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-life | 115.09 days (9.944e+6 s) |
| Decay mode | electron capture with beta-plus |
| Specific activity | 3.72e+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 m | 0.0706 mGy/h |
| Dose rate, 1 Ci at 1 m | 2.61 mGy/h |
| Kerma-weighted mean photon energy | 205.8 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 (%) |
|---|---|---|
| 391.70 | 64.97 | 48.70 |
| 24.21 | 52.15514 | 24.50 |
| 24.00 | 27.79869 | 13.30 |
| 27.58 | 17.41394 | 6.23 |
| 27.37 | 14.63357 | 5.32 |
| 255.13 | 2.11 | 0.98 |
| 27.86 | 2.78038 | 0.97 |
0.0684 mm of lead halves this spectrum
Solved numerically across all 7 lines, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 0.0684 | 5.78 | 84.40 |
| tungsten | 0.0525 | 4.11 | 78.24 |
| iron | 0.332 | 21.3 | 64.18 |
| copper | 0.231 | 18.7 | 80.68 |
| concrete | 5.77 | 70.4 | 12.20 |
| water | 26.2 | 150 | 5.71 |
| aluminum | 4.41 | 63.3 | 14.36 |
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.
| 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 | 1.05 years |
| Time to fall to 1 % | 2.09 years |
| Time to fall to 0.1 % | 3.14 years |
Limits of these dose rates
- 0.0706 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 0.0684 mm of lead halves this spectrum, narrow beam, scatter not added back.
- Γ excludes 1 line under 20 keV, carrying 8.57% of all emissions.
- What every sheet leaves out, internal dose included.
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.