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Ra-223 shielding — lead half-value layer and dose rate

Radium-223

Ra-223 · Radium, Z = 88, A = 223

At 1.90e+15 Bq/g — 5.12e+4 Ci/g — a gigabecquerel of Ra-223 amounts to 528 ng, which is why activity rather than mass is how anyone states the quantity. Radium-223 decays by alpha decay with a half-life of 11.43 days, falling to 65.41% of today's activity in a week and 0.40% in three months.

The air kerma rate constant recorded for Ra-223 is 0.0171 mGy·m²/(GBq·h). 1 GBq at 1 m reads 0.0171 mGy/h, and 1 Ci at the same distance 0.631 mGy/h — for that emission alone. No ranking against the other emitters here is drawn: for most of them the constant is the whole field, and for Ra-223 it is not.

57 lines clear the 20 keV cutoff, but 10 of them carry 90% of the dose rate. The leading one is 269.5 keV at 27.2% of the total — its emission probability is 13.3042%, which is lower than the 25.4% of the 83.8 keV line it outranks.

For Ra-223's own photons, 0.541 mm of lead halves the air kerma rate, 4.15 mm if the material is steel, and 3.84 mm of lead takes it to a tenth. What thickness the source in front of you needs is a question about its chain, not about this line list. The tenth-value layer runs 7.1 times the half-value layer, not the 3.32 a single energy would give.

These photon figures are Ra-223's own. What it decays into is not in this dataset, so nothing below Ra-223 is counted here. A source left sealed long enough for the chain to build up reads higher than this — how much higher is outside what this page can compute.

Alpha emission is led by 5.716 MeV at 51.2%, one of 12 recorded lines. None of it reaches through skin, so the alpha is an intake hazard rather than an external one — the photon figures above are the separate question.

Half-life, specific activity and dose rate

Half-life11.43 days (9.876e+5 s)
Decay modealpha decay
Specific activity1.90e+15 Bq/g (5.12e+4 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.0171 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.0171 mGy/h
Dose rate, 1 Ci at 1 m0.631 mGy/h
Kerma-weighted mean photon energy213.3 keV

57 lines above the cutoff, and what each contributes

3 further lines below the 20 keV cutoff, the highest at 14.40 keV and 23.0% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
269.4613.304227.19
83.7925.413.69
323.873.64219.18
81.0715.428.08
96.0511.647.04
338.282.600646.88
154.216.026.28
94.888.825.28
445.031.218454.32
144.243.473543.34
97.532.821.73
371.680.434641.27
122.321.304531.03
158.630.738050.80

Showing the 14 largest contributors of 57 lines above the cutoff; the remainder together carry 3.88% of the dose rate.

0.541 mm of lead halves this spectrum

Solved numerically across all 57 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead0.5413.847.10
tungsten0.2832.799.85
iron4.1519.94.81
copper3.2317.05.27
concrete21.876.63.52
water49.11693.43
aluminum19.268.13.55

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

12 alpha lines, strongest 5.716 MeV

12 recorded lines from 5.283 to 5.871 MeV, the strongest 5.716 MeV at 51.2% of 98.98% total alpha emission.

Energy (MeV)Emission probability (%)
5.716251.2
5.606725
5.53988.9
5.74708.9
5.43361.8
5.50161
5.87131
5.42400.39
5.85750.31
5.28730.2

Activity over months and years

Ten half-lives is 114 days — a storage problem rather than a disposal one, with 2.4e-8% of today's activity still there after a year. The mean life 1/λ is 16.5 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 activity38.0 days
Time to fall to 1 %75.9 days
Time to fall to 0.1 %114 days

Limits of these dose rates

Gamma and decay calculators for Ra-223

Other Radium nuclides: Ra-224, Ra-226, Ra-228

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