A09 Gepulste Kernspinresonanz

<< Graphics`Graphics`

<< NumericalMath`PolynomialFit`

<< Statistics`LinearRegression`

<< Graphics`MultipleListPlot`

Konstanten

γI = 2.67522 10^8;

Bestimmung der Inhomogenität des Magnetfeldes

Probe 1 (Repetitionsrate 1ms)

InhP1Rf=({{11.6, 610, \[Placeholder], \[Placeholder]}, {12.1, 582, \[Placeholder], \[Placeholder]}, {12.6, 514, \[Placeholder], \[Placeholder]}, {13.1, 450, \[Placeholder], \[Placeholder]}, {13.6, 394, \[Placeholder], \[Placeholder]}, {14.1, 348, \[Placeholder], \[Placeholder]}, {14.6, 308, \[Placeholder], \[Placeholder]}, {15.1, 270, \[Placeholder], \[Placeholder]}, {15.6, 238, \[Placeholder], \[Placeholder]}, {16.1, 212, \[Placeholder], \[Placeholder]}, {16.6, 186, \[Placeholder], \[Placeholder]}, {17.1, 166, \[Placeholder], \[Placeholder]}, {17.6, 148, \[Placeholder], \[Placeholder]}, {18.1, 130, \[Placeholder], \[Placeholder]}, {18.6, 116, \[Placeholder], \[Placeholder]}, {19.1, 106, \[Placeholder], \[Placeholder]}, {19.6, 94, \[Placeholder], \[Placeholder]}, {20.1, 82, \[Placeholder], \[Placeholder]}, {20.6, 76, \[Placeholder], \[Placeholder]}, {21.1, 68, \[Placeholder], \[Placeholder]}, {21.6, 64, \[Placeholder], \[Placeholder]}, {22.1, 60, \[Placeholder], \[Placeholder]}, {22.6, 54, \[Placeholder], \[Placeholder]}, {23.1, 50, \[Placeholder], \[Placeholder]}, {23.6, 46, \[Placeholder], \[Placeholder]}, {24.1, 42, \[Placeholder], \[Placeholder]}, {24.6, 40, \[Placeholder], \[Placeholder]}, {31.1, 26, \[Placeholder], \[Placeholder]}, {38.6, 26, \[Placeholder], \[Placeholder]}});

InhP1RfErr = 
        Replace[InhP1Rf, {de_, df_, dg_, dh_} -> {{de - 11.6, df}, 
              ErrorBar[0.1, df 0.03]}, 2];

MultipleListPlot[InhP1RfErr, ImageSize -> 550];

Probe 2 (Repetitionsrate 1ms)

InhP2Rf=({{11.3, 708, \[Placeholder], \[Placeholder]}, {11.8, 696, \[Placeholder], \[Placeholder]}, {12.3, 644, \[Placeholder], \[Placeholder]}, {12.8, 564, \[Placeholder], \[Placeholder]}, {13.3, 500, \[Placeholder], \[Placeholder]}, {13.8, 440, \[Placeholder], \[Placeholder]}, {14.3, 388, \[Placeholder], \[Placeholder]}, {14.8, 344, \[Placeholder], \[Placeholder]}, {15.3, 304, \[Placeholder], \[Placeholder]}, {15.8, 268, \[Placeholder], \[Placeholder]}, {16.3, 240, \[Placeholder], \[Placeholder]}, {16.8, 212, \[Placeholder], \[Placeholder]}, {17.3, 192, \[Placeholder], \[Placeholder]}, {17.8, 168, \[Placeholder], \[Placeholder]}, {18.3, 150, \[Placeholder], \[Placeholder]}, {18.8, 136, \[Placeholder], \[Placeholder]}, {19.3, 120, \[Placeholder], \[Placeholder]}, {19.8, 108, \[Placeholder], \[Placeholder]}, {20.3, 100, \[Placeholder], \[Placeholder]}, {20.8, 88, \[Placeholder], \[Placeholder]}, {21.3, 84, \[Placeholder], \[Placeholder]}, {21.8, 76, \[Placeholder], \[Placeholder]}, {22.3, 68, \[Placeholder], \[Placeholder]}, {22.8, 64, \[Placeholder], \[Placeholder]}, {23.3, 60, \[Placeholder], \[Placeholder]}, {25.3, 48, \[Placeholder], \[Placeholder]}, {28.5, 36, \[Placeholder], \[Placeholder]}, {39.3, 36, \[Placeholder], \[Placeholder]}});

