Radiocarbon dating does not work on anything inorganic, like rocks or fossils.
Only things that once were alive and now are dead: bones, teeth, flesh, leaves, etc.
When we know how much has decayed, we know how old the sample is.
Many archaeological sites have been dated by applying radiocarbon dating to samples of bone, wood, or cloth found there. One is that the thing being dated is organic in origin.
Some isotopes can break down in more than one way -- in these cases, each different breakdown type has its own half-life.
The decay rate and therefore the half-life are fixed characteristics of an isotope. That's the first axiom of radiometric dating techniques: the half-life of a given isotope is a constant.
Presented with a new method that gave answers different than existing methods, the scientists involved did not simply assume that either the old method or the new one was wrong.
They viewed the problem as a challenge, dug into it with all their energy, and didn't stop until they understood exactly why their C14 dates disagreed with traditional dates, what was wrong with their C14 procedures, and how to compensate for the problems in the future. When Professor William Libby developed the C14 dating system in 1949, he assumed that the amount of C14 in the atmosphere was a constant.
Thus this essay, which is my attempt at producing such a source.So, if we know how much of the isotope was originally present, and how much there is now, we can easily calculate how long it would take for the missing amount to decay, and therefore how long it's been since that particular sample was formed.That's the essence of radiometric dating: measure the amount that's present, calculate how much is missing, and figure out how long it would take for that quantity of the isotope to break down.(Note that this doesn't mean the half-life of an element is a constant.Different isotopes of the same element can have substantially different half-lives.) It's important to understand that the half-life is a purely statistical measurement. A sample of U238 ten thousand years old will have precisely the same half-life as one ten billion years old.