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Sn-113 shielding — lead half-value layer and dose rate

Tin-113

Sn-113 · Tin, Z = 50, A = 113

At 3.72e+14 Bq/g — 1.00e+4 Ci/g — a gigabecquerel of Sn-113 amounts to 2.69 µg, which is why activity rather than mass is how anyone states the quantity. Tin-113 decays by electron capture with beta-plus with a half-life of 115.09 days, falling to 83.47% of today's activity in a month and 11.08% in a year.

1 GBq at 1 m reads 0.0706 mGy/h, and 1 Ci at the same distance 2.61 mGy/h, from an air kerma rate constant of 0.0706 mGy·m²/(GBq·h) — 1.1× less than Cs-137 and 4.3× less than Co-60, and 31 of 96 among the photon emitters carried here.

7 lines clear the 20 keV cutoff, but 4 of them carry 90% of the dose rate. The leading one is 391.7 keV at 48.7% of the total — its emission probability is 64.97%, which is also the highest.

Shielding barely arises: 0.0684 mm of lead halves the air kerma rate and 5.78 mm takes it to a tenth, thicknesses a source capsule is likely to exceed on its own. Steel does the halving in 0.332 mm. Reaching 20 µSv/h from 1 GBq at a metre takes 2.01 mm of lead. The tenth-value layer runs 84.4 times the half-value layer, not the 3.32 a single energy would give.

Half-life, specific activity and dose rate

Half-life115.09 days (9.944e+6 s)
Decay modeelectron capture with beta-plus
Specific activity3.72e+14 Bq/g (1.00e+4 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.0706 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.0706 mGy/h
Dose rate, 1 Ci at 1 m2.61 mGy/h
Kerma-weighted mean photon energy205.8 keV

7 lines above the cutoff, and what each contributes

1 further line below the 20 keV cutoff, the highest at 3.57 keV and 8.57% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
391.7064.9748.70
24.2152.1551424.50
24.0027.7986913.30
27.5817.413946.23
27.3714.633575.32
255.132.110.98
27.862.780380.97

0.0684 mm of lead halves this spectrum

Solved numerically across all 7 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead0.06845.7884.40
tungsten0.05254.1178.24
iron0.33221.364.18
copper0.23118.780.68
concrete5.7770.412.20
water26.21505.71
aluminum4.4163.314.36

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

Activity over months and years

Ten half-lives is 3.15 years — a storage problem rather than a disposal one, with 11.08% of today's activity still there after a year. The mean life 1/λ is 166 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 activity1.05 years
Time to fall to 1 %2.09 years
Time to fall to 0.1 %3.14 years

Limits of these dose rates

Gamma and decay calculators for Sn-113

Other Tin nuclides: Sn-113m

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