Phosphorus-33
P-33 · Phosphorus, Z = 15, A = 33
At 5.77e+15 Bq/g — 1.56e+5 Ci/g — a gigabecquerel of P-33 amounts to 173 ng, which is why activity rather than mass is how anyone states the quantity. Phosphorus-33 decays by beta-minus decay with a half-life of 25.38 days, falling to 82.60% of today's activity in a week and 8.33% in three months.
The beta endpoint is 0.248 MeV, mean 0.0759 MeV over 1 branch. That endpoint stops in 0.499 mm of acrylic or 0.235 mm of glass. Of the beta energy, 0.05% turns into X-rays in acrylic and 0.71% in lead.
Decay is the only handle: a week leaves 82.60% of today's activity and three months leaves 8.33%, with ten half-lives at 254 days and a mean life of 36.6 days per atom.
Half-life, specific activity and beta endpoint
| Half-life | 25.38 days (2.193e+6 s) |
| Decay mode | beta-minus decay |
| Specific activity | 5.77e+15 Bq/g (1.56e+5 Ci/g) |
| Beta endpoint / mean | 0.248 MeV / 0.0759 MeV |
0.499 mm of acrylic stops the 0.248 MeV endpoint
Katz–Penfold fit to the 0.248 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 | 0.499 |
| aluminum | 0.218 |
| water | 0.588 |
| glass | 0.235 |
| Shield material | Fraction of beta energy converted to X-rays |
|---|---|
| acrylic (Z ≈ 6) | 0.05% |
| lead (Z = 82) | 0.71% |
Activity over months and years
Ten half-lives is 254 days — a storage problem rather than a disposal one, with 4.7e-3% of today's activity still there after a year. The mean life 1/λ is 36.6 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 | 84.3 days |
| Time to fall to 1 % | 169 days |
| Time to fall to 0.1 % | 253 days |
Limits of these range figures
- 0.499 mm of acrylic for the 0.248 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Beta and decay calculators for P-33
Other Phosphorus nuclides: P-32
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.