How do scientists date the age of the earth?

You have probably come across carbon dating. A small proportion (a few parts per million) of the #""^14N# in the atmosphere is converted into radioactive #""^14C# by cosmic rays. This carbon is absorbed by living organisms along with the much more common stable #""^12C# isotope. When an organism dies, it stops absorbing carbon from the atmosphere. From that point on, the proportion of #""^14C# to #""^12C# incorporated in the organism decreases as the #""^14C# reverts to #""^14N# by beta decay, with a half life of about #5730# years.

So by measuring the proportion of #""^14C# to #""^12C# we can determine the age of (say) a piece of wood.

This method needs some calibration for several factors, including the industrial revolution, which significantly decreased the proportion of #""^14C# in the atmosphere. Why decrease? There was a dramatic increase in #CO_2# from fossil fuels, which contain only trace amounts of #""^14C#, since they come from organisms that died a long time ago. It is further complicated by the above ground nuclear testing in the 1950's and '60s.

Nevertheless, with calibration, #""^14C# dating is useful for dates up to about #75,000# years.

When we look at other elements, such as Uranium, which have a much longer half life, the series of elements into which they decay and the proportions thereof allow us to date rocks and inclusions as old as several billion years.

The oldest Earth rocks we have found are about #4# billion years old. Some contain zircon crystals which we can date to #4.4# billion years.

We also get samples of early rocks in the form of meteorites. According to our models of how the Earth formed, these would have a similar age to the Earth. Some inclusions in meteorites have been dated to as early as #4.68+-0.15# billion years.