Carbon Dating — OCR A Level Physics
Module 6 · Particles and Medical Physics

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

By the end of this topic you should be able to…
  • 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.

Part 1

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.

Decay equation for carbon-14¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄

Its half-life is about 5730 years, which makes it useful for dating once-living material on archaeological timescales.

OCR phrasing

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.

Part 2

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.

Formation reaction¹⁴₇N + ¹₀n → ¹⁴₆C + ¹₁p

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.

Part 3

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.

Key model assumption

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.

Decay lawA = A₀e-λt    and    N = N₀e-λt
Half-life relationshipλt1/2 = ln 2
Part 4

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.

Useful formsA/A₀ = e-λt    and    t = (1/λ) ln(A₀/A)
Worked example 1
A wooden sample has carbon-14 activity 25% of that in living wood. Estimate its age.
25% means the activity is one quarter of the original value.
One quarter corresponds to two half-lives.
Age = 2 × 5730 = 11 460 years.
Worked example 2
A sample has activity 40% of modern living material. Estimate its age using the decay equation.
Use A/A₀ = 0.40 and λ = ln2 / 5730 = 1.21 × 10⁻⁴ y⁻¹.
t = (1/λ)ln(A₀/A) = (1 / 1.21 × 10⁻⁴) ln(1/0.40)
t ≈ 8260 × 0.916 = 7.6 × 10³ years.
Common misconception

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”.

Part 5

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.

Evaluation line

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

Knowledge Check

1
How is carbon-14 formed in the atmosphere?
2 marks
  • Cosmic rays produce neutrons in the atmosphere
  • Neutrons are absorbed by nitrogen-14 nuclei, forming carbon-14 and a proton
2
Why does the carbon-14 activity of a sample decrease after death?
2 marks
  • No new carbon is taken in after death
  • The existing carbon-14 continues to decay so activity falls
3
Why are calibration curves needed in radiocarbon dating?
2 marks
  • The atmospheric carbon-14 level has varied over time
  • So measured radiocarbon ages need correction against known-age records
Exam Practice

Exam-Style Questions

1
Explain why carbon dating can be used for wood from an ancient settlement but not for a granite rock from the same site.
4 marks
  • 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
2
A piece of charcoal has carbon-14 activity 12.5% of that in modern living wood. Estimate the age of the charcoal.
3 marks
  • 12.5% = 1/8 of original activity
  • That corresponds to 3 half-lives
  • Age = 3 × 5730 = 17 190 years
3
State two assumptions made when using carbon dating to estimate the age of a sample.
2 marks
  • 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
4
A sample has carbon-14 activity 30% of modern living material. The half-life of carbon-14 is 5730 years. Use the decay equation to estimate the age of the sample.
4 marks
  • 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
5
A student says, “Carbon dating tells you exactly when something was made.” Evaluate this statement.
5 marks
  • 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.

A = A₀e^-λt
N = N₀e^-λt
λt₁/₂ = ln2
t₁/₂ = 5730 years