InhP2RfErr = 
        Replace[InhP2Rf, {de_, df_, dg_, dh_} -> {{de - 11.3, df}, 
              ErrorBar[0.1, df 0.03]}, 2];

MultipleListPlot[InhP2RfErr, ImageSize -> 550];

Probe 1 (Repetitionsrate 100ms)

InhP1=({{5, 636, \[Placeholder], \[Placeholder]}, {10, 626, \[Placeholder], \[Placeholder]}, {15, 610, \[Placeholder], \[Placeholder]}, {20, 592, \[Placeholder], \[Placeholder]}, {25, 574, \[Placeholder], \[Placeholder]}, {30, 548, \[Placeholder], \[Placeholder]}, {35, 520, \[Placeholder], \[Placeholder]}, {40, 488, \[Placeholder], \[Placeholder]}, {45, 458, \[Placeholder], \[Placeholder]}, {50, 424, \[Placeholder], \[Placeholder]}, {55, 388, \[Placeholder], \[Placeholder]}, {60, 360, \[Placeholder], \[Placeholder]}, {65, 326, \[Placeholder], \[Placeholder]}, {70, 290, \[Placeholder], \[Placeholder]}, {75, 262, \[Placeholder], \[Placeholder]}, {80, 232, \[Placeholder], \[Placeholder]}, {85, 206, \[Placeholder], \[Placeholder]}, {90, 182, \[Placeholder], \[Placeholder]}, {95, 160, \[Placeholder], \[Placeholder]}, {100, 140, \[Placeholder], \[Placeholder]}, {110, 106, \[Placeholder], \[Placeholder]}, {120, 82, \[Placeholder], \[Placeholder]}, {130, 66, \[Placeholder], \[Placeholder]}, {140, 54, \[Placeholder], \[Placeholder]}, {150, 46, \[Placeholder], \[Placeholder]}, {160, 42, \[Placeholder], \[Placeholder]}, {170, 36, \[Placeholder], \[Placeholder]}, {180, 30, \[Placeholder], \[Placeholder]}, {190, 26, \[Placeholder], \[Placeholder]}, {250, 16, \[Placeholder], \[Placeholder]}});

InhP1Err = 
        Replace[InhP1, {de_, df_, dg_, 
              dh_} -> {{(de - 5)*10*10^-6, df*10^-3}, 
              ErrorBar[1*10*10^-6, df*10^-3 0.03]}, 2];

InhP1lnErr = 
        Replace[InhP1, {de_, df_, dg_, 
              dh_} -> {{(de - 5)*10*10^-6, Log[df/636]}, 
              ErrorBar[1*10*10^-6, Log[df] 0.03]}, 2];

InhP1ln = 
        Replace[InhP1, {de_, df_, dg_, 
              dh_} -> {(de - 5)*10*10^-6, Log[df/636]}, 
          2];

Regress[InhP1ln, {1, x^2}, x]

\(\(DisplayTogether[MultipleListPlot[InhP1Err], 
        Plot[636*10^\(-3\)\ Exp[\(-767259.662376704`\)\ x^2], {x, 0, 
            2450*10^\(-6\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

Fit per Auge, da Mathematica keinen befriedigenden Wert fittet: (Fehler 0.1*10^6)

\(\(DisplayTogether[MultipleListPlot[InhP1Err], 
        Plot[636*10^\(-3\)\ Exp[\(-\ 1.845*^6\)\ x^2], {x, 0, 
            2450*10^\(-6\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2starP1 = Sqrt[1/1.845*^6]

δT2starP1 = 0.1*10^6/1.845*^6;

ΔT2starP1 = δT2starP1*Sqrt[1/1.845*^6]

ΔB0P1 = Log[2]/(γI T2starP1)

ΔΔB0P1 = δT2starP1 ΔB0P1

Probe 2 (Repetitionsrate 100ms)

