Silicon-32
Si-32 · Silicon, Z = 14, A = 32
Silicon-32 decays by beta-minus decay, half-life 157 years. Specific activity is 2.64e+12 Bq/g (71.2 Ci/g), so a gigabecquerel comes to 380 µg — weighable, but on an analytical balance. Over forty years the activity falls to 83.81%, and over ten thousand years to 6.7e-18%.
The beta endpoint is 0.227 MeV, mean 0.0696 MeV over 1 branch. That endpoint stops in 0.434 mm of acrylic or 0.205 mm of glass. Of Si-32's own beta energy, 0.05% turns into X-rays in acrylic and 0.65% in lead.
Si-32 does not stand alone. P-32 follows it with a half-life of 14.268 days, so ingrowth is complete within 99.9 days of separation. Its endpoint is 1.71 MeV and stops in 6.70 mm of acrylic, 15× the thickness above. The shield is sized on P-32, and so is the bremsstrahlung: 0.36% of that energy turns into X-rays in acrylic and 4.91% in lead.
Decay is the only handle: forty years leaves 83.81% of today's activity and ten thousand years leaves 6.7e-18%, with ten half-lives at 1,570 years and a mean life of 226 years per atom.
Half-life, specific activity and beta endpoint
| Half-life | 157 years (4.954e+9 s) |
| Decay mode | beta-minus decay |
| Specific activity | 2.64e+12 Bq/g (71.2 Ci/g) |
| Beta endpoint / mean | 0.227 MeV / 0.0696 MeV |
0.434 mm of acrylic stops the 0.227 MeV endpoint
Katz–Penfold fit to the 0.227 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 | 0.434 |
| aluminum | 0.190 |
| water | 0.513 |
| glass | 0.205 |
| Shield material | Fraction of beta energy converted to X-rays |
|---|---|
| acrylic (Z ≈ 6) | 0.05% |
| lead (Z = 82) | 0.65% |
Activity over millennia
Ten half-lives is 1,570 years, which puts decay storage out of reach: 83.81% survives forty years. The mean life 1/λ, the quantity that enters an integrated dose, is 226 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 | 522 years |
| Time to fall to 1 % | 1,043 years |
| Time to fall to 0.1 % | 1,565 years |
Limits of these range figures
- 0.434 mm of acrylic for the 0.227 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Beta and decay calculators for Si-32
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.