f_2a_dsys,
plot=True,
prange=(2, 16))[0:2]
pltext.set_layout(legend=True, xlim=(2, 16), ylim=(0, 5))
B_exp_2a = slope_2a / (2 * pi * A_i * N_i)
B_exp_2a_dsys = dslope_2a / (2 * pi * A_i * N_i)
mu_0 = 4 * pi * 1e-7
B_theo_2a = (8 / sqrt(125)) * mu_0 * I_2a * N_h / s_h
B_theo_2a_dsys = (8 / sqrt(125)) * mu_0 * I_2a_dsys * N_h / s_h
print('\nAufgabe 2a:\n')
print(val(B_exp_2a, B_exp_2a_dsys, 'B_exp '))
print(val(B_theo_2a, B_theo_2a_dsys, 'B_theo'))
print(dev(B_exp_2a, B_exp_2a_dsys, B_theo_2a, B_theo_2a_dsys, 'Abw'))
# Aufgabe 2b
f_2b = 9.46
f_2b_dsys = 0.10
I_2b = npfarray([0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5])
I_2b_dsys = sqrt(
npfarray([0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01])**2 +
0.005**2 + (0.012 * I_2b)**2)
Vss_2b = npfarray([0.724, 1.41, 2.04, 2.68, 3.32, 4.00, 4.65, 5.32, 6.12])
Vss_2b_dsys = npfarray([0.01, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05])
Uind_2b = Vss_2b / 2
Uind_2b_dsys = Vss_2b_dsys / 2
pltext.initplot(
V1_T = R1_G / R1_E
V2_T = R2_G / R2_E
V3_T = R3_G / R3_E
V4_T = R4_G / R4_E
print()
print(
ms.tbl([
ms.lst(npfarray([R1_E, R2_E]), name='R_E', unit='Ω'),
ms.lst(npfarray([R1_G, R2_G]), name='R_G', unit='Ω'),
ms.lst(npfarray([V1, V2]), npfarray([d_V1, d_V2]), name='V'),
ms.lst(npfarray([V1_T, V2_T]), name='V'),
ms.dev(npfarray([V1, V2]),
npfarray([d_V1, d_V2]),
npfarray([V1_T, V2_T]),
name='V',
perc=True)
]))
print()
print(
ms.tbl([
ms.lst(npfarray([R3_E, R4_E]), name='R_E', unit='Ω'),
ms.lst(npfarray([R3_G, R4_G]), name='R_G', unit='Ω'),
ms.lst(npfarray([V3, V4]), npfarray([d_V3, d_V4]), name='V'),
ms.lst(npfarray([V3_T, V4_T]), name='V'),
ms.dev(npfarray([V3, V4]),
npfarray([d_V3, d_V4]),
npfarray([V3_T, V4_T]),
name='V',
perc=True)
V_ew_274k_mv = mv(V_ew_274k)
V_ew_274k_mv_dtot = dtot_mv(V_ew_274k,V_ew_274k_dsys)
V_ew_680k = Uaw_680k / U1w
V_ew_680k_dsys = 1/U1w * sqrt(Uaw_680k_dsys**2 + (Uaw_680k * U1w_dsys / U1w)**2)
V_ew_680k_mv = mv(V_ew_680k)
V_ew_680k_mv_dtot = dtot_mv(V_ew_680k,V_ew_680k_dsys)
R_E = 3e3
R_G = npfarray([48.7e3,274e3,680e3])
V_t = R_G / R_E
print('\nAufgabe 1:\n')
print(tbl([['Widerstand','48k7 (g)','274k (g)','274k (w)','680k (w)'],lst([V_t[0],V_t[1],V_t[1],V_t[2]],name='V_t'),lst([V_eg_48k7_mv,V_eg_274k_mv,V_ew_274k_mv,V_ew_680k_mv],[V_eg_48k7_mv_dtot,V_eg_274k_mv_dtot,V_ew_274k_mv_dtot,V_ew_680k_mv_dtot],'V_e'),['Abw',sig('',V_eg_48k7_mv,V_eg_48k7_mv_dtot,V_t[0],perc=True),sig('',V_eg_274k_mv,V_eg_274k_mv_dtot,V_t[1],perc=True),sig('',V_ew_274k_mv,V_ew_274k_mv_dtot,V_t[1],perc=True),sig('',V_ew_680k_mv,V_ew_680k_mv_dtot,V_t[2],perc=True)]]))