InhP2=({{5, 392, \[Placeholder], \[Placeholder]}, {10, 386, \[Placeholder], \[Placeholder]}, {15, 376, \[Placeholder], \[Placeholder]}, {20, 362, \[Placeholder], \[Placeholder]}, {25, 348, \[Placeholder], \[Placeholder]}, {30, 332, \[Placeholder], \[Placeholder]}, {35, 314, \[Placeholder], \[Placeholder]}, {40, 294, \[Placeholder], \[Placeholder]}, {45, 274, \[Placeholder], \[Placeholder]}, {50, 256, \[Placeholder], \[Placeholder]}, {55, 234, \[Placeholder], \[Placeholder]}, {60, 214, \[Placeholder], \[Placeholder]}, {65, 194, \[Placeholder], \[Placeholder]}, {70, 176, \[Placeholder], \[Placeholder]}, {75, 158, \[Placeholder], \[Placeholder]}, {80, 140, \[Placeholder], \[Placeholder]}, {85, 124, \[Placeholder], \[Placeholder]}, {90, 108, \[Placeholder], \[Placeholder]}, {100, 80, \[Placeholder], \[Placeholder]}, {110, 58, \[Placeholder], \[Placeholder]}, {120, 40, \[Placeholder], \[Placeholder]}, {130, 24, \[Placeholder], \[Placeholder]}, {140, 14, \[Placeholder], \[Placeholder]}, {145, 10, \[Placeholder], \[Placeholder]}, {150, 8, \[Placeholder], \[Placeholder]}, {165, 4, \[Placeholder], \[Placeholder]}});

InhP2Err = 
        Replace[InhP2, {de_, df_, dg_, 
              dh_} -> {{de*10*10^-6, df*10^-3}, 
              ErrorBar[1*10*10^-6, df*10^-3 0.03]}, 2];

InhP2lnErr = 
        Replace[InhP2, {de_, df_, dg_, 
              dh_} -> {{(de - 5)*10*10^-6, Log[df/392]}, 
              ErrorBar[1*10*10^-6, Log[df] 0.03]}, 2];

InhP2ln = 
        Replace[InhP2, {de_, df_, dg_, 
              dh_} -> {(de - 5)*10*10^-6, Log[df/392]}, 
          2];

Regress[InhP2ln, {1, x^2}, x]

\(\(DisplayTogether[MultipleListPlot[InhP2Err], 
        Plot[392*10^\(-3\)\ Exp[\(-\ 1.792147963985144`*^6\)\ \ x^2], {x, 0, 
            1650*10^\(-6\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2starP2 = Sqrt[1/1.792147963985144`*^6]

ΔT2starP2 = δT2starP2*
        Sqrt[1/1.792147963985144`*^6]

δT2starP2 = 
        14050.392265306096`/1.792147963985144`*^6;

ΔB0P2 = Log[2]/(γI T2starP2)

ΔΔB0P2 = δT2starP2 ΔB0P2

gewichteter Mittelwert für die Inhomogenität

Mx = (ΔB0P1/ΔΔB0P1^2 + ΔB0P2/ΔΔB0P2^2)/(1/ΔΔB0P1^2 + 
            1/ΔΔB0P2^2)

ΔMx = 
      1/Sqrt[(1/ΔΔB0P1^2 + 
              1/ΔΔB0P2^2)]

Bestimmung von T2

Probe 1 mit Spin-Echo

SEP1=({{1.15, 560, \[Placeholder], \[Placeholder]}, {1.35, 536, \[Placeholder], \[Placeholder]}, {1.8, 528, \[Placeholder], \[Placeholder]}, {18, 252, \[Placeholder], \[Placeholder]}, {14, 292, \[Placeholder], \[Placeholder]}, {12, 332, \[Placeholder], \[Placeholder]}, {10, 356, \[Placeholder], \[Placeholder]}, {8, 396, \[Placeholder], \[Placeholder]}, {6, 424, \[Placeholder], \[Placeholder]}, {4, 472, \[Placeholder], \[Placeholder]}, {2, 520, \[Placeholder], \[Placeholder]}, {0.6, 588, \[Placeholder], \[Placeholder]}, {16, 276, \[Placeholder], \[Placeholder]}, {20, 232, \[Placeholder], \[Placeholder]}, {40, 84, \[Placeholder], \[Placeholder]}, {60, 28, \[Placeholder], \[Placeholder]}, {80, 8, \[Placeholder], \[Placeholder]}, {1.57, 532, \[Placeholder], \[Placeholder]}});

