# Historical Geology/U-Th, U-Pa, and Ra-Pb dating

In this article we shall discuss three similar methods that can be used to date marine and lacustrine sediments: the U-Th, U-Pa, and Ra-Pb methods.

## The isotopes

The methods discussed in this article each require two isotopes: a parent isotope which is soluble (or the commonly occurring compounds of which are soluble) and a radioactive daughter isotope which is not soluble.
The table below shows three such systems together with the half-life of the daughter isotope, since this is the crucial figure.
| Method | Parent | Daughter | Half-life |
| U-Th | $^{234}$U | $^{230}$Th | 75,000 yrs |
| U-Pa | $^{235}$U | $^{231}$Pa | 32,800 yrs |
| Ra-Pb | $^{226}$Ra | $^{210}$Pb | 22 yrs |

## The method

The parent isotope will be present dissolved in the ocean or in lakes, but when decay takes place the insoluble daughter isotope will precipitate out as sediment and will form part of the upper layer of marine or lacustrine sediment. It will subsequently be buried in its turn by further sediment, and being radioactive will undergo decay.
Now, if there was absolutely none of the parent isotope present in the sediment, then the calculation would be very simple: when we have dug down through the sediment up to the point where the daughter isotope is only half as abundant as it is on the surface, then we would have dug back through one half-life's worth of time; and in general we could write:
    t = h × log$_2$(N/N$_s$)
where
* t is the age of the sediment;
* h is the half-life of the daughter isotope;
* N$_s$ is the quantity of the daughter isotope on the surface layer of sediment;
* N is the quantity of the daughter isotope at the depth we're trying to date.
That would be the simple case: however it will not necessarily be true that there will be none of the parent isotope in the sediment. There may well be some, but this is not a problem, since we can measure the quantity of the parent isotope present in the upper layers of sediment and take this into account in our calculations. The crucial point is that there will be more of the daughter isotope than could be accounted for by the decay of the parent within the sediment.

## Note on the use of Ra-Pb

All the methods described in this article are somewhat limited in their usefulness by the short half-lives of the daughter isotopes. This is particularly true of $^{210}$Pb; since it has a half-life of only 22 years, this makes it useless for most geological purposes. However, it can be used to gauge the rates of deposition of marine sediment as an alternative to the use of sediment traps.
This method has a couple of advantages over sediment traps. First, it is quicker: it doesn't take long to obtain a sediment core sample, whereas a sediment trap has to be left in place for at least a year to produce useful results.
Second, use of Ra-Pb allows us to measure the sedimentation that has taken place over the course of a century or so and average it, reducing the effect of small-scale fluctuations on the figures we obtain.

## Alternate use of U-Th

We can make an alternative use of the fact that $^{234}$U is soluble and $^{230}$Th is not.
First of all, this means that $^{234}$U will be incorporated into the structure of marine organisms such as corals. Secondly, it means that $^{234}$U will be incorporated into speleothems and $^{230}$Th will not, just as with the U-Pb method discussed in the article on U-Pb and related methods.
There is, however, a difference between U-Pb and U-Th: $^{230}$Th is radioactive. Whereas this was essential to its use in dating marine sediments, it is actually an inconvenience when dating organic remains or speleothems, since it means that the $^{230}$Th will not only be produced by decay, but also destroyed by it.
As a consequence, what happens is that the quantity of $^{230}$Th in the sample will tend towards secular equilibrium: the point at which the thorium is being produced at the same rate as it is being destroyed. This fact, combined with the practical difficulty of measuring whether the level of $^{230}$Th has reached 99.9%, 99.99%, or 99.999% of secular equilibrium, limits the useful range of the method to about 500,000 years.
Because this method can be applied to organic materials, it can be correlated with the radiocarbon method, and the dates produced by both methods can be shown to be concordant.
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