This first interactive is designed to allow you to explore what happens during radioactive decay of some isotope. An isotope refers to a particular version of an element. For example, the non-radioactive Carbon-12 isotope has 6 protons and 6 neutrons in its nucleus but the radioactive Carbon-14 isotope has 6 protons and 8 neutrons in its nucleus. Different isotopes of the same element behave identically in terms of chemistry and bonding to other atoms, but their nuclear properties can differ.
During radioactive decay, a parent isotope is said to decay into a daughter isotope. So, for example, the parent isotope of Carbon-14 decays into Nitrogen-14. There is no way to predict when any one nucleus of a parent isotope will decay into a daughter isotope. That said, if you look at a large number of nuclei of a parent isotope, they exhibit a very simple property:
The same fraction of a radioactive parent isotope will decay over the same amount of time.
The time it takes for one-half of a population of parent isotopes to decay (on average) into daughter isotopes is called the half-life of that isotope. Different parent isotopes can have very different half-lifes. NOTE: This interactive shows a simulation of the decay of only 900 atoms. The radioactive decay is still modelled as occurring randomly for any one atom, so the simulation will show slightly different results on different runs!!
Assuming a non-radiogenic isotope (that is, an isotope that is not the result of radioactive decay) that also will not decay, its amount should be constant. This means that for different mineral samples we can measure the ratio of parent isotope versus the non-radiogenic isotope ($P/D_i$) and daughter isotope ($D$) versus the non-radiogenic isotope ($D/D_i$) to build an geochron plot. For example, using the following isotopes
an geochron plot could plot $D/D_i$ versus $P/D_i$.
What sets the geochron method (also known as the isochron method) apart from the just measuring parent and daughter abundances is the use of the non-radiogenic isotope of the daughter element. This avoids the assumption of no initial daughter isotope before the rock solidified (radioactive decay can occur while rock is molten).
Some minerals in the rock incorporate the parent better than daughter which is why the initial amount of parent isotope versus daughter isotope can vary. We expect daughter versus non-radiogenic isotope ratio to be constant if we pick the non-radiogenic isotope to be the same element as the daughter isotope.
With all this said, it is actually often not this simple as many daughter isotopes are themselves radioactive and decay, leading to a chain of reactions, so comparing abundances of parent to daughter isotopes is not simple.
Note: The idea for the geochron dating interactive came from a Isochron Diagram Java app at ScienceCourseware.org. However that app had some issues in that it didn't divide by a non-radiogenic isotope (or at least didn't mention it). In fact, they used $D_i$ for the initial amount of daughter isotope instead of the non-radiogenic isotope of the same element as the daughter isotope.