SEP1Err = 
        Replace[SEP1, {de_, df_, dg_, 
              dh_} -> {{de 10^-3, df 10^-3}, 
              ErrorBar[0.1 10^-3, df 0.03 10^-3]}, 
          2];

SEP1ln = 
        Replace[SEP1, {de_, df_, dg_, dh_} -> {de 10^-3, 
              Log[df/602]}, 2];

Regress[SEP1ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[SEP1Err], 
        Plot[602\ 10^\(-3\)\ Exp[\ \(-52.200450976127144`\)\ x], {x, 0, 
            80\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2P1 = 1/52.200450976127144`

δT2P1 = 0.7053388727912404` T2P1;

ΔT2P1 = δT2P1 T2P1

Probe 1 mit Carr-Purcell

PCP1=({{2, 512, \[Placeholder], \[Placeholder]}, {4, 460, \[Placeholder], \[Placeholder]}, {6, 408, \[Placeholder], \[Placeholder]}, {8, 360, \[Placeholder], \[Placeholder]}, {10, 320, \[Placeholder], \[Placeholder]}, {12, 284, \[Placeholder], \[Placeholder]}, {14, 256, \[Placeholder], \[Placeholder]}, {16, 228, \[Placeholder], \[Placeholder]}, {18, 208, \[Placeholder], \[Placeholder]}, {20, 188, \[Placeholder], \[Placeholder]}});

PCP1Err = 
        Replace[PCP1, {de_, df_, dg_, 
              dh_} -> {{de 10^-3, df 10^-3}, 
              ErrorBar[0.1 10^-3, df 0.03 10^-3]}, 
          2];

PCP1ln = 
        Replace[PCP1, {de_, df_, dg_, dh_} -> {de 10^-3, 
              Log[df/570]}, 2];

Regress[PCP1ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[PCP1Err], 
        Plot[570\ 10^\(-3\)\ Exp[\(-\ 56.437869921671904`\)\ x], {x, 0, 
            20\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2P1CP = 1/56.437869921671904`

δT2P1CP = 0.7509372594449993` T2P1CP;

ΔT2P1CP = δT2P1CP T2P1CP

Probe 2 mit Spin-Echo

SEP2=({{0.87, 360, \[Placeholder], \[Placeholder]}, {1.08, 340, \[Placeholder], \[Placeholder]}, {1.27, 312, \[Placeholder], \[Placeholder]}, {1.53, 296, \[Placeholder], \[Placeholder]}, {1.99, 288, \[Placeholder], \[Placeholder]}, {4, 230, \[Placeholder], \[Placeholder]}, {6, 192, \[Placeholder], \[Placeholder]}, {8, 152, \[Placeholder], \[Placeholder]}, {10, 120, \[Placeholder], \[Placeholder]}, {12, 100, \[Placeholder], \[Placeholder]}, {14, 76, \[Placeholder], \[Placeholder]}, {16, 64, \[Placeholder], \[Placeholder]}, {18, 52, \[Placeholder], \[Placeholder]}, {20, 40, \[Placeholder], \[Placeholder]}});

SEP2Err = 
        Replace[SEP2, {de_, df_, dg_, 
              dh_} -> {{de 10^-3, df 10^-3}, 
              ErrorBar[0.1 10^-3, df 0.03 10^-3]}, 
          2];

SEP2ln = 
        Replace[SEP2, {de_, df_, dg_, dh_} -> {de 10^-3, 
              Log[df/370]}, 2];

Regress[SEP2ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[SEP2Err], 
        Plot[370\ 10^\(-3\)\ Exp[\ \(-\ 110.25196917216472`\)\ x], {x, 0, 
            20\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2P2 = 1/110.25196917216469`

δT2P2 = 1.4261379971027337` T2P2;

ΔT2P2 = δT2P2 T2P2

Probe 2 mit Carr-Purcell

PCP2=({{1, 320, \[Placeholder], \[Placeholder]}, {2, 276, \[Placeholder], \[Placeholder]}, {3, 248, \[Placeholder], \[Placeholder]}, {4, 220, \[Placeholder], \[Placeholder]}, {5, 196, \[Placeholder], \[Placeholder]}, {6, 168, \[Placeholder], \[Placeholder]}, {7, 156, \[Placeholder], \[Placeholder]}, {8, 132, \[Placeholder], \[Placeholder]}, {9, 120, \[Placeholder], \[Placeholder]}, {10, 104, \[Placeholder], \[Placeholder]}, {11, 92, \[Placeholder], \[Placeholder]}, {12, 80, \[Placeholder], \[Placeholder]}, {13, 68, \[Placeholder], \[Placeholder]}, {14, 56, \[Placeholder], \[Placeholder]}, {15, 52, \[Placeholder], \[Placeholder]}});

