Radio metric dating
In other words there was originally 4 parts per million Parentium-123 and 0 parts per million Daughterium-123.Since there is now only 1/4 of the original amount of Parentium-123, we know that two half-lives of Parentium-123 have elapsed.But there are some questions that come to mind: Calculus students typically meet this problem somewhere in the second semester.It is one of the simplest examples of a differential equation.If you don't have minerals with those elements, you can't date the rock.In particular, quartzites and carbonate rocks almost always don't have enough to permit dating.Crystallization of a mineral is a good way to close a system. Any disturbance of the system effectively resets the clock to zero by allowing decay products to escape or reshuffling the abundances of elements.Weathering and metamorphism are the two most common ways to disturb a system.
If the decay constant is very small, even tiny amounts of contamination by other radioactive materials can be very significant.
Carbon-14 dating is often used for historical objects and young prehistoric objects, but it's based on the fact that all living things start out with a known amount of carbon-14. If the arrowhead is stuck in a bone, you can date the bone.
The most common dating methods for rocks are based on radioactive isotopes of potassium, rubidium, uranium, and thorium.
Uranium-lead dating methods often use this approach because some of the minerals used in dating lose the lead decay products over time.
It's amazing how often people fail to realize that you can't date materials if they don't have the necessary ingredients. You can't use carbon-14 to date an arrowhead with no carbon in it.