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-life | 2.6234 years (8.279e+7 s) |
| Decay mode | beta-minus decay |
| Specific activity | 3.43e+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 m | 5.19e-7 mGy/h |
| Dose rate, 1 Ci at 1 m | 0.0000192 mGy/h |
| Kerma-weighted mean photon energy | 99.73 keV |
| Beta endpoint / mean | 0.225 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 (%) |
|---|---|---|
| 121.22 | 0.00285 | 73.50 |
| 40.12 | 0.0011 | 26.50 |
0.119 mm of lead halves this spectrum
Solved numerically across all 2 lines, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 0.119 | 0.513 | 4.29 |
| tungsten | 0.0901 | 0.380 | 4.22 |
| iron | 1.80 | 9.23 | 5.13 |
| copper | 1.33 | 6.86 | 5.15 |
| concrete | 13.7 | 54.8 | 4.00 |
| water | 37.4 | 129 | 3.46 |
| aluminum | 11.6 | 48.0 | 4.15 |
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.
| Absorber | Range for the endpoint (mm) |
|---|---|
| acrylic | 0.426 |
| aluminum | 0.186 |
| water | 0.503 |
| glass | 0.201 |
| Shield material | Fraction 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.
| Elapsed | Fraction remaining |
|---|---|
| 1 half-life | 50.0 % |
| 2 half-lives | 25.0 % |
| 5 half-lives | 3.13 % |
| 10 half-lives | 0.0977 % |
| Time to fall to 10 % of today's activity | 8.71 years |
| Time to fall to 1 % | 17.4 years |
| Time to fall to 0.1 % | 26.1 years |
Limits of these dose rates
- 5.19e-7 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 0.119 mm of lead halves this spectrum, narrow beam, scatter not added back.
- 0.426 mm of acrylic for the 0.225 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Gamma, beta and decay calculators for Pm-147
- Gamma dose rate and shielding
- Beta dose rate and shielding
- Decay and half-life
- Mass and activity
- Detection limits (MDA / MDC)
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.