PCP2Err = 
        Replace[PCP2, {de_, df_, dg_, 
              dh_} -> {{de 10^-3, df 10^-3}, 
              ErrorBar[0.1 10^-3, df 0.03 10^-3]}, 
          2];

PCP2ln = 
        Replace[PCP2, {de_, df_, dg_, dh_} -> {de 10^-3, 
              Log[df/370]}, 2];

Regress[PCP2ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[PCP2Err], 
        Plot[370\ 10^\(-3\)\ Exp[\(-\ 129.6297625484729`\)\ x], {x, 0, 
            15\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2P2CP = 1/129.6297625484729`

δT2P2CP = 1.9379150324259444` T2P2CP;

ΔT2P2CP = δT2P2CP T2P2CP

Probe 3 mit Spin-Echo

SEP3=({{0.69, 440, \[Placeholder], \[Placeholder]}, {1.46, 340, \[Placeholder], \[Placeholder]}, {1.80, 314, \[Placeholder], \[Placeholder]}, {1.22, 360, \[Placeholder], \[Placeholder]}, {1.03, 388, \[Placeholder], \[Placeholder]}, {0.84, 414, \[Placeholder], \[Placeholder]}, {8, 86, \[Placeholder], \[Placeholder]}, {10, 56, \[Placeholder], \[Placeholder]}, {12, 34, \[Placeholder], \[Placeholder]}, {14, 22, \[Placeholder], \[Placeholder]}, {16, 12, \[Placeholder], \[Placeholder]}, {18, 6, \[Placeholder], \[Placeholder]}, {20, 4, \[Placeholder], \[Placeholder]}});

SEP3Err = 
        Replace[SEP3, {de_, df_, dg_, 
              dh_} -> {{de 10^-3, df 10^-3}, 
              ErrorBar[0.1 10^-3, df 0.03 10^-3]}, 
          2];

SEP3ln = 
        Replace[SEP3, {de_, df_, dg_, dh_} -> {de 10^-3, 
              Log[df/512]}, 2];

Regress[SEP3ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[SEP3Err], 
        Plot[512\ 10^\(-3\)\ Exp[\ \(-\ 236.24611322778568`\)\ x], {x, 0, 
            20\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2P3 = 1/236.24611322778568`

δT2P3 = 4.486569481386122` T2P3;

ΔT2P3 = δT2P3 T2P3

Probe 3 mit Carr-Purcell

PCP3=({{2, 306, \[Placeholder], \[Placeholder]}, {4, 204, \[Placeholder], \[Placeholder]}, {6, 122, \[Placeholder], \[Placeholder]}, {8, 76, \[Placeholder], \[Placeholder]}, {10, 36, \[Placeholder], \[Placeholder]}, {12, 18, \[Placeholder], \[Placeholder]}, {14, 4, \[Placeholder], \[Placeholder]}, {16, 2, \[Placeholder], \[Placeholder]}});

PCP3Err = 
        Replace[PCP3, {de_, df_, dg_, 
              dh_} -> {{de 10^-3, df 10^-3}, 
              ErrorBar[0.1 10^-3, df 0.03 10^-3]}, 
          2];

PCP3ln = 
        Replace[PCP3, {de_, df_, dg_, dh_} -> {de 10^-3, 
              Log[df/512]}, 2];

Regress[PCP3ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[PCP3Err], 
        Plot[512\ 10^\(-3\)\ Exp[\(-\ 365.24021354589394`\)\ x], {x, 0, 
            16\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T2P3CP = 1/365.2402135458939`

δT2P3CP = 29.67134949139955` T2P3CP;

