Lutetium-177m
Lu-177m · Lutetium, Z = 71, A = 177 · isomeric state m
At 1.70e+14 Bq/g — 4.60e+3 Ci/g — a gigabecquerel of Lu-177m amounts to 5.87 µg, which is why activity rather than mass is how anyone states the quantity. Lutetium-177m decays by beta-minus decay with a half-life of 160.4 days, falling to 87.84% of today's activity in a month and 20.63% in a year.
1 GBq at 1 m reads 0.131 mGy/h, and 1 Ci at the same distance 4.86 mGy/h, from an air kerma rate constant of 0.131 mGy·m²/(GBq·h) — 1.7× Cs-137 and 2.3× less than Co-60, and 15 of 96 among the photon emitters carried here.
57 lines clear the 20 keV cutoff, but 26 of them carry 90% of the dose rate. The leading one is 378.5 keV at 11.4% of the total — its emission probability is 29.4%, which is lower than the 55.4% of the 208.4 keV line it outranks.
A half-value layer of 0.926 mm in lead puts this in foil and thin sheet, with 5.94 mm needed if the material is steel; ten-fold attenuation comes at 5.33 mm of lead. Reaching 20 µSv/h from 1 GBq at a metre takes 3.99 mm of lead. The tenth-value layer runs 5.8 times the half-value layer, not the 3.32 a single energy would give.
Half-life, specific activity and dose rate
| Half-life | 160.4 days (1.386e+7 s) |
| Decay mode | beta-minus decay |
| Specific activity | 1.70e+14 Bq/g (4.60e+3 Ci/g) |
| Air kerma rate constant Γ (δ = 20 keV) | 0.131 mGy·m²/(GBq·h) |
| Dose rate, 1 GBq at 1 m | 0.131 mGy/h |
| Dose rate, 1 Ci at 1 m | 4.86 mGy/h |
| Kerma-weighted mean photon energy | 267.7 keV |
57 lines above the cutoff, and what each contributes
3 further lines below the 20 keV cutoff, the highest at 14.05 keV and 53.2% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.
| Energy (keV) | Emission probability (%) | Share of dose rate (%) |
|---|---|---|
| 378.50 | 29.4 | 11.42 |
| 208.37 | 55.4 | 10.87 |
| 418.54 | 21.72 | 9.39 |
| 228.48 | 35.9 | 7.85 |
| 413.66 | 17.62 | 7.52 |
| 327.68 | 18.43 | 6.12 |
| 281.79 | 13.97 | 3.91 |
| 55.79 | 57.79857 | 3.86 |
| 319.02 | 10.51 | 3.39 |
| 204.10 | 13.51 | 2.59 |
| 54.61 | 33.0261 | 2.24 |
| 153.28 | 16.54 | 2.22 |
| 112.95 | 21.4 | 2.01 |
| 174.40 | 12.47 | 1.97 |
Showing the 14 largest contributors of 57 lines above the cutoff; the remainder together carry 24.65% of the dose rate.
0.926 mm of lead halves this spectrum
Solved numerically across all 57 lines, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 0.926 | 5.33 | 5.75 |
| tungsten | 0.678 | 3.81 | 5.62 |
| iron | 5.94 | 24.1 | 4.05 |
| copper | 5.00 | 20.7 | 4.14 |
| concrete | 23.9 | 85.2 | 3.57 |
| water | 53.4 | 184 | 3.44 |
| aluminum | 21.1 | 76.3 | 3.61 |
A single energy would give 3.32. What a spread of energies does instead.
Activity over months and years
Ten half-lives is 4.39 years — a storage problem rather than a disposal one, with 20.63% of today's activity still there after a year. The mean life 1/λ is 231 days.
| 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 | 1.46 years |
| Time to fall to 1 % | 2.92 years |
| Time to fall to 0.1 % | 4.38 years |
Limits of these dose rates
- 0.131 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 0.926 mm of lead halves this spectrum, narrow beam, scatter not added back.
- Γ excludes 3 lines under 20 keV, carrying 53.2% of all emissions.
- What every sheet leaves out, internal dose included.
Gamma and decay calculators for Lu-177m
Other Lutetium nuclides: Lu-177
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.