print('\nEinzelwerte für 48k7 (g):\n')
print(tbl([lst(V_eg_48k7,V_eg_48k7_dsys,'Verstärkung'),dev(V_eg_48k7,V_eg_48k7_dsys,V_t[0],name='Abw',perc=True)]))
print('\nEinzelwerte für 274k (g):\n')
print(tbl([lst(V_eg_274k,V_eg_274k_dsys,'Verstärkung'),dev(V_eg_274k,V_eg_274k_dsys,V_t[1],name='Abw',perc=True)]))
print('\nEinzelwerte für 274k (w):\n')
print(tbl([lst(V_ew_274k,V_ew_274k_dsys,'Verstärkung'),dev(V_ew_274k,V_ew_274k_dsys,V_t[1],name='Abw',perc=True)]))
print('\nEinzelwerte für 680k (w):\n')
print(tbl([lst(V_ew_680k,V_ew_680k_dsys,'Verstärkung'),dev(V_ew_680k,V_ew_680k_dsys,V_t[2],name='Abw',perc=True)]))
# Plots
f_uncert = 50e-6
f_1 = npfarray([0.3,0.6,0.9,3,6,9,30,60,90,150,200,300])*1e3
f_1_dsys = f_1 * f_uncert
U_A1 = npfarray([6.76,6.70,6.68,5.46,3.82,2.78,0.900,0.456,0.306,0.187,0.140,0.095])
U_A1_dsys = npfarray([0.01,0.03,0.05,0.03,0.03,0.05,0.005,0.005,0.003,0.003,0.001,0.001])
U_A2 = npfarray([2.65,2.64,2.67,2.56,2.30,2.00,0.852,0.450,0.304,0.186,0.139,0.094])
l = 2 * d * sin(a1)
l_err = 2 * d * cos(a1) * a1_err
h = l * e * U / c
h_err = l_err * e * U / c
a2 = arcsin(l / d)
a2_err = 1 / (d * sqrt(1 - (l / d)**2)) * l_err
print('\nAufgabe 1a:\n')
print(val(a1_uncorr * rad_to_deg, a1_uncorr_err * rad_to_deg, 'a1 (uncorr)'))
print(val(Ug, Ug_err, 'Ug'))
print(val(a1 * rad_to_deg, a1_err * rad_to_deg, 'a1'))
print(val(l, l_err, 'l'))
print(val(h, h_err, 'h'))
print(dev(h, h_err, h_lit, name='Abw', perc=True))
print(val(a2 * rad_to_deg, a2_err * rad_to_deg, 'a2'))
# Aufgabe 1b
alpha_1o, rate_1o = loadtxt('data/255_1b_1o.txt', unpack=True)
rate_1o_err = sqrt(rate_1o)
alpha_2o, rate_2o = loadtxt('data/255_1b_2o.txt', unpack=True)
rate_2o_err = sqrt(rate_2o)
def gauss(x, A, mu, sig, Ug):
return A / (sqrt(2 * pi) * sig) * exp(-(x - mu)**2 / (2 * sig**2)) + Ug
l_kb_lit = 63.1e-12
l_ka_lit = 71.1e-12
k1_CoA = A1_CoA / A_CoA
k2_CoA = A2_CoA / A1_CoA
print(
ms.tbl([
ms.lst(A_CoA, d_A_CoA, name='A', unit='Bq'),
ms.lst(A1_CoA, d_A1_CoA, name='A1', unit='Bq'),
ms.lst(A2_CoA, d_A2_CoA, name='A2', unit='Bq')
]))
print(ms.tbl([ms.lst(k1_CoA, name='k1'), ms.lst(k2_CoA, name='k2')]))
print(ms.val("T", T_CoA / cs.year, unit='yr'))
print(ms.val("A", A_l_CoA, unit='Bq'))
print(
ms.tbl([
ms.dev(A_CoA, d_A_CoA, [A_l_CoA] * 3, name='A'),
