Learning outcomes
- Describe the principle of carbon-14 dating.
- Explain why carbon intake stops at death.
- Relate remaining activity to age.
- Recognise assumptions and limitations.
10.1 Carbon in living organisms
Living organisms continually exchange carbon with the environment through food, respiration and photosynthesis. This includes a small proportion of radioactive carbon-14. While the organism is alive, the carbon-14 proportion remains approximately linked to the environment.
Carbon-14 decays by beta-minus emission. Its long half-life makes it useful for dating once-living material over archaeological timescales.
10.2 What changes at death
When an organism dies, it no longer takes in new carbon. Existing carbon-14 nuclei continue to decay, so the activity per unit mass decreases over time. Stable carbon remains, allowing the remaining carbon-14 proportion or activity to be compared with a living reference.
A lower corrected activity indicates that more half-lives have elapsed and the material is older. The method applies to once-living material such as wood, bone or cloth made from natural fibres, not directly to an ordinary ancient metal object.
10.3 Estimating age
Measure the sample’s carbon-14 activity, correct for background and compare with the expected initial activity of similar living material. Determine the fraction remaining, translate it into a number of half-lives, and multiply by the carbon-14 half-life.
For example, one-quarter of the initial activity corresponds to two half-lives. Exact work may require calibration and correction, but O Level questions usually focus on the half-life principle.
10.4 Limitations and uncertainty
Contamination by newer carbon can make a sample appear younger, while loss or addition of material can alter the measured activity. Very old samples have activity close to background, making percentage uncertainty large.
The initial carbon-14 proportion has varied over time, so real dating uses calibration. These limitations do not invalidate the method; they explain why careful sample preparation and comparison data are needed.
Worked examples
Simple age
A sample has one-eighth the activity of living material. One-eighth = (1/2)³, so three half-lives have elapsed. Using 5730 years gives about 17 190 years.
Half activity
A wooden sample has half the corrected activity of modern wood. Its age is approximately one carbon-14 half-life, subject to calibration and uncertainty.
Practical focus
Investigation
Use a decay-curve simulation with “living” initial activity and a hidden sample age. Measure simulated counts with background, calculate the corrected fraction remaining and infer the age. Discuss how low counts affect uncertainty.
Examination guidance
- State that carbon intake stops when the organism dies.
- Compare corrected activity with a living or initial reference.
- Use carbon-14 only for once-living material.
- A smaller activity means an older sample.
- Mention contamination or low count rate when evaluating reliability.
Check your understanding
- Why is carbon-14 activity approximately maintained while an organism is alive?
- A sample has 1/4 of its initial activity. How many half-lives have elapsed?
- Why are extremely old samples difficult to date accurately?
Answers
- The organism continually exchanges carbon with its environment.
- Two half-lives.
- The carbon-14 activity becomes very close to background, giving large relative uncertainty.
