Chromium-51
Cr-51 · Chromium, Z = 24, A = 51
At 3.42e+15 Bq/g — 9.25e+4 Ci/g — a gigabecquerel of Cr-51 amounts to 292 ng, which is why activity rather than mass is how anyone states the quantity. Chromium-51 decays by electron capture with a half-life of 27.704 days, falling to 83.93% of today's activity in a week and 10.26% in three months.
The air kerma rate constant is small — 0.00421 mGy·m²/(GBq·h), 18× less than Cs-137 and 73× less than Co-60, ranking 76 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 0.00421 mGy/h, and 1 Ci at the same distance 0.156 mGy/h. It takes 4.75 GBq at a metre to reach 20 µSv/h from the photons alone.
One line at 320.1 keV carries all of that.
Halving the air kerma rate calls for 1.72 mm of lead, or 8.30 mm of steel where lead is unwelcome, and a factor of ten calls for 5.70 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.
Half-life, specific activity and dose rate
| Half-life | 27.704 days (2.394e+6 s) |
| Decay mode | electron capture |
| Specific activity | 3.42e+15 Bq/g (9.25e+4 Ci/g) |
| Air kerma rate constant Γ (δ = 20 keV) | 0.00421 mGy·m²/(GBq·h) |
| Dose rate, 1 GBq at 1 m | 0.00421 mGy/h |
| Dose rate, 1 Ci at 1 m | 0.156 mGy/h |
| Kerma-weighted mean photon energy | 320.1 keV |
A single photon line at 320 keV
3 further lines below the 20 keV cutoff, the highest at 5.44 keV and 22.8% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.
| Energy (keV) | Emission probability (%) | Share of dose rate (%) |
|---|---|---|
| 320.08 | 9.91 | 100.00 |
1.72 mm of lead halves this spectrum
Solved numerically across all 1 line, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 1.72 | 5.70 | 3.32 |
| tungsten | 1.25 | 4.14 | 3.32 |
| iron | 8.30 | 27.6 | 3.32 |
| copper | 7.19 | 23.9 | 3.32 |
| concrete | 28.2 | 93.6 | 3.32 |
| water | 59.9 | 199 | 3.32 |
| aluminum | 25.3 | 84.0 | 3.32 |
A single energy would give 3.32. What a spread of energies does instead.
Activity over months and years
Ten half-lives is 277 days — a storage problem rather than a disposal one, with 0.01% of today's activity still there after a year. The mean life 1/λ is 40.0 days.
| Elapsed | Fraction remaining |
|---|---|
| 1 half-life | 50.0 % |
| 2 half-lives | 25.0 % |
| 5 half-lives | 3.13 % |
| 10 half-lives | 0.0977 % |
| Time to fall to 10 % of today's activity | 92.0 days |
| Time to fall to 1 % | 184 days |
| Time to fall to 0.1 % | 276 days |
Limits of these dose rates
- 0.00421 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 1.72 mm of lead halves this spectrum, narrow beam, scatter not added back.
- Γ excludes 3 lines under 20 keV, carrying 22.8% of all emissions.
- What every sheet leaves out, internal dose included.
Gamma and decay calculators for Cr-51
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.