Radiometric dating and isochrons

Meteorites are the reason we know the Solar System is about 4,567 million years old. The age comes from radiometric dating: measuring how far radioactive atoms in a rock have decayed. This explainer shows how the clock works, why scientists plot an isochron rather than trusting a single measurement, and how lead in meteorites gave the age of the Earth itself.

1. Step 1 of 7

   Atoms that change at a steady rate

   Most atoms are stable, but some isotopes, versions of an element with a particular number of neutrons, are radioactive. A radioactive parent atom eventually changes into a different daughter atom. Rubidium-87, for example, becomes strontium-87 when a neutron in its nucleus turns into a proton and gives out an electron.

   No one can predict when any one atom will decay, but in a large number of atoms the rate is fixed, set by the nucleus itself. Heat, pressure and chemistry on Earth do not change it measurably. That steadiness is what makes radioactive atoms usable as clocks.

2. Step 2 of 7

   The half-life

   The half-life is the time it takes for half of the parent atoms in a sample to decay. After one half-life, half remain; after two, a quarter; after three, an eighth. The daughter atoms build up in step, so the ratio of daughter to parent climbs steadily and predictably with time.

   Different isotopes have wildly different half-lives, from fractions of a second to many billions of years. Long-lived ones such as uranium-238, with a half-life of about 4,470 million years, suit the oldest rocks. Short-lived ones such as aluminium-26, at about 720,000 years, are only useful for events in the first few million years of the Solar System, before nearly all of it had gone.

3. Step 3 of 7

   The problem: what was there at the start?

   If every rock started with no daughter atoms at all, dating would be easy: measure the daughter-to-parent ratio and read off the age. But most rocks begin with some daughter atoms already mixed in. Strontium-87, for example, is present in almost all rock from the moment it forms.

   So a single measurement is ambiguous. A rock with a lot of strontium-87 might be very old, or it might simply have started with a lot. To get a reliable age, scientists need a way to separate the daughter atoms made by decay from those that were there from the start. The isochron method does exactly that.

4. Step 4 of 7

   The isochron idea: start in a flat line

   When a rock crystallises from a melt, its different minerals take in different amounts of rubidium: feldspar takes a lot, pyroxene little. But they all inherit the same proportion of strontium-87 to the stable isotope strontium-86, because minerals cannot sort isotopes of the same element by chemistry.

   Plot each mineral on a graph with its rubidium-87 to strontium-86 ratio along the bottom and its strontium-87 to strontium-86 ratio up the side. At the moment the rock forms, all the points lie on a flat line: same height, different positions. Dividing by the stable strontium-86 is the trick that makes points from different minerals comparable.

5. Step 5 of 7

   Time tilts the line

   As time passes, rubidium-87 in each mineral decays to strontium-87. Each point moves a little to the left, because it loses rubidium, and upwards, because it gains strontium-87. A mineral with twice as much rubidium gains twice as much strontium-87, so the points move in proportion and stay on a straight line.

   That line simply rotates around its left-hand end, where a mineral with no rubidium would sit unchanged. The longer the time, the steeper the line. This line of equal age is the isochron, from Greek words meaning equal time.

6. Step 6 of 7

   Reading the age

   Now the method pays off. The slope of the line depends only on how much time has passed, so it gives the age. Where the line meets the left-hand axis, the intercept, gives the starting strontium ratio, which no longer needs to be guessed. The method also checks itself: if the points do not fall on a straight line, the rock has been disturbed, for example by heating or alteration, and the age cannot be trusted.

   The same idea works for other parent–daughter pairs, such as samarium-147 to neodymium-143 and the two uranium–lead decays. Meteorites dated this way give ages from about 4,567 million years for the oldest solids to a few hundred million years for some rocks from Mars.

7. Step 7 of 7

   Lead, meteorites and the age of the Earth

   Uranium decays to lead by two routes at different speeds: uranium-238 to lead-206 and uranium-235 to lead-207. Comparing the two lead isotopes gives an age without needing to measure the uranium at all, the lead–lead method. In 1956 Clair Patterson plotted lead from several meteorites, including the almost uranium-free troilite of the Canyon Diablo iron, and found they lay on one isochron with an age of about 4.55 billion years. Lead from Earth's ocean sediments fell on the same line, so Earth shared that age.

   Today's best figure comes from lead–lead dating of CAIs, the first solids, which gives about 4,567.3 million years. Short-lived isotopes such as aluminium-26 then act as a stopwatch for the next few million years, putting chondrules, iron cores and the first lavas in order.

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See where these events sit in deep time on the 4.6-billion-year timeline.