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Zn-65 shielding — lead half-value layer and dose rate

Zinc-65

Zn-65 · Zinc, Z = 30, A = 65

At 3.05e+14 Bq/g — 8.24e+3 Ci/g — a gigabecquerel of Zn-65 amounts to 3.28 µg, which is why activity rather than mass is how anyone states the quantity. Zinc-65 decays by electron capture with beta-plus with a half-life of 243.93 days, falling to 91.83% of today's activity in a month and 35.42% in a year.

1 GBq at 1 m reads 0.0719 mGy/h, and 1 Ci at the same distance 2.66 mGy/h, from an air kerma rate constant of 0.0719 mGy·m²/(GBq·h) — 1.1× less than Cs-137 and 4.3× less than Co-60, and 30 of 96 among the photon emitters carried here.

4 lines clear the 20 keV cutoff, but one of them carries 90% of the dose rate. The leading one is 1115.5 keV at 97.2% of the total — its emission probability is 50.04%, which is also the highest.

This is a shield that has to be designed: 9.20 mm of lead for a factor of two and 31.0 mm for a factor of ten, or 15.4 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 17.1 mm of lead.

Half-life, specific activity and dose rate

Half-life243.93 days (2.108e+7 s)
Decay modeelectron capture with beta-plus
Specific activity3.05e+14 Bq/g (8.24e+3 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.0719 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.0719 mGy/h
Dose rate, 1 Ci at 1 m2.66 mGy/h
Kerma-weighted mean photon energy1099 keV

1116 keV carries 97% of the dose rate

3 further lines below the 20 keV cutoff, the highest at 8.94 keV and 39.5% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
1115.5450.0497.25
511.002.8422.75
770.600.002680.00
344.950.002530.00

9.20 mm of lead halves this spectrum

Solved numerically across all 4 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead9.2031.03.37
tungsten5.7719.43.36
iron15.451.23.33
copper13.745.73.33
concrete48.51623.33
water1023413.33
aluminum43.71463.33

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

Activity over months and years

Ten half-lives is 6.68 years — a storage problem rather than a disposal one, with 35.42% of today's activity still there after a year. The mean life 1/λ is 352 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 activity2.22 years
Time to fall to 1 %4.44 years
Time to fall to 0.1 %6.66 years

Limits of these dose rates

Gamma and decay calculators for Zn-65

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