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Zr-95 shielding — lead half-value layer and dose rate

Zirconium-95

Zr-95 · Zirconium, Z = 40, A = 95

At 7.95e+14 Bq/g — 2.15e+4 Ci/g — a gigabecquerel of Zr-95 amounts to 1.26 µg, which is why activity rather than mass is how anyone states the quantity. Zirconium-95 decays by beta-minus decay with a half-life of 64.032 days, falling to 72.27% of today's activity in a month and 1.92% in a year.

1 GBq at 1 m reads 0.0975 mGy/h, and 1 Ci at the same distance 3.61 mGy/h, from an air kerma rate constant of 0.0975 mGy·m²/(GBq·h) — 1.3× Cs-137 and 3.1× less than Co-60, and 22 of 96 among the photon emitters carried here.

3 lines clear the 20 keV cutoff, but 2 of them carry 90% of the dose rate. The leading one is 756.7 keV at 56.1% of the total — its emission probability is 54.38%, which is also the highest.

This is a shield that has to be designed: 6.29 mm of lead for a factor of two and 20.9 mm for a factor of ten, or 12.7 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 14.4 mm of lead.

Half-life, specific activity and dose rate

Half-life64.032 days (5.532e+6 s)
Decay modebeta-minus decay
Specific activity7.95e+14 Bq/g (2.15e+4 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.0975 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.0975 mGy/h
Dose rate, 1 Ci at 1 m3.61 mGy/h
Kerma-weighted mean photon energy742.0 keV

757 keV leads, and 2 lines make 90%

6 further lines below the 20 keV cutoff, the highest at 18.95 keV and 0.672% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
756.7354.3856.07
724.1944.2743.85
235.690.270.08

6.29 mm of lead halves this spectrum

Solved numerically across all 3 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead6.2920.93.33
tungsten4.1113.73.33
iron12.742.13.32
copper11.337.53.32
concrete40.31343.32
water85.22833.32
aluminum36.31203.32

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

Activity over months and years

Ten half-lives is 1.75 years — a storage problem rather than a disposal one, with 1.92% of today's activity still there after a year. The mean life 1/λ is 92.4 days.

ElapsedFraction remaining
1 half-life50.0 %
2 half-lives25.0 %
5 half-lives3.12 %
10 half-lives0.0977 %
Time to fall to 10 % of today's activity213 days
Time to fall to 1 %1.16 years
Time to fall to 0.1 %1.75 years

Limits of these dose rates

Gamma and decay calculators for Zr-95

Other Zirconium nuclides: Zr-93

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