ms.dev(A1_CoA, d_A1_CoA, [A_l_CoA] * 3, name='A'),
ms.dev(A2_CoA, d_A2_CoA, [A_l_CoA] * 3, name='A')
]))
# Measurement of Am-Radiation absorption and energy, Am 241, AP 15.2
s_c = 4.2 * cs.centi
sigma_c = 2.25 * cs.milli / cs.centi**2
A_Am = 90 * cs.kilo
a_Am = 3.95 * cs.centi
d_a_Am = 0.05 * cs.centi
t_Am = cs.minute
p1_Am = npf([
18, 98, 120, 225, 324, 383, 416, 450, 475, 515, 617, 721, 813, 911, 1013
]) * cs.milli * cs.bar
p2_Am = npf([
d_T1_12 = npfarray([0.03, 0.01, 0.01]) * cs.milli
f1 = npfarray([110, 600, 600])
U1_pp = npfarray([0.95, 0.95, 0.95])
d_U1_pp = npfarray([0.02, 0.02, 0.02])
tau1_O = T1_12 / ln(2)
d_tau1_O = d_T1_12 / ln(2)
tau1_T = R1 * C1
d_tau1_T = tau1_T * sqrt((d_R1 / R1)**2 + (d_C1 / C1)**2)
print()
print('1. Determination of the response time of a RC-element:')
print(ms.tbl([ms.lst(C1, d_C1, name='C', unit='F'),
ms.lst(R1, d_R1, name='R', unit='Ω'),
ms.lst(tau1_O, d_tau1_O, name='τ', unit='s'),
ms.lst(tau1_T, d_tau1_T, name='τ', unit='s'), ms.dev(tau1_O, d_tau1_O, tau1_T, d_tau1_T, name='τ')]))
# (3) Frequency and phase of a RC-element
R3 = cs.kilo
d_R3 = 0.05 * R3
C3 = 47 * cs.nano
d_C3 = 0.10 * C3
f3_G_low = 3.0 * cs.kilo
d_f3_G_low = 0.3 * cs.kilo
f3_G_high = 3.1 * cs.kilo
d_f3_G_high = 0.3 * cs.kilo
f3 = np.arange(1, 11, 1) * cs.kilo
delta_t3 = npfarray([0.20, 0.08, 0.042, 0.027, 0.019, 0.013, 0.010, 0.007, 0.007, 0.005]) * cs.milli
d_delta_t3 = npfarray([0.03, 0.02, 0.015, 0.015, 0.010, 0.010, 0.005, 0.005, 0.005, 0.004]) * cs.milli
phi3 = 2 * pi * f3 * delta_t3
val(chi2_red_pf),
val(prob_pf)],
['mf', val(chi2_mf),
val(chi2_red_mf), val(prob_mf)]]))
print()
print(
tbl([['Isotop', 'Ag 108', 'Ag 110'],
[
'Thalb (fit)',
val(Thalb_Ag108, Thalb_Ag108_dsys),
val(Thalb_Ag110, Thalb_Ag110_dsys)
], ['Thalb (theo)',
val(Thalb_Ag108_lit),
val(Thalb_Ag110_lit)],
dev([Thalb_Ag108, Thalb_Ag110], [Thalb_Ag108_dsys, Thalb_Ag110_dsys],
[Thalb_Ag108_lit, Thalb_Ag110_lit],
name='Abw',
perc=True)]))
# Indium
n5 = loadtxt('data/252_n5.dat', usecols=[1])
n5_dsto = sqrt(n5)
t = arange(60, 3060, 120)
unterg_in_mv = mv(12 * unterg)
unterg_in_mv_dsto = dsto_mv(12 * unterg, ddof=0)
N_in = n5 - unterg_in_mv
N_in_err = sqrt(n5_dsto**2 + unterg_in_mv_dsto**2)
pltext.initplot(num=2,
val(rel_anstieg_1min,
rel_anstieg_1min_dsto,
name='rel Anstieg (1min)',
percerr=True))
print(
val(anstieg_3min,
anstieg_3min_dsto,
name='abs Anstieg (3min)',
percerr=True))
print(
val(rel_anstieg_3min,
rel_anstieg_3min_dsto,
