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.
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.