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Cs-134 shielding — lead half-value layer and dose rate

Cesium-134

Cs-134 · Cesium, Z = 55, A = 134

Cesium-134 decays by beta-minus decay, half-life 2.0652 years. Specific activity is 4.78e+13 Bq/g (1.29e+3 Ci/g), so a gigabecquerel comes to 20.9 µg — weighable, but on an analytical balance. Over a year the activity falls to 71.49%, and over forty years to 1.5e-4%.

Among the strong external emitters here: Γ of 0.207 mGy·m²/(GBq·h) ranks 9 of 96, 2.7× Cs-137 and 1.5× less than Co-60. 1 GBq at 1 m reads 0.207 mGy/h, and 1 Ci at the same distance 7.67 mGy/h — a metre-scale hazard at gigabecquerel activities, and 96.4 MBq is already 20 µSv/h at that distance.

17 lines clear the 20 keV cutoff, but 4 of them carry 90% of the dose rate. The leading one is 795.9 keV at 43.4% of the total — its emission probability is 85.46%, which is lower than the 97.62% of the 604.7 keV line it outranks.

This is a shield that has to be designed: 5.85 mm of lead for a factor of two and 20.2 mm for a factor of ten, or 12.3 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 20.5 mm of lead.

Half-life, specific activity and dose rate

Half-life2.0652 years (6.517e+7 s)
Decay modebeta-minus decay
Specific activity4.78e+13 Bq/g (1.29e+3 Ci/g)
Air kerma rate constant Γ (δ = 20 keV)0.207 mGy·m²/(GBq·h)
Dose rate, 1 GBq at 1 m0.207 mGy/h
Dose rate, 1 Ci at 1 m7.67 mGy/h
Kerma-weighted mean photon energy719.9 keV

17 lines above the cutoff, and what each contributes

1 further line below the 20 keV cutoff, the highest at 4.97 keV and 0.105% emission probability in all, is excluded here and from Γ. Why the two columns rank differently.

Energy (keV)Emission probability (%)Share of dose rate (%)
795.8685.4643.40
604.7297.6238.55
569.3315.3735.73
801.958.6884.44
563.258.3383.07
1365.183.0172.38
1167.971.791.25
1038.610.990.63
475.371.4770.46
32.190.4390.04
31.820.2380.02
36.830.16180.01
36.480.12920.01
242.740.0270.00

Showing the 14 largest contributors of 17 lines above the cutoff; the remainder together carry 0.01% of the dose rate.

5.85 mm of lead halves this spectrum

Solved numerically across all 17 lines, narrow beam. Why not one representative energy.

MaterialHVL (mm)TVL (mm)TVL / HVL
lead5.8520.23.44
tungsten3.8613.23.42
iron12.341.33.35
copper11.036.83.35
concrete39.41323.35
water83.22783.34
aluminum35.41183.35

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

Activity over decades and centuries

Ten half-lives is 20.7 years, which puts decay storage out of reach: 1.5e-4% survives forty years. The mean life 1/λ, the quantity that enters an integrated dose, is 2.98 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 activity6.86 years
Time to fall to 1 %13.7 years
Time to fall to 0.1 %20.6 years

Limits of these dose rates

Gamma and decay calculators for Cs-134

Other Cesium nuclides: Cs-134m, Cs-135, Cs-137

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