Question: How do we know the earth's age? How do we know the age of rocks?

Susan Cartwright answered on 19 Jun 2015:

Radioactivity.

Radioactive elements decay according to a law which essentially means that it takes a constant time – the half-life – for half of the material to decay. So if you take 1 kg of carbon-14, which has a half-life of 5730 years, then after 5730 years there will be 500 g left, after 11460 years 250 g, after 17190 years 125 g, after 22920 years 62.5 g, and so on. We know what fraction the carbon in the atmosphere is carbon-14, so if we compare that with the fraction in something dead, we can work out how long it has been since it stopped breathing (i.e. exchanging carbon with the atmosphere). This is why carbon dating is useful in archaeology.

5730 years is not long enough to be useful for dating rocks or the solar system, but other radioactive isotopes have much longer half-lives. The half-life of potassium-40 is 1.251 billion years, of uranium-238 4.468 billion years, and thorium-232 14.05 billion years. By looking at these isotopes we can calculate the ages of rocks, and the Earth must be older than the oldest rocks. In fact, we get the age of the solar system from radioactive dating of meteorites, small rocks which fall on to the Earth from space. We believe that meteorites have been around since the birth of the solar system.

The result we get for the age of the Earth is about 4.6 billion years. This is consistent with the age of the Sun that we estimate by working out how a star of the Sun’s mass should evolve over time, though the age from radioactivity is more precise because our knowledge of how the Sun evolves depends on quantities that are not precisely known, like its exact chemical composition.