ΔT2P3CP = δT2P3CP T2P3CP

Bestimmung von T1

Probe 1

piP1=({{1.39, -222, \[Placeholder], \[Placeholder]}, {2.42, -190, \[Placeholder], \[Placeholder]}, {3.4, -156, \[Placeholder], \[Placeholder]}, {4.42, -148, \[Placeholder], \[Placeholder]}, {5.46, -140, \[Placeholder], \[Placeholder]}, {6.5, -116, \[Placeholder], \[Placeholder]}, {7.5, -100, \[Placeholder], \[Placeholder]}, {8.52, -90, \[Placeholder], \[Placeholder]}, {9.52, -74, \[Placeholder], \[Placeholder]}, {10.6, -54, \[Placeholder], \[Placeholder]}, {20.45, 62, \[Placeholder], \[Placeholder]}, {30.6, 132, \[Placeholder], \[Placeholder]}, {40.6, 184, \[Placeholder], \[Placeholder]}, {51, 210, \[Placeholder], \[Placeholder]}, {61, 240, \[Placeholder], \[Placeholder]}});

piP1Err = 
        Replace[piP1, {de_, df_, dg_, 
              dh_} -> {{(de - 0.3) 10^-3, df 10^-3}, 
              ErrorBar[Abs[0.1 10^-3], Abs[df 0.03 10^-3]]}, 
          2];

piP1ln = 
        Replace[piP1, {de_, df_, dg_, 
              dh_} -> {(de - 0.3) 10^-3, 
              Log[(260 - df)/(2 260)]}, 2];

Regress[piP1ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[piP1Err], 
        Plot[260\ 10^\(-3\) \((1 - 
                2\ Exp[\(-\ 49.457530248150306`\)\ x])\), {x, 0, 
            61\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T1P1 = 1/49.457530248150306`

δT1P1 = 1.3237334711426225` T1P1;

ΔT1P1 = δT1P1 T1P1

Probe 2

piP2=({{1.44, -166, \[Placeholder], \[Placeholder]}, {2.48, -124, \[Placeholder], \[Placeholder]}, {3.48, -84, \[Placeholder], \[Placeholder]}, {4.48, -60, \[Placeholder], \[Placeholder]}, {5.62, -40, \[Placeholder], \[Placeholder]}, {6.62, -14, \[Placeholder], \[Placeholder]}, {7.26, 16, \[Placeholder], \[Placeholder]}, {8.28, 30, \[Placeholder], \[Placeholder]}, {9.3, 50, \[Placeholder], \[Placeholder]}, {10.4, 64, \[Placeholder], \[Placeholder]}, {20.45, 162, \[Placeholder], \[Placeholder]}, {30.6, 202, \[Placeholder], \[Placeholder]}, {40.6, 222, \[Placeholder], \[Placeholder]}, {51, 240, \[Placeholder], \[Placeholder]}});

piP2Err = 
        Replace[piP2, {de_, df_, dg_, 
              dh_} -> {{(de - 0.3) 10^-3, df 10^-3}, 
              ErrorBar[Abs[0.1 10^-3], Abs[df 0.03 10^-3]]}, 
          2];

piP2ln = 
        Replace[piP2, {de_, df_, dg_, 
              dh_} -> {(de - 0.3) 10^-3, 
              Log[(241.4 - df)/(2 241.4)]}, 2];

Regress[piP2ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[piP2Err], 
        Plot[241.4\ 10^\(-3\) \((1 - 
                2\ Exp[\ \(-97.92634907884579`\)\ x])\), {x, 0, 
            51\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T1P2 = 1/97.92634907884579`

δT1P2 = 6.491113612060064` T1P2;

ΔT1P2 = δT1P2 T1P2

Probe 3

piP3=({{1.4, -170, \[Placeholder], \[Placeholder]}, {2.46, -92, \[Placeholder], \[Placeholder]}, {3.58, -36, \[Placeholder], \[Placeholder]}, {4.26, 22, \[Placeholder], \[Placeholder]}, {5.3, 64, \[Placeholder], \[Placeholder]}, {6.32, 98, \[Placeholder], \[Placeholder]}, {7.34, 122, \[Placeholder], \[Placeholder]}, {8.36, 154, \[Placeholder], \[Placeholder]}, {9.38, 162, \[Placeholder], \[Placeholder]}, {10.45, 178, \[Placeholder], \[Placeholder]}, {20.5, 250, \[Placeholder], \[Placeholder]}, {30.7, 260, \[Placeholder], \[Placeholder]}});

piP3Err = 
        Replace[piP3, {de_, df_, dg_, 
              dh_} -> {{(de - 0.3) 10^-3, df 10^-3}, 
              ErrorBar[Abs[0.1 10^-3], Abs[df 0.03 10^-3]]}, 
          2];

piP3ln = 
        Replace[piP3, {de_, df_, dg_, 
              dh_} -> {(de - 0.3) 10^-3, 
              Log[(261.7 - df)/(2 261.7)]}, 2];

