Radioactive half-life is the time it takes for half of a sample of unstable atoms to decay into more stable atoms. It matters because radioactive decay works like a natural clock that can measure time far beyond ordinary human records. Chemists, geologists, and archaeologists use half-life to estimate the ages of fossils, rocks, artifacts, and once-living materials.
The key idea is that the amount of parent isotope decreases in a predictable exponential pattern.
In radioactive dating, scientists compare how much radioactive parent isotope remains with how much stable daughter product has formed. After one half-life, 1/2 of the parent remains, after two half-lives, 1/4 remains, and after three half-lives, 1/8 remains. Carbon-14 dating is useful for once-living materials because living organisms take in carbon, but after death the carbon-14 slowly decays.
Different isotopes are used for different dating ranges because each isotope has its own half-life.
Understanding Chemistry: Half-Life and Radioactive Dating
Radioactive decay begins inside an unstable atomic nucleus. The nucleus has an arrangement of protons and neutrons that can change into a more stable arrangement. During that change, it may release a particle or energy.
No one can predict the exact moment when one particular atom will decay. Its decay is random. A large group of identical atoms behaves predictably because each atom has the same small chance of decaying during a given period.
This is why a sample can act as a reliable clock even though its individual atoms are unpredictable. A half-life describes the behavior of the whole group, not a deadline for every atom.
Carbon-14 forms high in the atmosphere when radiation from space changes nitrogen atoms. It becomes carbon dioxide, which plants absorb during photosynthesis. Animals obtain carbon by eating plants or other animals.
While an organism is alive, it exchanges carbon with its surroundings, so its carbon-14 level stays close to the level in the atmosphere. When it dies, this exchange stops. The carbon-14 already in its tissues continues to decay, but no new carbon enters.
Wood, bone, cloth, paper, seeds, and charcoal can therefore preserve a record of time since death. Carbon dating measures the death of the organism, not necessarily the time when an object was made or used.
Modern laboratories often count the remaining carbon-14 atoms directly with a machine called an accelerator mass spectrometer. This method can work with very small samples. Scientists must prepare samples carefully because contamination can seriously change a result.
A newer source of carbon, such as glue on a museum object or plant roots in buried soil, can make a sample seem younger. Older carbon from limestone, groundwater, or fossil fuels can make it seem older.
Researchers remove surface material, test several samples when possible, and compare the result with the object’s location and history. A date is usually reported as a range because every measurement has uncertainty.
Carbon-14 levels in the atmosphere have not stayed perfectly constant through history. Changes in solar activity, Earth’s magnetic field, and human activity have affected them. Scientists correct for this using calibration curves made from materials of known age, especially tree rings.
Each ring represents one year of growth, so long tree-ring records provide a comparison scale for carbon dates. Beyond the useful range of carbon-14, too little remains for a dependable measurement. Scientists then choose other radioactive clocks.
Potassium-40 can help date very old volcanic rocks. Uranium isotopes can date minerals that formed long ago. A strong dating conclusion depends on choosing the right isotope, understanding how the sample formed, and checking whether it remained chemically unchanged over time.
Key Facts
- Half-life, t1/2, is the time required for half of the radioactive parent atoms in a sample to decay.
- Fraction remaining after n half-lives: remaining fraction = (1/2)^n.
- Number of half-lives: n = elapsed time / t1/2.
- Amount remaining: N = N0(1/2)^n, where N0 is the starting amount and N is the amount left.
- Radioactive decay is exponential, so equal time intervals remove equal fractions, not equal amounts.
- Carbon-14 has a half-life of about 5730 years and is mainly used to date once-living materials up to about 50,000 years old.
Vocabulary
- Half-life
- The time needed for half of the radioactive atoms in a sample to decay.
- Parent isotope
- The original unstable radioactive isotope that decays over time.
- Daughter isotope
- The product isotope formed when a parent isotope undergoes radioactive decay.
- Exponential decay
- A decrease in which the same fraction of a quantity is removed during each equal time interval.
- Radiometric dating
- A method of finding age by measuring the ratio of parent isotopes to daughter isotopes in a sample.
Common Mistakes to Avoid
- Treating half-life as a constant amount lost each time is wrong because decay removes a constant fraction, not a constant mass or number of atoms.
- Using the wrong isotope for the age range is wrong because each radioactive isotope is useful only over times comparable to its half-life.
- Confusing parent and daughter atoms is wrong because the parent decreases while the daughter usually increases as decay happens.
- Assuming carbon-14 can date any old rock is wrong because carbon-14 dating works best for once-living materials and is not suitable for very ancient rocks.
Practice Questions
- 1 A sample starts with 80.0 g of a radioactive isotope. Its half-life is 10.0 years. How many grams remain after 30.0 years?
- 2 Carbon-14 has a half-life of 5730 years. A bone contains 25.0 percent of its original carbon-14. About how old is the bone?
- 3 A fossil is estimated to be millions of years old. Explain why carbon-14 would not be a good isotope to date it, and describe what kind of isotope would be better.