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Sr-89 beta shielding — range and bremsstrahlung

Strontium-89

Sr-89 · Strontium, Z = 38, A = 89

At 1.07e+15 Bq/g — 2.90e+4 Ci/g — a gigabecquerel of Sr-89 amounts to 930 ng, which is why activity rather than mass is how anyone states the quantity. Strontium-89 decays by beta-minus decay with a half-life of 50.563 days, falling to 66.28% of today's activity in a month and 0.67% in a year.

The air kerma rate constant is small — 0.0000113 mGy·m²/(GBq·h), 7.0e+3× less than Cs-137 and 2.8e+4× less than Co-60, ranking 89 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 0.0000113 mGy/h, and 1 Ci at the same distance 0.000417 mGy/h. It takes 1.77 TBq at a metre to reach 20 µSv/h from the photons alone.

One line at 909.0 keV carries all of that.

This is a shield that has to be designed: 7.82 mm of lead for a factor of two and 26.0 mm for a factor of ten, or 14.0 mm of steel to halve it, at which point the mass of the shield is part of the problem. At 1 GBq and a metre it is already under 20 µSv/h with nothing in the way.

The beta endpoint is 1.50 MeV, mean 0.587 MeV over 2 branches. That endpoint stops in 5.75 mm of acrylic or 2.71 mm of glass. Of the beta energy, 0.32% turns into X-rays in acrylic and 4.31% in lead.

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

Half-life50.563 days (4.369e+6 s)
Decay modebeta-minus decay
Specific activity1.07e+15 Bq/g (2.90e+4 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.0000113 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.0000113 mGy/h
Dose rate, 1 Ci at 1 m0.000417 mGy/h
Kerma-weighted mean photon energy909.0 keV
Beta endpoint / mean1.50 MeV / 0.587 MeV

A single photon line at 909 keV

No recorded line for Sr-89 falls below the 20 keV cutoff, so this table is the whole photon spectrum. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
908.960.00956100.00

7.82 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
lead7.8226.03.32
tungsten4.9916.63.32
iron14.046.53.32
copper12.541.53.32
concrete44.31473.32
water93.73113.32
aluminum39.91333.32

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

5.75 mm of acrylic stops the 1.50 MeV endpoint

Katz–Penfold fit to the 1.50 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)
acrylic5.75
aluminum2.51
water6.78
glass2.71
Shield materialFraction of beta energy converted to X-rays
acrylic (Z ≈ 6)0.32%
lead (Z = 82)4.31%

Activity over months and years

Ten half-lives is 1.38 years — a storage problem rather than a disposal one, with 0.67% of today's activity still there after a year. The mean life 1/λ is 72.9 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 activity168 days
Time to fall to 1 %336 days
Time to fall to 0.1 %1.38 years

Limits of these dose rates

Gamma, beta and decay calculators for Sr-89

Other Strontium nuclides: Sr-85, Sr-85m, Sr-90

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