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In-111 shielding — lead half-value layer and dose rate

Indium-111

In-111 · Indium, Z = 49, A = 111

Indium-111 (In-111) carries 1.55e+16 Bq/g, or 4.20e+5 Ci/g: a gigabecquerel is 64.4 ng, no weighable quantity at all. It decays by electron capture with a half-life of 2.8047 days, which leaves 17.73% of today's activity after a week and 1.7e-8% after three months.

1 GBq at 1 m reads 0.0807 mGy/h, and 1 Ci at the same distance 2.98 mGy/h, from an air kerma rate constant of 0.0807 mGy·m²/(GBq·h) — 1.0× Cs-137 and 3.8× less than Co-60, and 27 of 96 among the photon emitters carried here.

8 lines clear the 20 keV cutoff, but 5 of them carry 90% of the dose rate. The leading one is 245.3 keV at 36.4% of the total — its emission probability is 94.09%, which is also the highest.

Shielding barely arises: 0.158 mm of lead halves the air kerma rate and 1.94 mm takes it to a tenth, thicknesses a source capsule is likely to exceed on its own. Steel does the halving in 1.49 mm. Reaching 20 µSv/h from 1 GBq at a metre takes 0.874 mm of lead. The tenth-value layer runs 12.2 times the half-value layer, not the 3.32 a single energy would give.

Half-life, specific activity and dose rate

Half-life2.8047 days (2.423e+5 s)
Decay modeelectron capture
Specific activity1.55e+16 Bq/g (4.20e+5 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.0807 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.0807 mGy/h
Dose rate, 1 Ci at 1 m2.98 mGy/h
Kerma-weighted mean photon energy138.0 keV

8 lines above the cutoff, and what each contributes

1 further line below the 20 keV cutoff, the highest at 3.39 keV and 6.76% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
245.3594.0936.40
171.2890.6522.75
23.1744.3250719.97
22.9823.5676410.80
26.3814.603725.01
26.1812.355094.31
26.642.248630.76
150.810.0030.00

0.158 mm of lead halves this spectrum

Solved numerically across all 8 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead0.1581.9412.22
tungsten0.1181.4412.17
iron1.4916.010.77
copper1.2213.310.85
concrete7.3961.98.38
water26.81334.98
aluminum6.0955.39.09

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

Activity over days and weeks

Ten half-lives is 28.0 days — a storage problem rather than a disposal one, with 6.3e-38% of today's activity still there after a year. The mean life 1/λ is 4.05 days.

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 activity9.32 days
Time to fall to 1 %18.6 days
Time to fall to 0.1 %28.0 days

Limits of these dose rates

Gamma and decay calculators for In-111

Other Indium nuclides: In-111m

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