Counting Atomic Clocks
Every radioactive atom is a tiny clock, ticking at a rate set by the fundamental forces. When a mineral crystallizes from magma or precipitates from solution, it traps parent isotopes and starts the clock. As parent atoms decay to daughters, the ratio shifts predictably according to the exponential decay law. By measuring the present-day ratio with a mass spectrometer, geochemists calculate when the clock started.
The Exponential Decay Law
The number of parent atoms decreases as N(t) = N₀ × exp(−λt), where λ = ln(2)/t½. This first-order kinetics is remarkably robust — neither temperature, pressure, nor chemical environment can alter the nuclear decay rate. The daughter atoms accumulate as D* = N₀ × (1 − exp(−λt)), providing a complementary check on the age.
Choosing the Right System
Different isotope pairs suit different timescales. Carbon-14 (t½ = 5730 yr) dates organic material up to ~50,000 years. Potassium-40 (t½ = 1248 Myr) works for volcanic rocks from thousands to billions of years old. Uranium-238 (t½ = 4468 Myr) in zircon crystals provides the gold-standard ages for the earliest Earth. This simulation lets you explore how half-life and elapsed time control dating precision.
Sources of Error
Real geochronology must account for initial daughter contamination, open-system behavior (leaching or addition of parent/daughter), and analytical uncertainties. The isochron method (see companion simulation) elegantly handles unknown initial daughter by analyzing multiple co-genetic samples. Concordia diagrams for U-Pb reveal whether zircons have lost lead, enabling correction for open-system disturbance.