See the decay chain link in the See Also section below for decay chain details. It involves the radioactive nuclide Carbon-14 (aka radiocarbon) decaying to Nitrogen-14 with a 5730 year half-life.

As you can imagine, this half-life is short with respect to the age of the Earth, so it can’t be used to date rocks.

Several radioactive nuclides exist in nature with half-lives long enough to be useful for geologic dating.

Let’s go through an example of calculating the age of a rock with the radioactive nuclide Rubidium-87 (Rb87).

As time goes on, the Rb87 in the rock slowly turns into Sr87.

Parts of the rock that have more Rb87 will end up with more Sr87.

By measuring a few samples of the rock and comparing the relative amounts of Sr87 and Rb87, we can figure out how old the rock is! If you think about it, the equation above is a lot like the formula for a line, $$y=mx b$$ with $$y=\text_$$, $$m= \left(e^-1 \right)$$, $$x=\text_$$, and $$b=\text_$$.

The slope of the line can then be solved for $$t$$, giving us the age of the rock.

As a bonus, the intercept ($$b$$) of the line tells us the value of $$\text_$$ because we know the line was flat when the age of the rock was zero. Note that the values of the axes are actually normalized by Sr86 because the mass spectrometers used to take these measurements are much more accurate at relative values than they are at absolutes.

The animation in Figure 2 shows the flat line and how it increases with time. It works because Sr86 is stable and not radiogenic and therefore stays constant with time.

Claire Patterson was the first to accurately date the crystallization of Earth to 4.55 /- 0.05 billion years ago.

He used a lead isotope isochron method using measurements from three different meteorites (lead-206, lead-207 are the eventual decay products of uranium-238 and uranium-235).