Radiometric dating works only if the clock fits the job. A clock must tick slowly enough that some parent remains, fast enough that daughter has built up, and it must have started at the event you want to date.
| Clock | Half-life | Good for | Dates |
|---|---|---|---|
| Carbon-14 → nitrogen-14 | 5,730 years | up to about 50,000 years | wood, bone, charcoal, shell: when the organism died |
| Potassium-40 → argon-40 | 1.25 billion years | about 100,000 years and older | volcanic rock and ash: when it cooled and trapped argon |
| Uranium-235 → lead-207 | 704 million years | about 1 million years and older | zircon crystals: when they crystallized |
| Uranium-238 → lead-206 | 4.47 billion years | about 1 million years to Earth's age | zircon crystals: when they crystallized |
| Rubidium-87 → strontium-87 | 48.8 billion years | about 10 million years and older | old igneous and metamorphic rocks |
Why it works
After about 10 half-lives, only $\tfrac{1}{1,024}$ of the parent remains, too little to measure well: that sets the upper limit. Too few half-lives and too little daughter has formed: that sets the lower limit. And the clock must start at the event: an organism stops taking in carbon-14 when it dies; a crystal traps uranium and shuts out lead when it forms; a lava flow lets argon gas escape until it cools solid. (Potassium-40 also decays to calcium-40, which labs account for.) Using two uranium clocks in one zircon gives two independent ages that must agree, a built-in check.
Key idea
Match the clock to the material and age: carbon-14 for remains up to about 50,000 years; potassium–argon for volcanic rock; uranium–lead in zircon for millions to billions of years. Sedimentary rock is dated by the igneous rocks around it.
Worked examples
Worked example: Pick the clock
Which clock would date a layer of volcanic ash about 2 million years old?
- Carbon-14 is far too short-lived, and ash was never alive.
- Potassium–argon (or uranium–lead in zircons from the ash) fits: volcanic material, millions of years old.
Answer: Potassium–argon, or uranium–lead in zircon.
Worked example: The carbon-14 limit
How many half-lives of carbon-14 pass in 50,000 years, and what fraction is left?
- $50,000 \div 5,730 \approx 8.7$ half-lives.
- $\left(\tfrac12\right)^{8.7} \approx 0.0024$: about 0.24% remains, near the limit of measurement.
Answer: About 8.7 half-lives; about 0.24% left.
Common mistake
It seems natural to date a sandstone by dating its grains. But each grain is a piece of an older rock, and its clock started when that rock crystallized, perhaps a billion years before the sand was laid down. Sedimentary layers are dated indirectly, by the ash beds, lava flows and dikes above, below and through them. Check: ask when the clock in your sample started.
See isotopes and half-lives up close in the Build an Atom lab.