tritium

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Tritium bremsstrahlung is easy to detect with a sensitive Geiger counter.

I used a GM45 which has a pancake detector with a beryllium window.

I measured 400 CPM from a tritium source used in a luminescent marker.

The tritium source was behind 1 mm of glass, 4 mm of acrylic, and 20 mm of air.

Tritium beta decay energy: 0.018590 MeV (kVp=18.6 keV, kVaverage=5.7 keV)

kVp = 1.8590E-02 MeV

kVavearge = 5.7E-03 MeV

linear attenuation coefficient

ρ
density in g*cm-3
μ
linear attenuation coefficient (μ is used in context of x-rays/gamma energy)
α
linear attenuation coefficient (α is used in the context of non-ionizing light)
x
thickness of absorber
Intensity
Ix = Io * exp(-μ * x)
μ/ρ
mass attenuation coefficient, μ/ρ = x-1*ln(Io*Ix)
linear attenuation coefficient
μ = (μ/ρ) * ρ, "Note: Shows μ in terms of mass attenuation coefficient and density."

Note that μ/ρ is usually found empirically for a given element, Z, and a given photon energy. Look these values up in a table rather than attempt to calculate them. The difficulty in calculating μ/ρ directly is due to the fact that the photon interaction cross section of a given atom is a function of the photon energy, which is composed of many subfunctions that are also a function of photon energy. Calculating all the components of σ requires a separate calculation that differs according to the mathematical model used for the given photon energy range. For example,

σ<sub>total</sub> = σ<sub>pe</sub> + σ<sub>coh</sub> + σ<sub>incoh</sub> + σ<sub>pair</sub> + σ<sub>trip</sub> + σ<sub>ph.n.</sub>

Where σpe is the atomic photoeffect cross section, σcoh and σincoh are the coherent (Rayleigh) and the incoherent (Compton) scattering cross sections, respectively, σpair and σtrip are the cross sections for electron-positron production in the fields of the nucleus and of the atomic electrons, respectively, and σph.n. is the photonuclear cross section.

Aluminum

Data for Z=13 Al Aluminum

Density
ρ = 2.6941 g*cm-3
  Energy       μ/ρ        μen
(MeV) (cm2/g) (cm2/g)
   1.00000E-03  1.185E+03  1.183E+03 
   1.50000E-03  4.022E+02  4.001E+02 
   1.55960E-03  3.621E+02  3.600E+02 
K  1.55960E-03  3.957E+03  3.829E+03 
   2.00000E-03  2.263E+03  2.204E+03 
   3.00000E-03  7.880E+02  7.732E+02 
   4.00000E-03  3.605E+02  3.545E+02 
   5.00000E-03  1.934E+02  1.902E+02 
   6.00000E-03  1.153E+02  1.133E+02 
   8.00000E-03  5.033E+01  4.918E+01 
   1.00000E-02  2.623E+01  2.543E+01 
   1.50000E-02  7.955E+00  7.487E+00 
   2.00000E-02  3.441E+00  3.094E+00 
   3.00000E-02  1.128E+00  8.778E-01 
   4.00000E-02  5.685E-01  3.601E-01 
   5.00000E-02  3.681E-01  1.840E-01 
   6.00000E-02  2.778E-01  1.099E-01 
   8.00000E-02  2.018E-01  5.511E-02 
   1.00000E-01  1.704E-01  3.794E-02 
   1.50000E-01  1.378E-01  2.827E-02 
   2.00000E-01  1.223E-01  2.745E-02 
   3.00000E-01  1.042E-01  2.816E-02 
   4.00000E-01  9.276E-02  2.862E-02 
   5.00000E-01  8.445E-02  2.868E-02 
   6.00000E-01  7.802E-02  2.851E-02 
   8.00000E-01  6.841E-02  2.778E-02 
   1.00000E+00  6.146E-02  2.686E-02 
   1.25000E+00  5.496E-02  2.565E-02 
   1.50000E+00  5.006E-02  2.451E-02 
   2.00000E+00  4.324E-02  2.266E-02 
   3.00000E+00  3.541E-02  2.024E-02 
   4.00000E+00  3.106E-02  1.882E-02 
   5.00000E+00  2.836E-02  1.795E-02 
   6.00000E+00  2.655E-02  1.739E-02 
   8.00000E+00  2.437E-02  1.678E-02 
   1.00000E+01  2.318E-02  1.650E-02 
   1.50000E+01  2.195E-02  1.631E-02 
   2.00000E+01  2.168E-02  1.633E-02 

