Radiocarbon dating worked example
Details about linear regression are available in any elementary statistics book, or online -- see [Linear2013].Here are just four examples of isochron graphs, which are entirely typical among the tens of thousands of examples that could be mentioned.A related article on the age of the earth and geologic ages presented the current best known values for these dates: Ages.The figures shown in that article are based on radiometric dating.Quantum mechanics is one of two cornerstones of modern physics (the other is general relativity), and has been precisely confirmed in thousands of very exacting experiments.For these reasons, scientists have considerable confidence in these dates when they are measured properly in accordance with procedures that have been developed and refined over several decades.Note how breathtakingly close these points are to the fitted lines (thus confirming with high statistical confidence the validity of the resulting dates): The data for the first graph (upper left) is a set of measurements of basaltic achondrites (meteorites) in [Basaltic1981, pg.938]; the data for the second graph (upper right) is from early Archaean gneisses rocks near Isua, Greenland [Morbath1977]; the data for the third graph (lower left) is from ancient gneiss rocks in Swaziland [Carlson1983]; the data for the fourth graph (lower right) is from lunar dunite rocks gathered during Apollo 17 [Papanastassiou1975]. For many years, fairly large samples were required to produce statistically reliable results.
This section may be omitted if readers do not wish to follow the math (although the math used here is nothing beyond what is typically taught in a good high-school math analysis class).
The corresponding dates obtained from these isochrons (based on the slopes of the lines), together with statistical standard deviations, are: 4.396 ± 0.18, 3.673 ± 0.014, 2.991 ± 0.15, and 4.478 ± 0.034 (each figure is in billions of years). But with the advent of mass spectrometry beginning in the 1970s, even very small samples can now be accurately dated.
For example, the "SHRIMP" ion microprobe now in use in numerous laboratories around the world can reliably measure U-Pb and Pb-Pb ages from spots only 0.02 mm (i.e., 20 micrometers) in size within a zircon crystal [Dalrymple2004, pg. It should be emphasized, though, that even relatively unsophisticated equipment can perform radiometric measurements of dates fairly well.
Some of the most commonly used radiometric schemes are [Dalrymple1991, pg. 55]: Each method has its own particular range of applicability, which derives from the half-life of the particular radioactive decay involved.
Uranium-thorium dating, for instance, can be used to date specimens up to about 500,000 years old (since the half-life of the U-Th decay is 75,000 years), but Rubidium-Strontium dating can be used to date specimens billions of years old (since the half-life of the Rb-Sr decay is 48.8 billion years).