name='rel Anstieg (3min)',
percerr=True))
print(
dev(anstieg_1min, anstieg_1min_dsto, anstieg_3min, anstieg_3min_dsto,
'Abw abs Anstiege'))
print(
dev(rel_anstieg_1min, rel_anstieg_1min_dsto, rel_anstieg_3min,
rel_anstieg_3min_dsto, 'Abw rel Anstiege'))
print(val(k0, k0_err, name='Zählrate U0+0V', percerr=True))
print(val(k100, k100_err, name='Zählrate U0+100V', percerr=True))
print(val(k_delta, k_delta_err, name='Zählrate U+100V', percerr=True))
print(val(t_1perc, name='t (1%)'))
# Aufgabe 4
anzahl, ereig = loadtxt('data/251_A4.dat', unpack=True)
fehler = sqrt(ereig)
def gauss(x, A, mu, sig):
return A / (sqrt(2 * pi) * sig) * exp(-(x - mu)**2 / (2 * sig**2))
s4 *= cs.milli**2 / cs.kilo
d_s4 *= cs.milli**2 / cs.kilo
b4 *= cs.milli**2 / cs.kilo
d_b4 *= cs.milli**2 / cs.kilo
# Determination of boltzmann's constant
k1 = s2 / (4 * T1 * B3)
d_k1_stat = k1 * sqrt((d_s2 / s2)**2 + (d_T1 / T1)**2)
d_k1_sys = k1 * d_B3 / B3
d_k1 = sqrt(d_k1_stat**2 + d_k1_sys**2)
k2 = s4 / (4 * B3)
d_k2_stat = k2 * d_s4 / s4
d_k2_sys = k2 * d_B3 / B3
d_k2 = sqrt(d_k2_stat**2 + d_k2_sys**2)
k_lit = cs.physical_constants["Boltzmann constant"]
d_k_lit = k_lit[2]
k_lit = k_lit[0]
print(ms.val('k', k1, d_k1_stat, d_k1_sys, unit='J/K', prefix=False))
print(ms.val('k', k2, d_k2_stat, d_k2_sys, unit='J/K', prefix=False))
print(ms.val('k', k_lit, d_k_lit, unit='J/K', prefix=False))
print(ms.dev(k1, d_k1, k_lit, d_k_lit, name='k'))
print(ms.dev(k2, d_k2, k_lit, d_k_lit, name='k'))
print()
# Show plots
ms.pltext.savefigs('figures/243')
ms.plt.show()
from scipy.stats import chi2
chisqr = np.sum((linear(R, *popt) - D)**2 / D_err**2)
dof = 5
chisqr_red = chisqr / dof
prob = 100 * (1 - chi2.cdf(chisqr, dof))
pltext.initplot(
num=3,
title='Abbildung : Rauschspannung als Funktion des Widerstandes',
xlabel='Widerstand in Ohm',
ylabel=r'$(U^{2}_{aus}-U^{2}_V)$ / $V^2$')
pltext.plotdata(R, D, D_err, R_dsys, label='Messwerte')
x_array = nplinspace(0, 3.2e4)
plt.plot(x_array, linear(x_array, *popt), label='Fitgerade durch Ursprung')
pltext.set_layout(legend=True, xlim=(0, 3.5e4), ylim=(0, 3e-5))
print(val(T, T_dsys, 'Temp'))
print(val(c, c_dsto, 'Steigung c'))
print(val(k, k_dtot, name='k'))
print(val(k_dc, name='k_dc'))
print(val(k_dB, name='k_dB'))
print(val(k_dT, name='k_dT'))
print(dev(k, k_dtot, kB, name='Abw', perc=True))
print(val(chisqr, name='chi2'))
print(val(chisqr_red, name='chi2_red'))
print(val(prob, name='prob') + '%')
plt.show()