Radiometric Dating Age
Age of a rock from parent and daughter isotopes.
Formula
Variables
Example
Equal parent and daughter means exactly one half-life has passed
How it works
Radiometric dating estimates how long a mineral or rock has been closed to isotope movement by comparing the amount of a radioactive parent isotope left with the amount of stable daughter product formed. The key idea is that parent atoms decay exponentially, so the daughter-to-parent ratio grows in a predictable way; rearranging the decay law gives t = (1/λ) ln(1 + D/P). This works only if the isotope system has behaved as a closed system and the initial daughter amount has been accounted for or is negligible in the specific dating method.
When to use it
Use this when dating rocks, minerals, meteorites, or sediments with a known parent-daughter radioactive decay pair such as uranium-lead, potassium-argon, or rubidium-strontium. It is most useful in geology and geochronology when you know the decay constant and have measured the present parent and radiogenic daughter quantities.
Worked example, step by step
Suppose a mineral contains 80,000 parent atoms and 240,000 daughter atoms from the same decay system. Given: P = 80,000, D = 240,000, and λ = 1.55 × 10^-10 yr^-1 Step 1: Compute the ratio D/P = 240,000 / 80,000 = 3 Step 2: Add 1: 1 + D/P = 1 + 3 = 4 Step 3: Take the natural log: ln(4) ≈ 1.3863 Step 4: Divide by λ: t = 1.3863 / (1.55 × 10^-10) Step 5: t ≈ 8.94 × 10^9 years Final answer: the mineral is about 8.9 billion years old.
Common mistakes to avoid
- Using the total daughter atoms when some daughter isotope may have been present initially
- Mixing units for λ and time, such as using seconds^-1 with years for the answer
- Forgetting that the logarithm is natural log, not base-10 log
Did You Know?
Uranium–lead dating of zircon crystals is how we know the Earth is about 4.54 billion years old.
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