Radiocarbon Dating
Radiocarbon dating (¹⁴C dating) is a radiometric technique used to determine the age of organic materials up to approximately 50,000 years old by measuring the decay of the radioactive carbon isotope ¹⁴C. Living organisms continuously incorporate ¹⁴C from the atmosphere through photosynthesis and respiration; at death, ¹⁴C incorporation ceases and the remaining ¹⁴C decays at a known rate with a half-life of 5,730 years. Developed by Willard Libby in 1949, for which he received the 1960 Nobel Prize in Chemistry, radiocarbon dating revolutionized archaeology, geology, and environmental science by providing absolute ages for recent geological and archaeological materials.
Key Formula
t = (t_half / ln2) × ln(N0 / N)
LaTeX: t = \frac{t_{1/2}}{\ln 2} \ln\left(\frac{N_0}{N}\right)
| Symbol | Meaning | Unit |
|---|---|---|
| t | Age of the sample | years |
| t_{1/2} | Half-life of ¹⁴C | years (5,730) |
| N_0 | Initial quantity of ¹⁴C atoms at time of death | atoms |
| N | Remaining quantity of ¹⁴C atoms in sample | atoms |
Worked Example
Problem
A charcoal sample from a hearth contains 25% of the ¹⁴C activity found in living wood. Estimate the age of the sample. (Half-life of ¹⁴C = 5,730 years)
Solution
Step 1: The ratio N/N₀ = 0.25, meaning 25% of the original ¹⁴C remains. Step 2: Use the decay equation: t = (t₁/₂ / ln 2) × ln(N₀/N) Step 3: t = (5730 / 0.6931) × ln(1 / 0.25) Step 4: t = 8,267 × ln(4) Step 5: t = 8,267 × 1.3863 Step 6: t = 11,459 years
Answer
The charcoal is approximately 11,460 years old (2 half-lives have elapsed, consistent with the 25% remaining)
Comparison of Radiometric Dating Methods
| Method | Isotope | Half-Life | Dating Range | Material Dated |
|---|---|---|---|---|
| Radiocarbon | ¹⁴C → ¹⁴N | 5,730 yr | Up to ~50,000 yr | Wood, bone, charcoal, shell |
| Potassium-Argon | ⁴⁰K → ⁴⁰Ar | 1.25 Ga | 100,000 yr–4.5 Ga | Volcanic minerals (feldspar, mica) |
| Uranium-Lead | ²³⁸U → ²⁰⁶Pb | 4.47 Ga | 1 Ma–4.5 Ga | Zircon, monazite crystals |
| Rubidium-Strontium | ⁸⁷Rb → ⁸⁷Sr | 48.8 Ga | 10 Ma–4.5 Ga | Granites, metamorphic rocks |
| Thermoluminescence | Trapped electrons | N/A (reset by heat) | 1,000–500,000 yr | Pottery, burnt flint, sediment |
Interactive Tools
Wolfram Alpha — Radioactive Decay Calculator
Compute remaining activity, elapsed time, and decay constants for radiocarbon and other isotopes.
Open ToolCALIB Radiocarbon Calibration Program
Official calibration tool that converts raw radiocarbon ages to calendar years using IntCal calibration curves.
Open ToolKhan Academy — Radioactive Decay and Half-Life
Worked video example of radiocarbon age calculations with half-life decay equations.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Fossil
A fossil is the preserved remains, trace, or impression of a once-living organism, typically found in sedimentary rock and dating to more than 10,000 years ago. Fossilization requires rapid burial by sediment, which prevents decay and allows mineral replacement of organic tissues (permineralization), leaving a durable record of past life. Fossils are the primary evidence for reconstructing the history of life on Earth, documenting evolutionary relationships, ancient environments, and the timing of major biological events through the fossil record.
Geologic Time Scale
The Geologic Time Scale (GTS) is the internationally standardized chronological framework that divides Earth's 4.54-billion-year history into hierarchical time units—eons, eras, periods, epochs, and ages—based on stratigraphic evidence, fossil assemblages, and radiometric dating. The boundaries between units correspond to major geological or biological events such as mass extinctions, sea-level changes, or tectonic reorganizations. The GTS is maintained by the International Commission on Stratigraphy (ICS) and is essential for communicating geological ages, correlating rock formations globally, and understanding Earth's evolutionary and environmental history.
Stratigraphic Layer
A stratigraphic layer (stratum, plural strata) is a single bed or layer of sedimentary rock, volcanic ash, or other deposited material that was laid down during a specific interval of geological time, distinguished from adjacent layers by differences in composition, texture, or fossil content. The principle of superposition, established by Nicolas Steno in 1669, states that in an undisturbed sequence, lower layers are older than upper ones, making stratigraphy the primary method for establishing relative geological time. Correlation of strata across regions using index fossils and radiometric dating allows geologists to reconstruct the geological history of continents and oceans.
The term combines "radio-" (relating to radioactivity, from Latin "radius," ray) with "carbon" (from Latin "carbo," charcoal). The method was invented and named by Willard Frank Libby at the University of Chicago in 1949. The unit "BP" (Before Present) used in radiocarbon results is standardized to 1950 CE, the year of the method's publication.