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Pm-147 beta shielding — range and bremsstrahlung

Promethium-147

Pm-147 · Promethium, Z = 61, A = 147

Promethium-147 decays by beta-minus decay, half-life 2.6234 years. Specific activity is 3.43e+13 Bq/g (928 Ci/g), so a gigabecquerel comes to 29.1 µg — weighable, but on an analytical balance. Over a year the activity falls to 76.78%, and over forty years to 2.6e-3%.

The air kerma rate constant is small — 5.19e-7 mGy·m²/(GBq·h), 7.7e+4× less than Cs-137 and 3.1e+5× less than Co-60, ranking 96 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 5.19e-7 mGy/h, and 1 Ci at the same distance 0.0000192 mGy/h. It takes 38.6 TBq at a metre to reach 20 µSv/h from the photons alone.

2 lines clear the 20 keV cutoff, but 2 of them carry 90% of the dose rate. The leading one is 121.2 keV at 73.5% of the total — its emission probability is 0.00285%, which is also the highest.

Shielding barely arises: 0.119 mm of lead halves the air kerma rate and 0.513 mm takes it to a tenth, thicknesses a source capsule is likely to exceed on its own. Steel does the halving in 1.80 mm. At 1 GBq and a metre it is already under 20 µSv/h with nothing in the way. The tenth-value layer runs 4.3 times the half-value layer, not the 3.32 a single energy would give.

The beta endpoint is 0.225 MeV, mean 0.0618 MeV over 2 branches. That endpoint stops in 0.426 mm of acrylic or 0.201 mm of glass. Of the beta energy, 0.05% turns into X-rays in acrylic and 0.64% in lead.

Half-life, specific activity, dose rate and beta energies

Half-life2.6234 years (8.279e+7 s)
Decay modebeta-minus decay
Specific activity3.43e+13 Bq/g (928 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)5.19e-7 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m5.19e-7 mGy/h
Dose rate, 1 Ci at 1 m0.0000192 mGy/h
Kerma-weighted mean photon energy99.73 keV
Beta endpoint / mean0.225 MeV / 0.0618 MeV

121 keV leads, and 2 lines make 90%

No recorded line for Pm-147 falls below the 20 keV cutoff, so this table is the whole photon spectrum. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
121.220.0028573.50
40.120.001126.50

0.119 mm of lead halves this spectrum

Solved numerically across all 2 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead0.1190.5134.29
tungsten0.09010.3804.22
iron1.809.235.13
copper1.336.865.15
concrete13.754.84.00
water37.41293.46
aluminum11.648.04.15

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

0.426 mm of acrylic stops the 0.225 MeV endpoint

Katz–Penfold fit to the 0.225 MeV endpoint — ±10%, and a stopping thickness rather than an attenuation length. Why the material matters more than the thickness.

AbsorberRange for the endpoint (mm)
acrylic0.426
aluminum0.186
water0.503
glass0.201
Shield materialFraction of beta energy converted to X-rays
acrylic (Z ≈ 6)0.05%
lead (Z = 82)0.64%

Activity over decades and centuries

Ten half-lives is 26.2 years, which puts decay storage out of reach: 2.6e-3% survives forty years. The mean life 1/λ, the quantity that enters an integrated dose, is 3.78 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 activity8.71 years
Time to fall to 1 %17.4 years
Time to fall to 0.1 %26.1 years

Limits of these dose rates

Gamma, beta and decay calculators for Pm-147

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