How Do We Know the Earth Is 4.6 Billion Years Old?
― The scientist who found the answer first had to fight "lead dirt" in his lab
There is no record of the Earth's birthday anywhere. We still know its age because rocks hold a clock that never stops. But reading that clock was much harder than it sounds, and the answer took nearly a century of detours.
Your science textbook says "the Earth was born about 4.6 billion years ago." You may half remember it. But it doesn't say who measured it, or how.
A person has a birth certificate. A tree has rings you can count. The Earth has neither.
What is more, the rocks at the Earth's surface have been remade many times by volcanoes and moving crust. Almost none of the rock from its birth is left on the surface.
Only two things made it possible
The element uranium slowly turns into lead over a very long time. Heat and pressure barely change how fast it happens. Measure the ratio of uranium to lead, and you know how much time has passed.
Meteorites are fragments that formed around the Sun at about the same time as the Earth. Unlike Earth's rocks, they were never remade. Measuring their lead let scientists look back to the time of Earth's birth.
But the road to putting these two together was far from smooth. Let's take it step by step.
The first answer was "tens of millions of years"
In the 19th century, the British physicist Lord Kelvin pictured the Earth as a hot ball that was cooling down. How long would a molten ball take to cool to today's temperature? From this calculation he estimated the Earth's age at 20 million to 400 million years. Late in life he cut it further, to a few tens of millions of years.
Geologists, and Darwin, who studied evolution, were troubled. Layers of rock seemed to need far more time to pile up, and living things seemed to need far more time to change. The physics and the evidence in the rocks did not agree.
What settled it was radioactivity, discovered in 1896. Uranium and other elements in rocks were giving off heat all the time. The assumption of a ball that only cools collapsed. And radioactivity carried not only heat but also a "clock."
How does the uranium clock tick?
A kind of uranium called uranium-238 turns half of itself into lead-206 in about 4.47 billion years. This time to fall by half is called the half-life. After the same time again, half of what is left changes. A quarter of the original remains.
Look at Figure 1. The solid line on the left shows the share of uranium still left. Move the slider below to advance time. In the column on the right, the lead part at the top grows and the uranium part at the bottom shrinks. If a rock had no lead when it solidified, the ratio of lead to uranium lets you work out the time since then.
In fact, uranium has another kind, uranium-235. It is a "fast clock" that halves in about 700 million years and turns into lead-207. Reading two clocks of different speeds in the same rock lets the two answers check each other.
What got in the way was lead, found everywhere
In the late 1940s, a young American researcher, Clair Patterson, set out to use this clock on meteorites. But every time he measured, the lead values came out scattered. Lead was already all around him, long before it was in the sample.
It was in dust, glassware, water, air, and even his own hair. At the time, lead was also mixed into petrol, so lead drifted in the air itself. Patterson scrubbed his rooms thoroughly and cleaned his equipment with acid. Even that was not enough, so he built a low-dust lab fed with filtered outside air.
It is said that in 1953 he was finally able to measure accurately the lead in an iron meteorite that fell in Arizona, in the United States. The age of the Earth he published in 1956 was about 4.55 billion years. As Figure 2 shows, that is more than 100 times older than Kelvin's answer. Later measurements have hardly changed this value.
After his fight with lead in the lab, Patterson began to ask where all this lead came from. He measured seawater and Antarctic ice, and is said to have shown that much of the lead in the air came from the lead mixed into petrol. This work fed into the move in many countries to remove lead from petrol. Research into the Earth's age ended up cleaning the air we breathe.
Summary
The Earth's age was found by reading the speed at which uranium turns into lead in rock as a clock, and applying it to meteorites that were never remade. The first answer, worked out from cooling, was far too short because radioactivity, which gives off heat, was not yet known. The right answer took the patience to remove invisible lead dirt.
The Earth's birthday was remembered by a stone that fell from the sky.
To read it, first the dust in the room had to be wiped away.
To learn why the Earth's interior still hasn't cooled, see "Why Hasn't the Earth's Interior Cooled After 4.6 Billion Years?". For how fast the slow-moving continents travel, see "How Far Do the Continents Move in a Year?".
- Get about 50 ten-yen coins, put them in a box, and shake well. One shake counts as "one unit of time."
- Take out the coins that land heads as "changed into lead," and write down how many are left.
- Repeat with the remaining coins. See on which shake the number falls to a quarter of the start.
You can't predict when any single coin will change, yet the whole pile shrinks by about half each time. Atomic clocks are accurate because they hold an enormous number of atoms.
For those who want more ― terms, formulas and links to textbooksEach part is labelled from junior-high science to university specialist courses
- Junior highCovered in junior-high science
- High schoolCovered in high-school physics and earth science
- High school+Advanced high-school level, or a textbook sidebar
- UniversityUniversity specialist courses (geochemistry, isotope geology), not taught in high school
- ResearchNot yet taught as settled fact, even at university; researchers are still working on it
Junior highTerms: this phenomenon has names
- Radioactive decay: an unstable atomic nucleus changes into another nucleus while giving off radiation.
