Radioactive dating

Radiometric dating uses the predictable statistical decay of unstable nuclei as a clock. The equation is simple; deciding what event the clock actually dates is the harder part. A reliable age depends on the isotope system, the material and whether parent or daughter atoms have been gained or lost.

The exponential clock

For a radioactive parent population, N(t) = N₀e^-λt, with half-life T½ = ln 2 / λ. If the initial parent amount can be established or inferred, the elapsed time follows from the surviving fraction.

Half-life explorer

Elapsed half-lives

Equal half-life intervals remove equal fractions, not equal numbers. The curve approaches zero continuously.

Parent and daughter isotopes

Many dating methods measure both a radioactive parent and a daughter produced by its decay. Mineral chemistry can be extremely useful because different elements enter a crystal in different proportions when it forms. Modern methods therefore use isotope ratios and internal consistency tests rather than simply measuring “how radioactive” a sample is.

An age refers to a physical or chemical closure event. Later heating, fluids or recrystallization can disturb parent-daughter relationships.

The closed-system requirement

The calculated age assumes the relevant parent and daughter species have behaved as required by the method since the dated event. Heating, weathering, fluid flow or recrystallization can move atoms and disturb the clock. Good geochronology therefore combines isotope measurements with mineralogy, geological context and tests for disturbance.

Choose an isotope system that fits the timescale

Carbon-14 is useful for once-living material over archaeological timescales, but it is not the standard tool for determining the formation age of ancient igneous rocks. Long-lived systems such as uranium-lead or potassium-argon are suited to much older geological events. The material being dated matters just as much as the numerical half-life.

Worked examples

1. Two half-lives

Solution

If 25% of the original parent remains, the sample has passed through 100% → 50% → 25%: two half-lives.

2. Convert fraction to age

Solution

A parent has T½ = 1.25 billion years and 25% remains. Two half-lives have elapsed, so the ideal model age is 2.50 billion years.

3. Spot a broken assumption

Solution

If a mineral lost some daughter isotope during heating, applying the closed-system equation without correction can give a misleading age. The first task is therefore to test whether the isotope system remained closed.