Bismuth-210
Bi-210 · Bismuth, Z = 83, A = 210
At 4.59e+15 Bq/g — 1.24e+5 Ci/g — a gigabecquerel of Bi-210 amounts to 218 ng, which is why activity rather than mass is how anyone states the quantity. Bismuth-210 decays by beta-minus decay with a half-life of 5.012 days, falling to 37.98% of today's activity in a week and 3.4e-4% in three months.
The beta endpoint is 1.16 MeV, mean 0.389 MeV over 1 branch. That endpoint stops in 4.21 mm of acrylic or 1.99 mm of glass. Of the beta energy, 0.24% turns into X-rays in acrylic and 3.33% in lead.
Decay is the only handle: a week leaves 37.98% of today's activity and three months leaves 3.4e-4%, with ten half-lives at 50.1 days and a mean life of 7.23 days per atom.
Half-life, specific activity and beta endpoint
| Half-life | 5.012 days (4.330e+5 s) |
| Decay mode | beta-minus decay |
| Specific activity | 4.59e+15 Bq/g (1.24e+5 Ci/g) |
| Beta endpoint / mean | 1.16 MeV / 0.389 MeV |
4.21 mm of acrylic stops the 1.16 MeV endpoint
Katz–Penfold fit to the 1.16 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 | 4.21 |
| aluminum | 1.84 |
| water | 4.97 |
| glass | 1.99 |
| Shield material | Fraction of beta energy converted to X-rays |
|---|---|
| acrylic (Z ≈ 6) | 0.24% |
| lead (Z = 82) | 3.33% |
Activity over months and years
Ten half-lives is 50.1 days — a storage problem rather than a disposal one, with 1.2e-20% of today's activity still there after a year. The mean life 1/λ is 7.23 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 | 16.6 days |
| Time to fall to 1 % | 33.3 days |
| Time to fall to 0.1 % | 49.9 days |
Limits of these range figures
- 4.21 mm of acrylic for the 1.16 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Beta and decay calculators for Bi-210
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.