Carbon Dating
Specification: OCR A H556 | Section: 6.4.3 Radioactivity — radioactive dating, e.g. carbon-dating | Use: OCR A classroom resource with worked calculations and exam practice
- explain what carbon-14 is and how it is formed in the atmosphere
- describe how carbon-14 enters living organisms and why the activity changes after death
- use half-life and decay equations to estimate the age of archaeological samples
- discuss assumptions, calibration and limitations in radiocarbon dating
- avoid common misconceptions about activity, age and contamination
Big idea: carbon dating does not tell you “how old carbon is”. It estimates when a once-living organism stopped exchanging carbon with the atmosphere.
What is carbon-14?
Carbon-14 is a radioactive isotope of carbon. It has 6 protons and 8 neutrons, unlike the much more common stable isotope carbon-12, which has 6 protons and 6 neutrons.
Carbon-14 is unstable and undergoes beta-minus decay to nitrogen-14.
Its half-life is about 5730 years, which makes it useful for dating once-living material on archaeological timescales.
Carbon-14 is useful because its half-life is long enough that measurable amounts remain for thousands of years, but short enough that its activity changes appreciably over archaeological timescales.
How carbon-14 forms in the atmosphere
High-energy cosmic rays strike the upper atmosphere and produce fast neutrons. Some of these neutrons collide with nitrogen-14 nuclei in the air.
The carbon-14 produced then combines with oxygen to form carbon dioxide, including radioactive ¹⁴CO₂. This mixes throughout the atmosphere.
Source
Cosmic rays generate neutrons in the atmosphere.
Target nucleus
Nitrogen-14 absorbs a neutron and emits a proton.
Product
Carbon-14 enters atmospheric carbon dioxide and joins the carbon cycle.
How living organisms acquire carbon-14
Plants take in carbon dioxide during photosynthesis, so they absorb a mixture of carbon-12 and carbon-14. Animals then eat plants, or eat other animals that ate plants, so carbon-14 passes through food chains.
While an organism is alive, it is continually exchanging carbon with the environment. This means the ratio of carbon-14 to carbon-12 in the organism stays approximately the same as the ratio in the atmosphere.
For basic OCR A calculations, we assume the carbon-14 activity of living tissue is the same as the atmospheric standard at the time the organism was alive.
What changes after death?
Once the organism dies, it stops taking in carbon. No new carbon-14 is added, but the carbon-14 already present continues to decay. So the activity due to carbon-14 falls with time.
Using half-life and activity to estimate age
Carbon dating usually compares the current activity of a sample with the activity expected in living material. Since activity is proportional to the number of undecayed nuclei, the same decay equations apply.
If activity halves, the age increases by one half-life, not “half the half-life”. Students often confuse “half the activity” with “half the time”.
Assumptions, calibration and limitations
Main assumptions
- The organism had the same carbon-14 to carbon-12 ratio as the atmosphere while alive.
- The sample has not been significantly contaminated since death.
- The decay constant for carbon-14 has remained constant.
Why calibration is needed
The atmospheric carbon-14 level has not been perfectly constant through time. Variations in cosmic ray flux, Earth’s magnetic field, solar activity and human activity can change the production or distribution of carbon-14.
So raw radiocarbon ages are often calibrated against independently dated records such as tree rings (dendrochronology).
Contamination
Newer carbon can make a sample appear too young. Older carbon contamination can make it appear too old.
Useful range
Carbon dating works best for once-living material up to around 50 000 years old. Beyond this, too little carbon-14 remains.
Not for rocks
Ordinary radiocarbon dating is not used for ancient igneous rocks because they are not part of the recent biological carbon cycle.
A high-quality OCR A answer often notes both the usefulness of carbon dating for archaeological organic remains and its limitations due to changing atmospheric carbon-14 levels and contamination.
Knowledge Check
- Cosmic rays produce neutrons in the atmosphere
- Neutrons are absorbed by nitrogen-14 nuclei, forming carbon-14 and a proton
- No new carbon is taken in after death
- The existing carbon-14 continues to decay so activity falls
- The atmospheric carbon-14 level has varied over time
- So measured radiocarbon ages need correction against known-age records
Exam-Style Questions
- Wood came from a once-living organism and so exchanged carbon with the atmosphere while alive
- Its carbon-14 activity then decreased after death
- Granite is not once-living biological material in the recent carbon cycle
- So radiocarbon dating is not appropriate for the granite sample
- 12.5% = 1/8 of original activity
- That corresponds to 3 half-lives
- Age = 3 × 5730 = 17 190 years
- The sample had the same carbon-14 proportion as the atmosphere while alive
- The sample has not been contaminated
- The decay constant has remained constant
- Use λ = ln2 / 5730 = 1.21 × 10⁻⁴ y⁻¹
- Use t = (1/λ)ln(A₀/A)
- t = (1 / 1.21 × 10⁻⁴) ln(1/0.30)
- t ≈ 9.9 × 10³ years
- Carbon dating estimates when a once-living organism stopped exchanging carbon with the atmosphere
- That is usually close to time of death, not necessarily time an artefact was made or used
- It relies on assumptions about atmospheric carbon-14 levels and contamination
- Calibration is often needed
- So it gives an estimate or date range, not an exact unquestionable date
Topic Summary
Formation
Carbon-14 is produced when atmospheric nitrogen-14 absorbs a neutron and emits a proton.
Living organisms
While alive, organisms exchange carbon with the environment and keep an approximately constant carbon-14 ratio.
After death
No new carbon enters; carbon-14 decays and the activity falls with time.
Limits
Carbon dating needs calibration and can be affected by contamination and changing atmospheric carbon-14 levels.
Activity and detector count rate
Compare equal carbon masses, or use activity per unit carbon mass. Total activity also scales with the amount of carbon. Detector count rate is not activity: only a fraction of decays are detected. Count-rate ratios follow activity ratios only with matched geometry, efficiency and measurement conditions.
Worked example · subtract background first
Equal carbon masses give gross count rates of 30 and 90 counts per minute for old and living material in the same detector. Background is 10 counts per minute. Net rates are 20 and 80 counts per minute, giving a ratio of ¼. The old sample is two half-lives old: with T½ = 5730 years, age = 11 460 years. Using 30/90 instead would give the wrong age.