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Kr-85 shielding — lead half-value layer and dose rate

Krypton-85

Kr-85 · Krypton, Z = 36, A = 85

Krypton-85 decays by beta-minus decay, half-life 10.739 years. Specific activity is 1.45e+13 Bq/g (392 Ci/g), so a gigabecquerel comes to 68.9 µg — weighable, but on an analytical balance. Over a year the activity falls to 93.75%, and over forty years to 7.56%.

The air kerma rate constant is small — 0.000303 mGy·m²/(GBq·h), 2.5e+2× less than Cs-137 and 1.0e+3× less than Co-60, ranking 83 of 96 by Γ — near the bottom of the photon emitters, but above the cutoff, which 51 nuclides in this dataset are not. 1 GBq at 1 m reads 0.000303 mGy/h, and 1 Ci at the same distance 0.0112 mGy/h. It takes 65.9 GBq at a metre to reach 20 µSv/h from the photons alone.

One line at 514.0 keV carries all of that.

Halving the air kerma rate calls for 3.93 mm of lead, or 10.6 mm of steel where lead is unwelcome, and a factor of ten calls for 13.1 mm of lead — sheet thicknesses that a glovebox or a transport container can carry. At 1 GBq and a metre it is already under 20 µSv/h with nothing in the way.

The beta endpoint is 0.687 MeV, mean 0.251 MeV over 2 branches. That endpoint stops in 2.14 mm of acrylic or 1.01 mm of glass. Of the beta energy, 0.14% turns into X-rays in acrylic and 1.97% in lead.

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

Half-life10.739 years (3.389e+8 s)
Decay modebeta-minus decay
Specific activity1.45e+13 Bq/g (392 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.000303 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.000303 mGy/h
Dose rate, 1 Ci at 1 m0.0112 mGy/h
Kerma-weighted mean photon energy514.0 keV
Beta endpoint / mean0.687 MeV / 0.251 MeV

A single photon line at 514 keV

1 further line below the 20 keV cutoff, the highest at 13.40 keV and 0.00103% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
514.000.434100.00

3.93 mm of lead halves this spectrum

Solved numerically across all 1 line, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead3.9313.13.32
tungsten2.708.973.32
iron10.635.23.32
copper9.3831.23.32
concrete34.21143.32
water72.42413.32
aluminum30.81023.32

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

2.14 mm of acrylic stops the 0.687 MeV endpoint

Katz–Penfold fit to the 0.687 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)
acrylic2.14
aluminum0.937
water2.53
glass1.01
Shield materialFraction of beta energy converted to X-rays
acrylic (Z ≈ 6)0.14%
lead (Z = 82)1.97%

Activity over decades and centuries

Ten half-lives is 107 years, which puts decay storage out of reach: 7.56% survives forty years. The mean life 1/λ, the quantity that enters an integrated dose, is 15.5 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 activity35.7 years
Time to fall to 1 %71.3 years
Time to fall to 0.1 %107 years

Limits of these dose rates

Gamma, beta and decay calculators for Kr-85

Other Krypton nuclides: Kr-85m

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