All the work that geologists do is to tell a story about the Earth's history that is ever more true. A hundred years ago, we had little idea of how long the story is—we had no good yardstick for time. Today, geologic time can be mapped nearly as well as the rocks themselves. For that we can thank radioactivity, discovered at the turn of the last century.
A hundred years ago, we had only the vaguest ideas about the age of rocks and of the Earth. Obviously most rocks are very old indeed—there is evidence in the geologic record of a long history of events like erosion, burial, fossilization, uplift. Judging from the imperceptible rate at which they happen today, each of those events must take many thousands of years. It is that insight, first expressed in 1785, that made James Hutton the father of geology.
So we knew about "deep time," but we needed a precise tool, some sort of clock, to begin to measure it. In 1896, Henri Becquerel's accidental discovery of radioactivity gave us that clock. Some atoms, we learned, are built a little different from the usual atoms of their species. They decay, that is, they spontaneously change to another type of atom while giving off a burst of radiation.
Atoms of potassium, for instance, come in three weights, depending on whether they have an extra neutron or two—it's the number of protons they have that makes them potassium. Potassium-39 and potassium-41 are stable, but potassium-40 undergoes a form of decay that turns it to argon-40. That decay takes place at a precisely constant rate, such that half of the atoms present decay in 1,277 million years.
Consider this analogy: a barbecue grill full of burning charcoal. The charcoal burns at a steady rate, and if you measure how much charcoal is left and how much ash has formed, you can tell how long ago the grill was lit.
And there's your geologic clock. If you can figure out how much potassium-40 has decayed, you can tell how long ago the rock formed. Finding the ages of rocks by measuring their radioactive elements is called radiometric dating. Of course the details get pretty hairy (for more see the dating methods list), but the principle is simple.
Bertram Boltwood first tried this method in 1907. He proposed that the radioactive element uranium decayed into lead, and simply measured total uranium and total lead in a set of ancient rocks. The results were astonishing—his rocks appeared to be more than 2 billion years old. Later we learned that doing radiometric dating right is a delicate and complex procedure, full of sources of error. Boltwood was lucky to find an element for which his crude method happened to work.
You'll notice that he didn't need to actually measure radiation. Radiometric dating from the start was really a matter of chemistry. Nowadays we prepare rock samples and run them through a mass spectrometer, which sifts them atom by atom according to weight as neatly as one of those coin-sorting machines. And radiometric dating has underlain the whole century of progress we have made on Earth's true history.
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And what happened in those billions of years? That's enough time to fit all the geologic events we ever heard of, with billions left over. But with radiometric dating tools we've been busy mapping deep time, and the story is getting more accurate every year.