Zirconium-93
Zr-93 · Zirconium, Z = 40, A = 93
Zirconium-93 (Zr-93) is slow enough to be handled as a material rather than as a trace: 8.84e+7 Bq/g, or 0.00239 Ci/g, puts a gigabecquerel at 11.3 g. Decay is by beta-minus decay, half-life 1.61 × 10⁶ years, and shedding even one per cent of the activity takes 23,344 years.
The beta endpoint is 0.0908 MeV, mean 0.0202 MeV over 2 branches. That endpoint stops in 0.0969 mm of acrylic or 0.0458 mm of glass. Of the beta energy, 0.02% turns into X-rays in acrylic and 0.26% in lead.
Decay is the only handle: forty years leaves 100.00% of today's activity and ten thousand years leaves 99.57%, with ten half-lives at 16.1 million years and a mean life of 2.32 million years per atom.
Half-life, specific activity and beta endpoint
| Half-life | 1.61 × 10⁶ years (5.081e+13 s) |
| Decay mode | beta-minus decay |
| Specific activity | 8.84e+7 Bq/g (0.00239 Ci/g) |
| Beta endpoint / mean | 0.0908 MeV / 0.0202 MeV |
0.0969 mm of acrylic stops the 0.0908 MeV endpoint
Katz–Penfold fit to the 0.0908 MeV endpoint — ±10%, and a stopping thickness rather than an attenuation length. Why the material matters more than the thickness.
| Absorber | Range for the endpoint (mm) |
|---|---|
| acrylic | 0.0969 |
| aluminum | 0.0424 |
| water | 0.114 |
| glass | 0.0458 |
| Shield material | Fraction of beta energy converted to X-rays |
|---|---|
| acrylic (Z ≈ 6) | 0.02% |
| lead (Z = 82) | 0.26% |
Activity over geological time
Ten half-lives is 16.1 million years. On any timescale a facility can be planned over the activity is constant — 100.00% is left after forty years — and the mean life 1/λ is 2.32 million years.
| 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 | 5.35 million years |
| Time to fall to 1 % | 10.7 million years |
| Time to fall to 0.1 % | 16.0 million years |
Limits of these range figures
- 0.0969 mm of acrylic for the 0.0908 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Beta and decay calculators for Zr-93
Other Zirconium nuclides: Zr-95
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.