Other minerals that also show these properties, but are less commonly used in radiometric dating are Apatite and sphene.
If a zircon crystal originally crystallizes from a magma and remains a closed system (no loss or gain of U or Pb) from the time of crystallization to the present, then the Discordant dates will not fall on the Concordia curve.
At any given moment, for a certain type of element or a certain type of isotope of an element, there's some probability that one of them will decay. If I wait carbon-14's half-life-- this is a specific isotope of carbon. So when you have the same element with varying number of neutrons, that's an isotope. Let's think about what happens after another half-life. And by the law of large numbers, half of them will have converted into nitrogen-14. This might be the one ultra-stable nucleus that just happened to, kind of, go against the odds and stay carbon-14.
But the way we think about half-life is, people have studied carbon and they said, look, if I start off with 10 grams-- if I have just a block of carbon that's 10 grams. Those five grams of carbon-14, every one of those atoms still has, over the next-- whatever that number was, 5,740 years-- after 5,740 years, all of those once again have a 50% chance. Well, after one billion years I'll say, well you know, it'll probably have turned into nitrogen-14 at that point, but I'm not sure. You don't know how well it calibrates against time.
Although we now recognize lots of problems with that calculation, the age of 25 my was accepted by most physicists, but considered too short by most geologists. Recognition that radioactive decay of atoms occurs in the Earth was important in two respects: Principles of Radiometric Dating Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential (Energy) barrier which bonds them to the nucleus.
The energies involved are so large, and the nucleus is so small that physical conditions in the Earth (i.e. The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i.e.
What's going to happen after one billion years? And then you didn't build your time machine well.
Prior to 1905 the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the amount of time necessary for the Earth to cool to its present temperature from a completely liquid state.
I mean, maybe if we really got in detail on the configurations of the nucleus, maybe we could get a little bit better in terms of our probabilities, but we don't know what's going on inside of the nucleus, so all we can do is ascribe some probabilities to something reacting. And it does that by releasing an electron, which is also call a beta particle. And I've actually seen this drawn this way in some chemistry classes or physics classes, and my immediate question is how does this half know that it must turn into nitrogen? So that after 5,740 years, the half-life of carbon, a 50% chance that any of the guys that are carbon will turn to nitrogen. But we'll always have an infinitesimal amount of carbon. Let's say I'm just staring at one carbon atom. You know, I've got its nucleus, with its c-14. I mean, if you start approaching, you know, Avogadro's number or anything larger-- I erased that. After two years, how much are we going to have left? And then after two more years, I'll only have half of that left again.
And so, like everything in chemistry, and a lot of what we're starting to deal with in physics and quantum mechanics, everything is probabilistic. So one of the neutrons must have turned into a proton and that is what happened. And you might say, oh OK, so maybe-- let's see, let me make nitrogen magenta, right there-- so you might say, OK, maybe that half turns into nitrogen. And over 5,740 years, you determine that there's a 50% chance that any one of these carbon atoms will turn into a nitrogen atom. And we could keep going further into the future, and after every half-life, 5,740 years, we will have half of the carbon that we started. Now, if you look at it over a huge number of atoms. But after two more years, how many are we going to have? So this is t equals 3 I'm sorry, this is t equals 4 years.
We can see how do deal with this if we take a particular case. For example the amount of Rb in mantle rocks is generally low, i.e. The mantle thus has a low If these two independent dates are the same, we say they are concordant.
We can also construct a Concordia diagram, which shows the values of Pb isotopes that would give concordant dates.After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.