About

Radiometric dating provides a chronometer for the ancient world. Carbon-14 (C-14) dating is the primary method used to determine the age of organic materials up to approximately 50,000 years old. The principle relies on the unstable isotope Carbon-14, which is constantly produced in the upper atmosphere and absorbed by living organisms. Upon death, the organism ceases to absorb C-14, and the isotope decays into Nitrogen-14 at a constant rate. By measuring the remaining ratio of C-14 to the stable C-12, and comparing it to the atmospheric standard, we can calculate the time elapsed since death. This tool applies the exponential decay law, assuming a standard half-life of 5,730 years (Cambridge half-life).

Formulas

The age t is derived from the decay equation:

N(t) = N₀ e^−λt

Solving for t:

t = −ln(N/N₀)λ

Where the decay constant λ is related to the half-life:

λ = ln(2)t_1/2 ≈ 1.21 × 10⁻⁴

Reference Data

Isotope	Half-Life (t_1/2)	Effective Dating Range
Carbon-14 (146C)	5,730 years	100 - 50,000 years
Uranium-235	704 million years	> 10 million years
Potassium-40	1.25 billion years	> 100,000 years
Rubidium-87	49 billion years	> 10 million years

Frequently Asked Questions

After approximately 9-10 half-lives (roughly 50,000 to 60,000 years), the amount of remaining C-14 becomes so minuscule that it is indistinguishable from background radiation and instrumentation noise, making accurate dating impossible.

This ratio represents the percentage of Carbon-14 remaining in the sample compared to a fresh, living sample. If a sample has 50% remaining, exactly one half-life has passed.

Yes. The "Suess Effect" (burning fossil fuels) releases old carbon depleted of C-14 into the atmosphere, while nuclear testing in the 20th century doubled atmospheric C-14. Modern calibration curves (IntCal) correct for these fluctuations.

No. Dinosaurs went extinct 65 million years ago. All C-14 in their remains decayed millions of years ago. Paleontologists use Uranium-Lead or Potassium-Argon dating for such geological time scales.