Radiometric geochronology · the isochron method
Isochron — the age of a rock, plotted from its decaying isotopes.
Seven mineral grains from one cooling event. Each began with the same strontium, then ⁷⁷Rb decayed to ⁷⁷Sr at its own rate. On this plot the grains slide down their evolution tracks while the line through them pivots up about the initial ratio — and its slope is the age. Watch it derive.
Reading time out of a straight line
Rb–Sr · whole-rock & mineralAt crystallisation, every grain shares one strontium.
When the rock cools, its minerals lock in the same ⁷⁷Sr/⁶⁶Sr — the initial ratio. On the diagram they line up flat, differing only in how much rubidium each took up. Time zero is a horizontal line.
Rubidium decays; strontium accrues, atom for atom.
Every ⁷⁷Rb that decays becomes a ⁷⁷Sr. A grain loses horizontal position and gains exactly that much height, sliding down a track of slope −1. Rubidium-rich grains move furthest.
The line stays straight — and its slope is the clock.
Because every grain moves by the same law, they remain colinear, pivoting about the initial ratio. Fit the line, read its slope m, and the age falls out: t = ln(m+1) / λ. No assumptions about starting amounts — the geometry supplies them.
4.51 Ga is a sliver. Rubidium-87 is so patient that the age of the oldest rocks is barely 9.2% of a single half-life — the clock has scarcely started ticking.