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Co-60 shielding — lead half-value layer and dose rate

Cobalt-60

Co-60 · Cobalt, Z = 27, A = 60

Cobalt-60 decays by beta-minus decay, half-life 1925.28 days. Specific activity is 4.19e+13 Bq/g (1.13e+3 Ci/g), so a gigabecquerel comes to 23.9 µg — weighable, but on an analytical balance. Over a year the activity falls to 87.68%, and over forty years to 0.52%.

Among the strong external emitters here: Γ of 0.306 mGy·m²/(GBq·h) ranks 4 of 96, 4.0× Cs-137. 1 GBq at 1 m reads 0.306 mGy/h, and 1 Ci at the same distance 11.3 mGy/h — a metre-scale hazard at gigabecquerel activities, and 65.4 MBq is already 20 µSv/h at that distance.

5 lines clear the 20 keV cutoff, but 2 of them carry 90% of the dose rate. The leading one is 1332.5 keV at 52.5% of the total — its emission probability is 99.9826%, which is also the highest.

This is a shield that has to be designed: 10.3 mm of lead for a factor of two and 34.4 mm for a factor of ten, or 16.5 mm of steel to halve it, at which point the mass of the shield is part of the problem. Reaching 20 µSv/h from 1 GBq at a metre takes 40.8 mm of lead.

The beta endpoint is 1.49 MeV, mean 0.0964 MeV over 2 branches; that endpoint comes from a branch of only 0.12%, while 99.88% of decays take the 0.318 MeV branch. Shielding is sized on the endpoint, dose on the mean. That endpoint stops in 5.70 mm of acrylic or 2.69 mm of glass. Of the beta energy, 0.31% turns into X-rays in acrylic and 4.28% in lead.

Half-life, specific activity, dose rate and beta energies

Half-life1925.28 days (1.663e+8 s)
Decay modebeta-minus decay
Specific activity4.19e+13 Bq/g (1.13e+3 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.306 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.306 mGy/h
Dose rate, 1 Ci at 1 m11.3 mGy/h
Kerma-weighted mean photon energy1257 keV
Beta endpoint / mean1.49 MeV / 0.0964 MeV

1332 keV leads, and 2 lines make 90%

3 further lines below the 20 keV cutoff, the highest at 8.30 keV and 0.0111% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
1332.4999.982652.49
1173.2399.8547.50
826.100.00760.00
347.140.00750.00
2158.570.00120.00

10.3 mm of lead halves this spectrum

Solved numerically across all 5 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead10.334.43.33
tungsten6.4221.43.33
iron16.554.83.32
copper14.748.93.32
concrete52.01733.32
water1103653.32
aluminum46.81563.32

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

5.70 mm of acrylic stops the 1.49 MeV endpoint

Katz–Penfold fit to the 1.49 MeV endpoint — ±10%, and a stopping thickness rather than an attenuation length. Why the material matters more than the thickness.

AbsorberRange for the endpoint (mm)
acrylic5.70
aluminum2.49
water6.73
glass2.69
Shield materialFraction of beta energy converted to X-rays
acrylic (Z ≈ 6)0.31%
lead (Z = 82)4.28%

Activity over decades and centuries

Ten half-lives is 52.7 years, which puts decay storage out of reach: 0.52% survives forty years. The mean life 1/λ, the quantity that enters an integrated dose, is 7.60 years.

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 activity17.5 years
Time to fall to 1 %35.0 years
Time to fall to 0.1 %52.5 years

Limits of these dose rates

Gamma, beta and decay calculators for Co-60

Other Cobalt nuclides: Co-57, Co-60m

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