Regress[piP3ln, {1, x}, x]

\(\(DisplayTogether[MultipleListPlot[piP3Err], 
        Plot[261.7\ 10^\(-3\) \((1 - 
                2\ Exp[\(-\ 188.3783195813661`\)\ x])\), {x, 0, 
            51\ 10^\(-3\)}], 
        ImageSize -> 
          550, 
AxesLabel -> {"t", "U"}];\)\)

T1P3 = 1/188.3783195813661`

δT1P3 = 1.5574032203651789` T1P3;

ΔT1P3 = δT1P3 T1P3

gewichteter Mittelwert für T2 in Abhängigkeit von c

Probe 1

T2P1g = (T2P1/ΔT2P1^2 + 
            T2P1CP/ΔT2P1CP^2)/(1/ΔT2P1^2 + 
            1/ΔT2P1CP^2)

ΔT2P1g = 
      1/Sqrt[(1/ΔT2P1^2 + 
              1/ΔT2P1CP^2)]

Probe 2

T2P2g = (T2P2/ΔT2P2^2 + 
            T2P2CP/ΔT2P2CP^2)/(1/ΔT2P2^2 + 
            1/ΔT2P2CP^2)

ΔT2P2g = 
      1/Sqrt[(1/ΔT2P2^2 + 
              1/ΔT2P2CP^2)]

Probe 3

T2P3g = (T2P3/ΔT2P3^2 + 
            T2P3CP/ΔT2P3CP^2)/(1/ΔT2P3^2 + 
            1/ΔT2P3CP^2)

ΔT2P3g = 
      1/Sqrt[(1/ΔT2P3^2 + 
              1/ΔT2P3CP^2)]

Proportionalitätsfaktoren

T1 gegen 1/c

PropT1=({{0.05, 20.22, 0.55}, {0.1, 10.21, 0.68}, {0.2, 5.31, 0.05}});
PropT1c = 
        Replace[PropT1, {de_, df_, dg_} -> {1/de, df}, 2];

PropT1cErr = 
        Replace[PropT1, {de_, df_, dg_} -> {1/de, df, dg}, 
          2];

Regress[PropT1c, {1, x}, x]

b = 0.9949999999999999`; Δb = 0.00519615242270648`; 
    a = 0.305000000000001`; Δa = 
      0.06873863542433555`;

DisplayTogether[ErrorListPlot[PropT1cErr], 
        Plot[{b x  + a,  (b +  Δb) x + 
              a + Δa, (b - Δb) x + 
              a - Δa}, {x, 0, 20}, 
          PlotStyle -> {Dashing[{ .0}], Dashing[{0.01}], 
              Dashing[{ .01}]}], ImageSize -> 550, 
        AxesLabel -> {"1/c", "T1"}];

T2 gegen 1/c

PropT2=({{0.05, 18.37, 0.18}, {0.1, 8.38, 0.09}, {0.2, 4.06, 0.08}});
PropT2c = 
        Replace[PropT2, {de_, df_, dg_} -> {1/de, df}, 2];

PropT2cErr = 
        Replace[PropT2, {de_, df_, dg_} -> {1/de, df, dg}, 
          2];

Regress[PropT2c, {1, x}, x]

b = 0.9604285714285714`; Δb = 0.03340383700311399`; 
    a = -0.9350000000000015`; Δa = 
      0.44189122772788325`;

DisplayTogether[ErrorListPlot[PropT2cErr], 
        Plot[{b x  + a,  (b +  Δb) x + 
              a + Δa, (b - Δb) x + 
              a - Δa}, {x, 0, 20}, 
          PlotStyle -> {Dashing[{ .0}], Dashing[{0.01}], 
              Dashing[{ .01}]}], ImageSize -> 550, 
        AxesLabel -> {"1/c", "T2"}];