Parsimony, you got into isochrons, but let's discuss how you got there.
From Jonathan Woolfe's "Essay on Radiometric Dating,"
"I. Theory of radiometric dating
...radiometric dating is a way of determining the age of a sample of material using the decay rates of radio-active nuclides to provide a 'clock.' It relies on three basic rules, plus a couple of critical assumptions. The rules are the same in all cases; the assumptions are different for each method. To explain those rules, I'll need to talk about some basic atomic physics.
There are 90 naturally occurring chemical elements. Elements are identified by their atomic number, the number of protons in the atom's nucleus. All atoms except the simplest, hydrogen-1, have nuclei made up of protons and neutrons. Hydrogen-1's nucleus consists of only a single proton. Protons and neutrons together are called nucleons, meaning particles that can appear in the atomic nucleus.
A nuclide of an element, also called an isotope of an element, is an atom of that element that has a specific number of nucleons. Since all atoms of the same element have the same number of protons, different nuclides of an element differ in the number of neutrons they contain. For example, hydrogen-1 and hydrogen-2 are both nuclides of the element hydrogen, but hydrogen-1's nucleus contains only a proton, while hydrogen-2's nucleus contains a proton and a neutron. Uranium-238 contains 92 protons and 146 neutrons, while uranium-235 contains 92 protons and 143 neutrons. To keep it short, a nuclide is usually written using the element’s abbreviation. Uranium’s abbreviation is U, so uranium-238 can be more briefly written as U238.
Many nuclides are stable -- they will always remain as they are unless some external force changes them. Some, however, are unstable -- given time, they will spontaneously undergo one of the several kinds of radioactive decay, changing in the process into another element.
There are two common kinds of radioactive decay, alpha decay and beta decay. In alpha decay, the radioactive atom emits an alpha particle. An alpha particle contains two protons and two neutrons. After emission, it quickly picks up two electrons to balance the two protons, and becomes an electrically neutral helium-4 (He4) atom. When a nuclide emits an alpha particle, its atomic number drops by 2, and its mass number (number of nucleons) drops by 4. Thus, an atom of U238 (uranium, atomic number 92) emits an alpha particle and becomes an atom of Th234 (thorium, atomic number 90).
A beta particle is an electron. When an atom emits a beta particle, a neutron inside the nucleus is transformed to a proton. The mass number doesn't change, but the atomic number goes up by 1. Thus, an atom of carbon-14 (C14), atomic number 6, emits a beta particle and becomes an atom of nitrogen-14 (N14), atomic number 7.
A third, very rare type of radioactive decay is called electron absorption. In electron absorption, a proton absorbs an electron to become a neutron. In other words, electron absorption is the exact reverse of beta decay. The mass number doesn’t change, while the atomic number goes down by 1. So an atom of potassium-40 (K40), atomic number 19 can absorb an electron to become an atom of argon-40 (Ar40), atomic number 18.
The half-life of a radioactive nuclide is defined as the time it takes half of a sample of the element to decay. A mathematical formula can be used to calculate the half-life from the number of breakdowns per second in a sample of the nuclide. Some nuclides have very long half-lives, measured in billions or even trillions of years. Others have extremely short half-lives, measured in tenths or hundredths of a second. The decay rate and therefore the half-life are fixed characteristics of a nuclide. They don’t change at all. That’s the first axiom of radiometric dating techniques: the half-life of a given nuclide is a constant. (Note that this doesn’t mean the half-life of an element is a constant. Different nuclides of the same element can have substantially different half-lives.)
The half-life is a purely statistical measurement. It doesn’t depend on the age of individual atoms. A sample of U238 ten thousand years old will have precisely the same half-life as one ten billion years old. So, if we know how much of the nuclide 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 nuclide to break down. Because it’s a statistical measurement, there’s always a margin of error in the age figure, but if the procedure is done properly, the margin is very small.
Obviously, the major question here is "how much of the nuclide was originally present in our sample?" In some cases, we don’t know. Such cases are useless for radiometric dating. We must know the original quantity of the parent nuclide in order to date our sample radiometrically. Fortunately, there are cases where we can do that.
In order to do so, we need a nuclide that’s part of a mineral compound. Why? Because there’s a basic law of chemistry that says "Chemical processes like those that form minerals cannot distinguish between different nuclides of the same element." They simply can’t do it. If an element has more than one nuclide present, and a mineral forms in a magma melt that includes that element, the element’s different nuclides will appear in the mineral in precisely the same ratio that they occurred in the environment where and when the mineral was formed. This is the second axiom of radiometric dating.
The third and final axiom is that when an atom undergoes radioactive decay, its internal structure and also its chemical behavior change. Losing or gaining atomic number puts the atom in a different row of the periodic table, and elements in different rows behave in different ways. The new atom doesn’t form the same kinds of chemical bonds that the old one did. It may not form the same kinds of compounds. It may not even be able to hold the parent atom’s place in the compound it finds itself in, which results in an immediate breaking of the chemical bonds that hold the atom to the others in the mineral.
Why not? you might ask. Well, an atom’s chemical activity pattern is a result of its electron shell structure. (The exact details of this are rather complicated, so I won’t go into them here.) When the number of electrons change, the shell structure changes too. So when an atom decays and changes into an atom of a different element, its shell structure changes and it behaves in a different way chemically.
That’s it. That’s the sum total of the chemical and physical basis of radiometric dating. That’s all you really need to know to understand radiometric dating techniques.
How do these axioms translate into useful science? In the next part of this article, I’ll examine several different radiometric dating techniques, and show how the axioms I cited above translate into useful age measurements."
As a layman (or former Chem 1A, 1B student), the above is understandable. I've seen the half-life curve can be shown experimentally with dice. The other parts can be shown via explanation using the periodic elements table and the using different elements to show alpha, beta and gamma decays and what elements they change to. Is there an experiment to show the different radioactive decay to get a visual feel of radioctive decay? On youtube are several explanations of half-life and radiation and radioactive decay, so you would have to come up with something else to differentiate yourself (assuming you want to teach radiometric dating). I agree with his axioms and with "how much of the nuclide was originally present in our sample? In some cases we do not know. Such cases are useless for radiometric dating. We must know the original quantity of the parent nuclide in order to date our sample radiometrically." Where the creation scientists disagree with is, "Fortunately, there are cases where we can do that." We can get into that next.
http://answersinscience.org/RadiometricDating-Woolf.htm
