Phosphorus-32
P-32 · Phosphorus, Z = 15, A = 32
Phosphorus-32 (P-32) carries 1.06e+16 Bq/g, or 2.86e+5 Ci/g: a gigabecquerel is 94.4 ng, no weighable quantity at all. It decays by beta-minus decay with a half-life of 14.268 days, which leaves 71.17% of today's activity after a week and 1.20% after three months.
The beta endpoint is 1.71 MeV, mean 0.695 MeV over 1 branch. That endpoint stops in 6.70 mm of acrylic or 3.16 mm of glass. Of the beta energy, 0.36% turns into X-rays in acrylic and 4.91% in lead.
Decay is the only handle: a week leaves 71.17% of today's activity and three months leaves 1.20%, with ten half-lives at 143 days and a mean life of 20.6 days per atom.
Half-life, specific activity and beta endpoint
| Half-life | 14.268 days (1.233e+6 s) |
| Decay mode | beta-minus decay |
| Specific activity | 1.06e+16 Bq/g (2.86e+5 Ci/g) |
| Beta endpoint / mean | 1.71 MeV / 0.695 MeV |
6.70 mm of acrylic stops the 1.71 MeV endpoint
Katz–Penfold fit to the 1.71 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 | 6.70 |
| aluminum | 2.93 |
| water | 7.90 |
| glass | 3.16 |
| Shield material | Fraction of beta energy converted to X-rays |
|---|---|
| acrylic (Z ≈ 6) | 0.36% |
| lead (Z = 82) | 4.91% |
Activity over months and years
Ten half-lives is 143 days — a storage problem rather than a disposal one, with 2.0e-6% of today's activity still there after a year. The mean life 1/λ is 20.6 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 | 47.4 days |
| Time to fall to 1 % | 94.8 days |
| Time to fall to 0.1 % | 142 days |
Limits of these range figures
- 6.70 mm of acrylic for the 1.71 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Beta and decay calculators for P-32
Other Phosphorus nuclides: P-33
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.