This has to do with figuring out the age of ancient things.If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict when that particular atom might decay.Relative age dating also means paying attention to crosscutting relationships.Say for example that a volcanic dike, or a fault, cuts across several sedimentary layers, or maybe through another volcanic rock type.Unlike people, you can’t really guess the age of a rock from looking at it.
A useful application of half-lives is radioactive dating.
It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.
It takes a certain amount of time for half the atoms in a sample to decay.
We could be sure that a mineral containing parentium originally had no daughterium.
If the mineral contained 1 part per million Parentium-123 and 3 parts per million Daughterium-123, we could be sure all the Daughterium-123 was originally Parentium-123.