Data for Z=13, E=2 keV to 120 keV

Density
ρ = 2.6941 g*cm-3
                 [µ]
       E         Total
     (keV)       cm-1
 2.080733E+00  5.4838E+03
 2.224304E+00  4.5961E+03
 2.377781E+00  3.8582E+03
 2.541848E+00  3.2426E+03
 2.717235E+00  2.7248E+03
 2.904724E+00  2.2882E+03
 3.105150E+00  1.9146E+03
 3.319406E+00  1.5873E+03
 3.548445E+00  1.3154E+03
 3.793288E+00  1.0902E+03
 4.055024E+00  9.0368E+02
 4.334821E+00  7.4915E+02
 4.633924E+00  6.2112E+02
 4.953664E+00  5.1506E+02
 5.295467E+00  4.2715E+02
 5.660855E+00  3.5430E+02
 6.051453E+00  2.9393E+02
 6.469004E+00  2.4389E+02
 6.915365E+00  2.0189E+02
 7.392525E+00  1.6634E+02
 7.902609E+00  1.3709E+02
 8.447890E+00  1.1303E+02
 9.030794E+00  9.3043E+01
 9.653919E+00  7.6127E+01
 1.032004E+01  6.2317E+01
 1.103212E+01  5.1040E+01
 1.179334E+01  4.1831E+01
 1.260708E+01  3.4307E+01
 1.347697E+01  2.8164E+01
 1.440688E+01  2.3141E+01
 1.540095E+01  1.9036E+01
 1.646362E+01  1.5679E+01
 1.759961E+01  1.2934E+01
 1.881398E+01  1.0688E+01
 2.011215E+01  8.8504E+00
 2.149988E+01  7.3452E+00
 2.298338E+01  6.1126E+00
 2.456923E+01  5.1024E+00
 2.626450E+01  4.2742E+00
 2.807676E+01  3.5821E+00
 3.001405E+01  3.0131E+00
 3.208502E+01  2.5482E+00
 3.429889E+01  2.1654E+00
 3.666551E+01  1.8501E+00
 3.919543E+01  1.5927E+00
 4.189992E+01  1.3823E+00
 4.479101E+01  1.2101E+00
 4.788159E+01  1.0688E+00
 5.118542E+01  9.5261E-01
 5.471721E+01  8.5680E-01
 5.849270E+01  7.7760E-01
 6.252870E+01  7.1186E-01
 6.684318E+01  6.5706E-01
 7.145536E+01  6.1118E-01
 7.638578E+01  5.7252E-01
 8.165640E+01  5.3974E-01
 8.729069E+01  5.1174E-01
 9.331374E+01  4.8763E-01
 9.975239E+01  4.6665E-01
 1.066353E+02  4.4819E-01
 1.139931E+02  4.3181E-01
 1.218587E+02  4.1710E-01

