Proton}
\rput(-3.3,1.78){\Proton}
\rput(-2.7,1.78){\Neutron}
\rput(-2.1,1.78){\Neutron}
\rput(3,2.52){\AtomKernHe}
\rput(-3,0.9){$2\mathrm{p}^+ + 2\mathrm{n}$}
\rput(3,1.4){$\mathrm{ ^{4}_{2}He}$}
\end{pspicture}
\end{center}
\end{document}



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