Lutetium-177
Lu-177 · Lutetium, Z = 71, A = 177
At 4.11e+15 Bq/g — 1.11e+5 Ci/g — a gigabecquerel of Lu-177 amounts to 243 ng, which is why activity rather than mass is how anyone states the quantity. Lutetium-177 decays by beta-minus decay with a half-life of 6.6443 days, falling to 48.18% of today's activity in a week and 7.5e-3% in three months.
The air kerma rate constant is small — 0.00420 mGy·m²/(GBq·h), 18× less than Cs-137 and 73× less than Co-60, ranking 77 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 0.00420 mGy/h, and 1 Ci at the same distance 0.155 mGy/h. It takes 4.76 GBq at a metre to reach 20 µSv/h from the photons alone.
11 lines clear the 20 keV cutoff, but 4 of them carry 90% of the dose rate. The leading one is 208.4 keV at 63.8% of the total — its emission probability is 10.41%, which is also the highest.
A half-value layer of 0.391 mm in lead puts this in foil and thin sheet, with 4.11 mm needed if the material is steel; ten-fold attenuation comes at 1.94 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 5.0 times the half-value layer, not the 3.32 a single energy would give.
Half-life, specific activity and dose rate
| Half-life | 6.6443 days (5.741e+5 s) |
| Decay mode | beta-minus decay |
| Specific activity | 4.11e+15 Bq/g (1.11e+5 Ci/g) |
| Air kerma rate constant Γ (δ = 20 keV) | 0.00420 mGy·m²/(GBq·h) |
| Dose rate, 1 GBq at 1 m | 0.00420 mGy/h |
| Dose rate, 1 Ci at 1 m | 0.155 mGy/h |
| Kerma-weighted mean photon energy | 172.9 keV |
11 lines above the cutoff, and what each contributes
1 further line below the 20 keV cutoff, the highest at 9.11 keV and 3.04% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.
| Energy (keV) | Emission probability (%) | Share of dose rate (%) |
|---|---|---|
| 208.37 | 10.41 | 63.79 |
| 112.95 | 6.23 | 18.26 |
| 55.79 | 2.75044 | 5.74 |
| 54.61 | 1.5716 | 3.33 |
| 64.06 | 1.14966 | 2.32 |
| 321.32 | 0.2186 | 2.22 |
| 63.33 | 0.90739 | 1.83 |
| 249.67 | 0.1997 | 1.51 |
| 64.94 | 0.24227 | 0.49 |
| 71.64 | 0.164 | 0.34 |
| 136.72 | 0.0465 | 0.17 |
0.391 mm of lead halves this spectrum
Solved numerically across all 11 lines, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 0.391 | 1.94 | 4.96 |
| tungsten | 0.293 | 1.45 | 4.94 |
| iron | 4.11 | 17.6 | 4.28 |
| copper | 3.28 | 14.5 | 4.42 |
| concrete | 20.3 | 71.5 | 3.52 |
| water | 46.6 | 158 | 3.39 |
| aluminum | 17.8 | 63.6 | 3.57 |
A single energy would give 3.32. What a spread of energies does instead.
Activity over months and years
Ten half-lives is 66.4 days — a storage problem rather than a disposal one, with 2.8e-15% of today's activity still there after a year. The mean life 1/λ is 9.59 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 | 22.1 days |
| Time to fall to 1 % | 44.1 days |
| Time to fall to 0.1 % | 66.2 days |
Limits of these dose rates
- 0.00420 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 0.391 mm of lead halves this spectrum, narrow beam, scatter not added back.
- Γ excludes 1 line under 20 keV, carrying 3.04% of all emissions.
- What every sheet leaves out, internal dose included.
Gamma and decay calculators for Lu-177
Other Lutetium nuclides: Lu-177m
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.