thomas@thinkix:~$ maple
    |\^/|     Maple 9 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2003
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> restart;
>
> # Halbwertszeiten
> lambda_230 := ln(2)/7.538e4;
                           lambda_230 := 0.00001326611833 ln(2)

> lambda_234 := ln(2)/2.455e5;
                                                        -5
                           lambda_234 := 0.4073319756 10   ln(2)

> lambda_231 := ln(2)/3.276e4;
                           lambda_231 := 0.00003052503052 ln(2)

>
> # Verhältnisse
> ThU := Th_230/U_238 = 0.868; #+0.001;
                                          Th_230
                                   ThU := ------ = 0.868
                                          U_238

> UU := U_234/U_238 = 1.0871; #+0.002;
                                         U_234
                                   UU := ----- = 1.0871
                                         U_238

> UU_0 := U_234_0/U_238_0 = 1.14;
                                          U_234_0
                                  UU_0 := ------- = 1.14
                                          U_238_0

> PaU := Pa_231/U_235 = 0.942; #+0.001;
                                          Pa_231
                                   PaU := ------ = 0.942
                                          U_235

> PaU_0 := Pa_231_0/U_235_0 = 0;
                                            Pa_231_0
                                   PaU_0 := -------- = 0
                                            U_235_0

>
> Th_230 := solve(ThU,Th_230);
                               Th_230 := 0.8680000000 U_238

> U_234 := solve(UU,U_234);
                                U_234 := 1.087100000 U_238

> U_234_0 := solve(UU_0,U_234_0);
                              U_234_0 := 1.140000000 U_238_0

> Pa_231 := solve(PaU,Pa_231);
                               Pa_231 := 0.9420000000 U_235

> Pa_231_0 := solve(PaU_0,Pa_231_0);
                                       Pa_231_0 := 0

>
> # 238U-234U
> eq_UU := U_234/U_238 = U_234_0/U_238_0 * exp(-lambda_234*t);
                                                                   -5
            eq_UU := 1.087100000 = 1.140000000 exp(-0.4073319756 10   ln(2) t)

> t_UU := fsolve(eq_UU,t);
                                    t_UU := 16828.82062

>
> # 238U-230Th
> eq_UTh := Th_230/U_234 = U_238/U_234 * (1-exp(-lambda_230*t)) + (1-U_238/U_234) * (lam> eq_UTh := Th_230/U_234 = U_238/U_234 * (1-ex\
> p(-lambda_230*t)) + (1-U_238/U_234) * (lambda_230/(lambda_230-lambda_234)) * (1-exp(-(> p(-lambda_230*t)) + (1-U_238/U_234) * (lambd\
> a_230/(lambda_230-lambda_234)) * (1-exp(-(lambda_230-lambda_234)*t));
eq_UTh := 0.7984546040 = 1.035501722 - 0.9198785760 exp(-0.00001326611833 ln(2) t)

                                        -5
     - 0.1156231460 exp(-0.9192798574 10   ln(2) t)

> t_UTh := fsolve(eq_UTh,t);
                                   t_UTh := 167441.9035

>
> # 231Pa-235U
> eq_PaU := Pa_231/U_235 = Pa_231_0/U_235_0 * exp(-lambda_231*t)+1-exp(-lambda_231*t);
                eq_PaU := 0.9420000000 = 1 - exp(-0.00003052503052 ln(2) t)

> t_PaU := fsolve(eq_PaU,t);
                                   t_PaU := 134571.6358

>
> # Alles auf einen Blick
> # 238U-234U, 238U-230Th, 231Pa-235U
> t_UU; t_UTh; t_PaU;
                                        16828.82062

                                        167441.9035

                                        134571.6358

>