Acrylic plastic -- Polymethyl Methacrylate

  • Molecular formula: (C5O2H8)n
  • Density: 1.18 g/cm<super>3</super>
Energy(MeV)  μ/ρ(cm2/g) μen/ρ(cm2/g)
1.00000E-03  2.794E+03  2.788E+03 
1.50000E-03  9.153E+02  9.131E+02 
2.00000E-03  4.037E+02  4.024E+02 
3.00000E-03  1.236E+02  1.228E+02 
4.00000E-03  5.247E+01  5.181E+01 
5.00000E-03  2.681E+01  2.627E+01 
6.00000E-03  1.545E+01  1.498E+01 
8.00000E-03  6.494E+00  6.114E+00 
1.00000E-02  3.357E+00  3.026E+00 
1.50000E-02  1.101E+00  8.324E-01 
2.00000E-02  5.714E-01  3.328E-01 
3.00000E-02  3.032E-01  9.645E-02 
4.00000E-02  2.350E-01  4.599E-02 
5.00000E-02  2.074E-01  3.067E-02 
6.00000E-02  1.924E-01  2.530E-02 
8.00000E-02  1.751E-01  2.302E-02 
1.00000E-01  1.641E-01  2.368E-02 
1.50000E-01  1.456E-01  2.657E-02 
2.00000E-01  1.328E-01  2.872E-02 
3.00000E-01  1.152E-01  3.099E-02 
4.00000E-01  1.031E-01  3.185E-02 
5.00000E-01  9.410E-02  3.206E-02 
6.00000E-01  8.701E-02  3.191E-02 
8.00000E-01  7.641E-02  3.116E-02 
1.00000E+00  6.870E-02  3.015E-02 
1.25000E+00  6.143E-02  2.882E-02 
1.50000E+00  5.591E-02  2.755E-02 
2.00000E+00  4.796E-02  2.533E-02 
3.00000E+00  3.844E-02  2.210E-02 
4.00000E+00  3.286E-02  1.995E-02 
5.00000E+00  2.919E-02  1.843E-02 
6.00000E+00  2.659E-02  1.731E-02 
8.00000E+00  2.317E-02  1.579E-02 
1.00000E+01  2.105E-02  1.482E-02 
1.50000E+01  1.820E-02  1.348E-02 
2.00000E+01  1.684E-02  1.282E-02

borosilicate glass

       Energy(MeV)  μ/ρ(cm2/g) μen/ρ(cm2/g)
       1.00000E-03  3.164E+03  3.155E+03 
       1.03542E-03  2.887E+03  2.879E+03 
       1.07210E-03  2.634E+03  2.627E+03 
       1.07210E-03  2.800E+03  2.790E+03 # 11K
       1.50000E-03  1.152E+03  1.148E+03 
       1.55960E-03  1.037E+03  1.033E+03 
       1.55960E-03  1.079E+03  1.073E+03 # 13K
       1.69350E-03  8.629E+02  8.583E+02 
       1.83890E-03  6.883E+02  6.845E+02 
       1.83890E-03  1.776E+03  1.723E+03 # 14K
       2.00000E-03  1.500E+03  1.457E+03 
       3.00000E-03  5.123E+02  5.011E+02 
       3.60740E-03  3.098E+02  3.036E+02 
       3.60740E-03  3.133E+02  3.067E+02 # 19K
       4.00000E-03  2.355E+02  2.307E+02 
       5.00000E-03  1.260E+02  1.235E+02 
       6.00000E-03  7.500E+01  7.337E+01 
       8.00000E-03  3.269E+01  3.178E+01 
       1.00000E-02  1.705E+01  1.642E+01 
       1.50000E-02  5.217E+00  4.828E+00 
       2.00000E-02  2.297E+00  1.995E+00 
       3.00000E-02  7.987E-01  5.684E-01 
       4.00000E-02  4.341E-01  2.361E-01 
       5.00000E-02  3.022E-01  1.235E-01 
       6.00000E-02  2.417E-01  7.648E-02 
       8.00000E-02  1.890E-01  4.230E-02 
       1.00000E-01  1.657E-01  3.209E-02 
       1.50000E-01  1.389E-01  2.727E-02 
       2.00000E-01  1.246E-01  2.757E-02 
       3.00000E-01  1.069E-01  2.885E-02 
       4.00000E-01  9.540E-02  2.946E-02 
       5.00000E-01  8.696E-02  2.957E-02 
       6.00000E-01  8.035E-02  2.941E-02 
       8.00000E-01  7.052E-02  2.868E-02 
       1.00000E+00  6.337E-02  2.774E-02 
       1.25000E+00  5.667E-02  2.650E-02 
       1.50000E+00  5.160E-02  2.533E-02 
       2.00000E+00  4.447E-02  2.337E-02 
       3.00000E+00  3.611E-02  2.069E-02 
       4.00000E+00  3.140E-02  1.904E-02 
       5.00000E+00  2.838E-02  1.795E-02 
       6.00000E+00  2.632E-02  1.721E-02 
       8.00000E+00  2.373E-02  1.629E-02 
       1.00000E+01  2.223E-02  1.579E-02 
       1.50000E+01  2.045E-02  1.522E-02 
       2.00000E+01  1.982E-02  1.503E-02