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Th-228 shielding — lead half-value layer and dose rate

Thorium-228

Th-228 · Thorium, Z = 90, A = 228

Thorium-228 decays by alpha decay, half-life 1.9116 years. Specific activity is 3.03e+13 Bq/g (820 Ci/g), so a gigabecquerel comes to 33.0 µg — weighable, but on an analytical balance. Over a year the activity falls to 69.59%, and over forty years to 5.0e-5%.

The air kerma rate constant is small — 0.000227 mGy·m²/(GBq·h), 3.4e+2× less than Cs-137 and 1.3e+3× less than Co-60, ranking 84 of 96 by Γ — near the bottom of the photon emitters, but above the cutoff, which 51 nuclides in this dataset are not. 1 GBq at 1 m reads 0.000227 mGy/h, and 1 Ci at the same distance 0.00840 mGy/h. It takes 88.1 GBq at a metre to reach 20 µSv/h from the photons alone.

10 lines clear the 20 keV cutoff, but 4 of them carry 90% of the dose rate. The leading one is 84.4 keV at 48.4% of the total — its emission probability is 1.188%, which is also the highest.

A half-value layer of 0.363 mm in lead puts this in foil and thin sheet, with 2.81 mm needed if the material is steel; ten-fold attenuation comes at 1.45 mm of lead. At 1 GBq and a metre it is already under 20 µSv/h with nothing in the way. The tenth-value layer runs 4.0 times the half-value layer, not the 3.32 a single energy would give.

Alpha emission is led by 5.423 MeV at 73.4%, one of 5 recorded lines. None of it reaches through skin, so the alpha is an intake hazard rather than an external one — the photon figures above are the separate question.

Half-life, specific activity and dose rate

Half-life1.9116 years (6.032e+7 s)
Decay modealpha decay
Specific activity3.03e+13 Bq/g (820 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.000227 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.000227 mGy/h
Dose rate, 1 Ci at 1 m0.00840 mGy/h
Kerma-weighted mean photon energy136.7 keV

10 lines above the cutoff, and what each contributes

1 further line below the 20 keV cutoff, the highest at 14.92 keV and 8.42% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
84.371.18848.40
215.980.2468729.21
166.410.100868.68
131.610.127128.26
205.930.019132.14
88.470.029561.25
85.430.018090.74
101.370.013770.66
100.120.010370.49
102.950.00340.17

0.363 mm of lead halves this spectrum

Solved numerically across all 10 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead0.3631.454.00
tungsten0.1170.9698.31
iron2.8113.04.62
copper2.0610.55.09
concrete18.664.03.43
water43.41463.37
aluminum16.256.23.46

A single energy would give 3.32. What a spread of energies does instead.

5 alpha lines, strongest 5.423 MeV

5 recorded lines from 5.138 to 5.423 MeV, the strongest 5.423 MeV at 73.4% of 100.1% total alpha emission.

Energy (MeV)Emission probability (%)
5.423173.4
5.340426
5.21100.408
5.17300.218
5.13800.036

Activity over decades and centuries

Ten half-lives is 19.1 years, which puts decay storage out of reach: 5.0e-5% survives forty years. The mean life 1/λ, the quantity that enters an integrated dose, is 2.76 years.

ElapsedFraction remaining
1 half-life50.0 %
2 half-lives25.0 %
5 half-lives3.13 %
10 half-lives0.0977 %
Time to fall to 10 % of today's activity6.35 years
Time to fall to 1 %12.7 years
Time to fall to 0.1 %19.1 years

Limits — intake, not external dose

Gamma and decay calculators for Th-228

Other Thorium nuclides: Th-229, Th-230, Th-232

Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.