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Half-life and carbon dating

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By the end of this lesson you should be able to

  • Describe how the half-life of a radioisotope can be used to tell the time.
  • Explain how carbon dating works.

Hook

Scientists can work out how old a bone, a piece of wood or an ancient campfire is, even when nobody wrote down when it was made.

  • How do you think they do it?
  • Why might it matter to know how old something from the past is?

Talk with a partner for one minute, then watch the video.

Watch: How to Date a Dead Thing · SciShow

More video options

How Does Radiocarbon Dating Work? · Scientific American

Half-life and carbon dating: another explanation

Quick recap: radioisotopes

Some atoms are unstable. Their nucleus has the wrong mix of protons and neutrons, so sooner or later it breaks down and gives off radiation. This is radioactive decay.

An unstable isotope is called a radioisotope. When it decays, it turns into a different, stable atom.

You can never predict when one particular atom will decay. But with millions of atoms, the pattern is very predictable.

Half-life: a clock inside the atom

The half-life is the time it takes for half of the radioactive atoms in a sample to decay.

  • After 1 half-life, ½ is left.
  • After 2 half-lives, ¼ is left.
  • After 3 half-lives, ⅛ is left, and so on.

Each radioisotope has its own half-life. Some are fractions of a second; some are billions of years.

Key idea: the half-life is constant. Heat, cold, pressure or how much you start with make no difference. That is why it works as a clock: if you know the half-life and how much is left, you can work out how much time has passed.

Try it: watch atoms decay

This animation starts with 100 carbon-14 atoms. Click Wait one half-life and watch. Each atom has a 50% chance of decaying in each half-life. The dashed line is what we expect; the solid line is what actually happened.

  1. After 1 half-life, did exactly 50 atoms decay? Click Reset and try again. Is it the same each time?
  2. Can you predict which atom will decay next?
  3. Even though each atom is random, what stays the same about the shape of the graph?
Worked example: using half-life to tell the time

A radioisotope has a half-life of 6 hours. A sample started with 640 radioactive atoms and now has 80. How much time has passed?

Halve until you reach 80: 640 → 320 → 160 → 80. That is 3 half-lives.

Time = 3 × 6 hours = 18 hours.

How carbon dating works

Carbon-14 is a radioisotope of carbon. Its half-life is about 5730 years. It decays into stable nitrogen-14.

1. Made in the airCosmic rays hit nitrogen high in the atmosphere and make carbon-14. It joins with oxygen to make carbon dioxide.
→
2. Taken in while alivePlants take in carbon dioxide. Animals eat the plants. Living things keep the same share of carbon-14 as the air.
→
3. Death stops the top-upWhen the organism dies, it stops taking in carbon. No new carbon-14 arrives.
→
4. The clock ticksThe carbon-14 left inside decays, halving every 5730 years.
→
5. Measure and count backScientists compare the carbon-14 left with a living sample, count the half-lives and work out the age.

So carbon dating works only on things that were once alive (wood, bone, shell, cloth, charcoal). It also has a limit: after about 50 000 years there is too little carbon-14 left to measure. Rocks, and fossils millions of years old, are dated with other radioisotopes that have much longer half-lives.

Worked example: carbon dating a bone

A bone has ⅛ of the carbon-14 found in a living animal. How old is it?

1 → ½ → ¼ → ⅛ is 3 half-lives.

Age = 3 × 5730 = about 17 190 years.

Real science: wasp nests and Kimberley rock art

Rock paintings in the Kimberley region of Western Australia are hard to date, because the paint usually has no carbon in it. Researchers working with the Traditional Owners found a clever way around this: mud wasps sometimes built nests on top of the paintings, or a painting was made over an old nest.

The nests contain tiny pieces of charcoal, which can be carbon dated. A nest on top of a painting must be younger than the painting, so it gives a minimum age. Using this method, scientists found that many paintings in the Gwion style are about 12 000 years old.

ANSTO: dating Aboriginal rock art using mud wasp nests

Self-check

How this works

Pick or type an answer to get feedback. Nothing is saved or sent anywhere; this is just for you.

1. What does half-life mean?

2. A radioisotope has a half-life of 3 hours. A sample starts with 1200 radioactive atoms. How many are left after 9 hours?

Worked solution

9 ÷ 3 = 3 half-lives. 1200 → 600 → 300 → 150 atoms.

3. A piece of ancient cloth has ¼ of the carbon-14 of new cloth. The half-life of carbon-14 is 5730 years. How old is the cloth (in years)?

Worked solution

1 → ½ → ¼ is 2 half-lives. 2 × 5730 = 11 460 years.

4. Why does the carbon-14 "clock" start when a living thing dies?

5. A student wants to use carbon dating to find the age of a 70-million-year-old dinosaur fossil. Why won't it work?

6. In the Kimberley, why did scientists carbon date mud wasp nests instead of the paint itself?

Exit question

In 2–3 sentences, explain to a friend how scientists could tell that a wooden spear is about 5700 years old. Use the words carbon-14, half-life and decay.

Model answer

While the tree was alive it took in carbon-14 from the air. When it was cut down, it stopped taking in carbon, and the carbon-14 began to decay. The spear has about half the carbon-14 of living wood, so one half-life (about 5730 years) has passed.

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