Dating Formula: t = (t½ / ln2) × ln(A₀ / A)
¹⁴C Half-life: 5,730 years
Living Organisms: ~15.3 dpm/g carbon (modern standard)
Disintegrations per minute per gram of carbon
Standard = 15.3 dpm/g (living organisms in 1950)
Radiocarbon dating, also known as carbon-14 dating, is a revolutionary method for determining the age of organic materials up to about 50,000 years old. Developed by Willard Libby in 1949 (Nobel Prize 1960), this technique has transformed archaeology, geology, and paleontology by providing absolute dates for ancient artifacts and fossils.
The method relies on measuring the ratio of radioactive ¹⁴C (carbon-14) to stable¹²C (carbon-12) in organic samples. Living organisms constantly exchange carbon with the environment, maintaining a steady ¹⁴C/¹²C ratio. After death, ¹⁴C decays while ¹²C remains constant, allowing age calculation from the remaining ¹⁴C activity.
Cosmic rays collide with atmospheric nitrogen, producing radioactive carbon-14:
¹⁴N + n → ¹⁴C + p (neutron capture)
¹⁴C oxidizes to CO₂ and mixes into the atmosphere and oceans
Living organisms absorb ¹⁴C through:
Once an organism dies, it stops exchanging carbon with the environment:
¹⁴C → ¹⁴N + β⁻ + ν̄ₑ (beta decay)
Half-life: 5,730 ± 40 years. After each half-life, ¹⁴C activity decreases by 50%.
Measure current ¹⁴C activity and calculate age using decay equation:
t = (t₁/₂ / ln2) × ln(A₀ / A)
Where t₁/₂ = 5730 years, A₀ = initial activity, A = current activity
Age Calculation Formula:
t = (t1/2 / ln2) × ln(A₀ / A)
t = Age of sample (years)
t1/2 = Half-life of ¹⁴C = 5,730 years
ln2 = Natural logarithm of 2 ≈ 0.693147
A₀ = Initial ¹⁴C activity (living organisms) = 15.3 dpm/g
A = Current ¹⁴C activity (measured in sample) dpm/g
A = A₀ × e-λt
λ = Decay constant = ln2 / t1/2 = 1.21 × 10⁻⁴ year⁻¹
e = Euler's number ≈ 2.71828
📊 Activity Units:
Problem: A linen sample from the Dead Sea Scrolls shows a ¹⁴C activity of 13.5 dpm/g. Calculate the age of the scroll.
Given Information:
Calculation:
t = (5730 / ln2) × ln(A₀ / A)
t = (5730 / 0.693) × ln(15.3 / 13.5)
t = 8268 × ln(1.133)
t = 8268 × 0.125
t ≈ 1,033 years
Result:
The scroll is approximately 1,033 years old, dating to around 991 CE (calculated from 2024). This agrees well with paleographic estimates of the Dead Sea Scrolls (200 BCE - 100 CE) when accounting for calibration curves and uncertainties.
Verification:
After 1033 years: A = 15.3 × e-0.000121×1033 = 15.3 × 0.882 ≈ 13.5 dpm/g ✓
Atmospheric ¹⁴C levels have not been constant over time due to:
Radiocarbon ages are calibrated using:
Date artifacts, settlement layers, ancient manuscripts, Egyptian mummies, and human remains. Revolutionized understanding of human prehistory and cultural chronology.
Determine ages of sediments, volcanic eruptions, ice cores, and fossil remains. Study climate change, glacial cycles, and extinction events.
Verify authenticity of paintings, sculptures, and antiques. Detect modern forgeries by identifying post-1950 nuclear bomb spike in ¹⁴C levels.
Track carbon cycle dynamics, ocean circulation, groundwater ages, and soil carbon turnover. Study past climate conditions and ecological changes.
Half-life
5,730 ± 40 years
Living Activity
15.3 dpm/g C
Valid Range
500-50,000 years
Decay Constant
1.21 × 10⁻⁴ yr⁻¹