Sodium-24
Na-24 · Sodium, Z = 11, A = 24
Sodium-24 (Na-24) carries 3.23e+17 Bq/g, or 8.73e+6 Ci/g: a gigabecquerel is 3.09 ng, no weighable quantity at all. It decays by beta-minus decay with a half-life of 14.956 hours, which leaves 32.88% of today's activity after a day and 0.04% after a week.
Among the strong external emitters here: Γ of 0.431 mGy·m²/(GBq·h) ranks 1 of 96, 5.6× Cs-137 and 1.4× Co-60. 1 GBq at 1 m reads 0.431 mGy/h, and 1 Ci at the same distance 15.9 mGy/h — a metre-scale hazard at gigabecquerel activities, and 46.4 MBq is already 20 µSv/h at that distance.
4 lines clear the 20 keV cutoff, but 2 of them carry 90% of the dose rate. The leading one is 2754.0 keV at 62.0% of the total — its emission probability is 99.867%, which is lower than the 99.994% of the 1368.6 keV line it outranks.
This is a shield that has to be designed: 12.9 mm of lead for a factor of two and 43.2 mm for a factor of ten, or 20.8 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 57.9 mm of lead.
Half-life, specific activity and dose rate
| Half-life | 14.956 hours (5.384e+4 s) |
| Decay mode | beta-minus decay |
| Specific activity | 3.23e+17 Bq/g (8.73e+6 Ci/g) |
| Air kerma rate constant Γ (δ = 20 keV) | 0.431 mGy·m²/(GBq·h) |
| Dose rate, 1 GBq at 1 m | 0.431 mGy/h |
| Dose rate, 1 Ci at 1 m | 15.9 mGy/h |
| Kerma-weighted mean photon energy | 2228 keV |
2754 keV leads, and 2 lines make 90%
No recorded line for Na-24 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 (%) |
|---|---|---|
| 2754.01 | 99.867 | 61.95 |
| 1368.63 | 99.994 | 37.99 |
| 3866.15 | 0.068 | 0.05 |
| 996.83 | 0.0021 | 0.00 |
12.9 mm of lead halves this spectrum
Solved numerically across all 4 lines, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 12.9 | 43.2 | 3.36 |
| tungsten | 7.88 | 26.5 | 3.36 |
| iron | 20.8 | 70.4 | 3.38 |
| copper | 18.5 | 62.5 | 3.38 |
| concrete | 67.7 | 230 | 3.41 |
| water | 144 | 491 | 3.41 |
| aluminum | 60.6 | 206 | 3.40 |
A single energy would give 3.32. What a spread of energies does instead.
Activity over days and weeks
Ten half-lives is 6.23 days, so the activity moves measurably while a count is running: every figure has to carry the time it was referred to. The mean life 1/λ is 21.6 hours.
| 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 | 2.07 days |
| Time to fall to 1 % | 4.14 days |
| Time to fall to 0.1 % | 6.21 days |
Limits of these dose rates
- 0.431 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 12.9 mm of lead halves this spectrum, narrow beam, scatter not added back.
- What every sheet leaves out, internal dose included.
Gamma and decay calculators for Na-24
Other Sodium nuclides: Na-22, Na-24m
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.