If the rocks have an interbedded lava flow or volcanic ash bed, it's gold.
The older our sample is, the more daughter isotope it will contain relative to the parent.
Furthermore, Parentium and Daughterium are so different in chemical properties that they don't otherwise occur together.
If there were such a pair of isotopes, radiometric dating would be very simple.
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.
In calculus terms, we write: d N(t)/dt = -K * N(t) or d N(t)/N(t) = -K dt The minus sign means that each decay decreases the total number of atoms.
Integrating both sides, we get: ln N(t) = -Kt C C is the constant of integration that we can often ignore, but not here.
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.
Potassium-argon dating is very susceptible to resetting because the argon decay products are merely held in place mechanically by surrounding atoms.
Argon, an inert gas, is not chemically bonded to neighboring atoms at all, and even minor thermal disturbance allows them to escape.
In other words there was originally 4 parts per million Parentium-123 and 0 parts per million Daughterium-123.