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Radiometric dating methods (i.e. isochron, concordia/discordia, etc) exploit the useful fact that radioactive atoms decay in accordance with a highly regular function: 50% of any given kind of radioactive atoms will decay in X amount of time, where the value of 'X' depends on exactly which kind of atoms you're measuring the decay of.

## The Decays

The most common radioactive decays used for this purpose are listed in the following table.

Parent -> Stable Daughter First Decay Particle First Decay Half-life
U238 -> Pb206 alpha 4.5 Gyr
U235 -> Pb207 alpha 0.704 Gyr
Th232 -> Pb208 alpha 14.0 Gyr
Rb87 -> Sr87 beta 48.8 Gyr
K40 -> Ar40 EC* 1.25 Gyr
Sm147 -> Nd143 alpha 106 Gyr
C14 -> N14 beta 5,730 years
• (EC = electron capture: beta-like)

Carbon-14 was included because it is often used to date various human artifacts. From the mathematics of radioactive decay, it is easy to see that it is useless beyond a few tens of thousands of years. Geologists prefer most of the others because most rocks are much older; creationists who talk about carbon dating of rocks reveal a remarkable ignorance of the subject.

We can be confident that radioactive-decay rates have not varied over geological time for several reasons:

1. There is no known physical reason that would cause them to vary noticeably. The two main types of radioactive decay used for radiometric dating are alpha and beta decay, which are both well-understood physical phenomena, and which have rates that can be calculated from the decay energies and various fundamental physical constants. In particular, alpha decay takes place by quantum-mechanical tunneling; the emitted helium-4 nucleus spreads through its "forbidden" region near the nucleus to where it can escape. And beta decay takes place by the weak elementary interaction, which can convert neutrons and protons and emit or absorb electrons.
The electrons in decaying atoms do have an influence on their decay rates, but all but the outermost ones are essentially unaffected by different states of chemical combination and different pressures in the Earth. In particular, it is mostly the innermost electrons that are captured in electron-capture decay, and these are relatively unaffected by the outside world. The main exception, beryllium-7 (which is not used for radiometric dating, hence any anomalies in its decay are irrelevant to the question of whether or not radiometric dating techniques are valid), is easily accounted for by noting that its outermost and innermost electrons are right next to each other (beryllium has only 4 electrons in 2 shells with 2 each).
2. If such variations happened, then it would be very unlikely that they would happen in exact sync, which is what would be necessary to produce the observed concordances. In fact, if such discrepancies existed, it would be possible to produce plots of U-Pb age vs. K-Ar age. However, searching for such discrepancies has resulted in some sensitive upper limits, as described in The fundamental constants and their variation: observational status and theoretical motivations
3. The physics of stars (and other objects) which we can observe is independent of how far they are away from earth. Observing stars which are very far away means also looking very far back in time. The physics of stars is strongly dependend on nuclear reactions and thus also connected to decay rates. Therefore a change in decay rates which would affect the accuracy of radiometric dating can be clearly ruled out.
4. Studies on the isotopes left behind by the Oklo reactor, a natural occuring nuclear reactor about two billion years ago, are giving an upper limit of the change of constants and excludes changes in constants which are big enough to affect the accuracy of radiometric dating.

## Dating the Rocks

That is easy if there is good reason to believe that the daughter element was originally absent from what one is attempting to date. Zircon, for example, tends to crystallize with much less lead than uranium, and is thus useful for finding U-Pb dates. The observed proportions of parent and daughter give the date:

• P = P0*f
• D = P0*(1-f)
• f = 2(-t/T)

->

• f = P/(P+D)
• t = - T*log((P/(P+D))/log(2)

But that cannot be universally assumed, and there is a way to get around the initial presence of daughter element. This uses the fact that the parent and daughter elements are likely to have different chemical affinities, thus preferring to crystallize in different minerals of a solidifying rock. So some of a rock's mineral crystals may have a lot of parent, and some a lot of daughter. And the daughter may have more than one isotope, with only one of them being the decay product of the parent. Thus,

• P = P0*f
• D = k*D0 + P0*(1-f)

where D0 is the original concentration of the non-decay daughter isotope and k is the ratio of decay to non-decay daughter isotope. That ratio is usually assumed to be constant, which is a reasonable hypothesis in most cases. Divide the observed P's and D's by the corresponding observed D0's, and you get

• P/D0 = (P0/D0)*f
• D/D0 = k + (P0/D0)*(1 - f)

Plotting D/D0 vs. P/D0 ought to give an "isochron", a straight line whose slope gives f, and thus the age. This helps make radiometric dating self-checking -- does it produce consistent results?

Inconsistencies are, however, known, and they can be produced by metamorphism; heating a rock may allow some of its elements to diffuse through it. However, such effects make a rock seem younger than it is; its "age" is the time since that heating rather than the time since its formation.

Another source of confusion is dating the wrong rock. Lava flows often contain xenoliths, stray rocks from elsewhere, and dating one of those will make a lava flow seem much older than it really is. Which is because that rock had solidified long before that lava flow.

Graphical representation of the creationist fallacy of using short tools to measure long object and long tools to measure short objects. Click to see full resolution.

Creationists claims about radiometric dating usually rest on erroneous dates given by testing objects of known ages. For example, testing a recent volcanic eruption with K-Ar dating, or testing coal with radiocarbon dating.

However, they fail to realise that these dating methods are not perfect - they cannot date just anything any more than a foot-long wooden rule can measure any object in existence. The markings on a wooden rule begin a millimetre or two from the very end, so cannot measure very small things like a bacterial cell. Furthermore, it will have a maximum length, so cannot measure a football stadium or even a tree. Likewise, creationists use radiocarbon dating to measure prehistoric objects (beyond the length of the tool) and K-Ar dating to date recent lava floes (within the error of the tool).

Furthermore, often radiometric dating can only measure certain types of materials, and in certain conditions will be invalid or erroneous. While scientists attempt to avoid these situations, often creationists will pounce upon any study that fails to do so as proof of the error in radiometric dating.