Earth and Space Science / Unit 5: Weathering, Erosion and Earth's History
5.6 Absolute Dating and Half-Life
Notes
Absolute dating gives an age in years using radioactive decay.
- A half-life is the time for half of a radioactive isotope to decay. It is constant.
- Number of half-lives $\displaystyle n = \frac{\text{time}}{\text{half-life}}$. Remaining fraction $\displaystyle = \left(\frac{1}{2}\right)^n$.
- Example: carbon-14 (half-life 5,730 years). A sample has 25% left: 2 half-lives, age $= 2 \times 5730 = 11{,}460$ years.
- Carbon-14 dates organic material up to about 50,000 years; uranium-238 (half-life 4.5 billion years) dates very old rocks.
- Date igneous rocks directly; sedimentary layers are dated using igneous layers above and below.
Practice
A radioactive isotope has a half-life of 10,000 years. After 30,000 years, what fraction remains?
Three half-lives: $\displaystyle \left(\frac{1}{2}\right)^3 = \frac{1}{8}$.
A fossil bone has 12.5% of its original carbon-14. Its age is about (half-life 5,730 years):
12.5% is $\displaystyle \frac{1}{8}$, three half-lives: $3 \times 5730 = 17{,}190$.
Carbon-14 is NOT useful for dating a 200-million-year-old rock because:
Half-life is too short for such old samples.
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