- Half-life: the time for the number of original atoms to fall by half. For uranium-238 it is about 4.47 billion years.
- Radiometric dating: a way to find the time since a rock formed, from the ratio of atoms made by decay to atoms still left.
Junior highHigh schoolCheck with a formula: how much uranium is left over the Earth's age?
Taking the Earth's age as 4.55 billion years, we calculate how far the two uranium clocks have run.
| In symbols | N = N0 × (1/2)^(t / T) 、 D / N = 2^(t / T) − 1 |
| In words | Number left = starting number × one half multiplied in "elapsed time ÷ half-life" times. The ratio to the lead formed is 2 multiplied in the same number of times, minus 1 |
| Where it comes from | Each atom decays with a fixed probability, so the number lost is always proportional to the number left (exponential decay). Every decayed atom becomes lead, so the total number of atoms is conserved |
| Symbol | Meaning and unit |
| N | Number of uranium atoms left now |
| N0 | Number of uranium atoms when the rock solidified |
| D | Number of lead atoms formed by decay |
| t | Elapsed time (hundred million years) |
| T | Half-life (hundred million years) |
| Age of the Earth (from meteorite lead) | About 4.55 billion years |
| Half-life of uranium-238 | About 4.47 billion years |
| Half-life of uranium-235 | About 0.704 billion years |
| Kelvin's late estimate (upper limit) | About 0.04 billion years |
| Number of half-lives for uranium-238 | 45.5 ÷ 44.7 ≒ 1.02 |
| One half multiplied in 1.02 times (share left) | About 0.494 |
| Starting number per atom left | 1 ÷ 0.494 ≒ 2.02 |
| Lead formed per atom left (D / N) | 2.02 − 1 = 1.02 |
| Number of half-lives for uranium-235 | 45.5 ÷ 7.04 ≒ 6.46 |
| One half multiplied in 6.46 times (share left) | About 0.011 |
| Ratio to Kelvin's estimate | 45.5 ÷ 0.4 ≒ 114 |
Of the uranium-238 present when the Earth formed, about half has now turned into lead. Of the fast clock, uranium-235, only about 1% is left. Conversely, solving for t from a measured ratio gives the age. That the two clocks point to the same age is what supports the answer.
High schoolHigh school+Why does a "lead-to-lead ratio" alone give the age?
High schoolHigh-school physics covers nuclear decay and half-life. The share left is "one half to some power" because the chance that a single atom decays stays the same over time.
High school+Real rocks contain a little lead from the start. So Patterson focused on the ratio of lead-207 to lead-206. From the difference in how fast the two clocks run, the age is fixed without measuring the amount of uranium directly. He estimated the lead present at the start from iron sulphide in a meteorite that has almost no uranium.
UniversityThe lead–lead isochron method
In university isotope geochemistry, this method is called the "lead–lead isochron method." Several samples with different uranium-to-lead ratios are plotted on a graph with lead-207/lead-204 and lead-206/lead-204 as the axes. Samples that solidified at the same time fall on one straight line, and its slope gives the age. This line is called an isochron ("equal-time line"). The speed of decay is given by the decay constant, and its link to the half-life is "half-life = natural log of 2 ÷ decay constant."
📖 Derivations and further reading: Radiometric dating (Wikipedia) / Patterson's original paper (1956)
ResearchWhat is still not clear
- Which moment counts as "birth"? The oldest grains in meteorites are said to be about 4.57 billion years old, and the Earth is thought to have reached its present size some tens of millions of years later. The value changes a little depending on which stage you call birth.
- What happened to the first crust? Mineral grains found in Australia are said to be about 4.4 billion years old. Whether oceans already existed then is still debated.
- How precise the half-life itself is. The half-life of uranium has been measured precisely, but a tiny error becomes an error in age. Re-measurements are still being made.
So this article, too, is "an explanation of what we know now." The value has settled at "about 4.6 billion years," but the details of the last few tens of millions of years are still being updated.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Junior high | Science: "Properties of radiation" | Uranium turning into lead |
| High school | Physics: "Atomic nuclei"; Earth science: "History of the Earth" | The half-life formula and Figure 1 |
| High school+ | Advanced earth science: "Radiometric ages" | Comparing the two clocks |
| University | Isotope geochemistry | Lead–lead isochron method |
| Research | Planet formation theory | Defining the moment of birth |
| ― | Links to daily life | Why lead disappeared from petrol |
- C. Patterson, "Age of meteorites and the earth", Geochimica et Cosmochimica Acta 10 (1956)
- Wikipedia, "Age of the Earth" (Japanese edition: 地球の年齢)
- G. Brent Dalrymple『The Age of the Earth』Stanford University Press(1991)
- Arthur Holmes『The Age of the Earth』Harper & Brothers(1913)
- National Astronomical Observatory of Japan (国立天文台), ed., Chronological Scientific Tables (理科年表), Maruzen Publishing (丸善出版)
* This article is a popular-science explanation. The numbers given are rough guides to help you understand how things work. Age values differ slightly between sources.