Carbon-14
C-14 · Carbon, Z = 6, A = 14
A gigabecquerel of C-14 is 6.03 mg of material, which follows from a specific activity of 1.66e+11 Bq/g (4.48 Ci/g). Carbon-14 decays by beta-minus decay with a half-life of 5700 years; forty years leaves 99.51% of today's activity and ten thousand years leaves 29.64%.
The beta endpoint is 0.156 MeV, mean 0.0495 MeV over 1 branch. That endpoint stops in 0.241 mm of acrylic or 0.114 mm of glass. Of the beta energy, 0.03% turns into X-rays in acrylic and 0.45% in lead.
Decay is the only handle: forty years leaves 99.51% of today's activity and ten thousand years leaves 29.64%, with ten half-lives at 56,999 years and a mean life of 8,223 years per atom.
Half-life, specific activity and beta endpoint
| Half-life | 5700 years (1.799e+11 s) |
| Decay mode | beta-minus decay |
| Specific activity | 1.66e+11 Bq/g (4.48 Ci/g) |
| Beta endpoint / mean | 0.156 MeV / 0.0495 MeV |
0.241 mm of acrylic stops the 0.156 MeV endpoint
Katz–Penfold fit to the 0.156 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 | 0.241 |
| aluminum | 0.105 |
| water | 0.284 |
| glass | 0.114 |
| Shield material | Fraction of beta energy converted to X-rays |
|---|---|
| acrylic (Z ≈ 6) | 0.03% |
| lead (Z = 82) | 0.45% |
Activity over millennia
Ten half-lives is 56,999 years. On any timescale a facility can be planned over the activity is constant — 99.51% is left after forty years — and the mean life 1/λ is 8,223 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 | 18,935 years |
| Time to fall to 1 % | 37,869 years |
| Time to fall to 0.1 % | 56,804 years |
Limits of these range figures
- 0.241 mm of acrylic for the 0.156 MeV endpoint: a ±10% fit, and not a skin dose.
- What every sheet leaves out, internal dose included.
Beta and decay calculators for C-14
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.