Radiometric dating and the age of the Earth.

Step 1 of 7

The clock starts at zero

Zircon is a mineral of zirconium, silicon and oxygen that grows as tiny, hard crystals in cooling magma, especially in granite. The Scene has one such crystal, and Zoom to the atoms is at Atoms inside: the glowing atoms are uranium, and the grey ones lead. Time since the crystal formed is at Just formed.

Step 2 of 7

A half-life

From then on the uranium decays and lead appears. Uranium-238 passes through a chain of fourteen decays, by way of thorium, radium and radon, to stable lead-206. Every step after the first is fast by comparison, so the pace is set by uranium-238 itself, with a half-life of 4.47 billion years: after that time half of any starting amount is left.

Each uranium atom that decays becomes one lead atom, so the crystal keeps a record of both what is left and what has gone. You don’t need to know how much uranium there was at the start: count the lead atoms for each uranium atom still there. The Clock is fixed at Uranium-238.

Step 3 of 7

Reading the age

After $n$⁠ half-lives $2^{-n}$⁠ of the uranium is left, and each atom left has $2^n - 1$⁠ lead atoms with it. Turn that round and you get the age from the ratio $\dfrac{D}{P}$⁠, the daughter (lead) atoms for each parent (uranium) atom:

$t = t_{1/2} \cdot \log_2\left(1 + \frac{D}{P}\right)$$t =$$t_{1/2} \cdot \log_2\left(1 + \frac{D}{P}\right)$⁠

In a laboratory the rock is crushed, the zircons sorted out, and an instrument called a mass spectrometer counts the uranium and lead isotopes. Here the Clock is on Uranium-235, which decays to lead-207, and the age is hidden.

Step 4 of 7

A spent clock

The same crystal carries two more clocks: Uranium-235 decays to lead-207 with a half-life of 0.704 billion years, and Thorium-232 to lead-208 with a half-life of 14 billion years. Each makes its own isotope of lead, so all three can be read at once. The crystal here is 4.4 billion years old, the Oldest crystal, and the chart beside the Scene shows the age each clock reads.

Step 5 of 7

Which clock

A clock reads best when its half-life is not far from the age being measured. Too few half-lives, and hardly any lead has formed; too many, and hardly any uranium is left. Either way a small error in the measurement becomes a large error in the age.

Step 6 of 7

Lead that leaks

A clock is only as good as its seal. Hot fluids, a later heating or damage to the crystal can let some of the lead out, and then the crystal looks younger than it is. The two uranium clocks in one crystal tick at rates six times apart, so they cannot agree by accident.

Step 7 of 7

The age of the Earth

The oldest crystals found, from the Jack Hills of Western Australia, are about 4.4 billion years old. The oldest whole rock, in northern Canada, is about 4.0 billion years old. Time since the crystal formed is at Age of the Earth, 4.54 billion years, but no crystal on Earth is that old.