Uranium–thorium dating

History

In 1908, John Joly, a professor of geology at Trinity College Dublin, found higher radium contents in deep sediments than in those of the continental shelf, and suspected that detrital sediments scavenged radium out of seawater. Piggot and Urry found in 1942, that radium excess corresponded with an excess of thorium. It took another 20 years until the technique was applied to terrestrial carbonates (speleothems and travertines). In the late 1980s, the method was refined by mass spectrometry, with significant contributions from Larry Edwards. After Viktor Viktorovich Cherdyntsev's landmark book about uranium-234 had been translated into English, U-Th dating came to widespread research attention in Western geology.

Methods

U-series dating is a family of methods which can be applied to different materials over different time ranges. Each method is named after the isotopes measured to obtain the date, mostly a daughter and its parent. Eight methods are listed in the table below.

The ²³⁴U/²³⁸U method is based on the fact that ²³⁴U is dissolved preferentially over ²³⁸U because when a ²³⁸U atom decays by emitting an alpha ray the daughter atom is displaced from its normal position in the crystal by atomic recoil. This produces a ²³⁴Th atom which quickly becomes a ²³⁴U atom. Once the uranium is deposited, the ratio of ²³⁴U to ²³⁸U goes back down to its secular equilibrium (at which the radioactivities of the two are equal), with the distance from equilibrium decreasing by a factor of 2 every 245,000 years.

A material balance gives, for some unknown constant A, these expressions for activity rations (assuming that the ²³⁰Th starts at zero):

${\displaystyle {}^{234}\text{U}{/}^{238}\text{U}=1+A\times 2^{-t/245000}}$

${\displaystyle {}^{230}\text{Th}{/}^{238}\text{U}=1+\frac{A}{1-75000/245000}\times 2^{-t/245000}-\left(1+\frac{A}{1-75000/245000}\right)\times 2^{-t/75000}}$

We can solve the first equation for A in terms of the unknown age, t:

${\displaystyle A={(}^{234}\text{U}{/}^{238}\text{U}-1)\times 2^{t/245000}}$

Putting this into the second equation gives us an equation to be solved for t:

${\displaystyle {}^{230}\text{Th}{/}^{238}\text{U}=1+\frac{{}^{234}\text{U}{/}^{238}\text{U}-1}{1-75000/245000}-2^{-t/75000}-\frac{{}^{234}\text{U}{/}^{238}\text{U}-1}{1-75000/245000}\times 2^{t/245000-t/75000}}$

Unfortunately there is no closed-form expression for the age, t, but it is easily found using equation solving algorithms.

Dating limits

Uranium–thorium dating has an upper age limit of somewhat over 500,000 years, defined by the half-life of thorium-230, the precision with which one can measure the thorium-230/uranium-234 ratio in a sample, and the accuracy to which one knows the half-lives of thorium-230 and uranium-234. Using this technique to calculate an age, the ratio of uranium-234 to its parent isotope uranium-238 must also be measured.

Precision

U-Th dating yields the most accurate results if applied to precipitated calcium carbonate, that is in stalagmites, travertines, and lacustrine limestones. Bone and shell are less reliable. Mass spectrometry can achieve a precision of ±1%. Conventional alpha counting's precision is ±5%. Mass spectrometry also uses smaller samples.