Historical Geology/Other isochron methods

In this article I shall point out some other dating methods which work the same way as the Rb-Sr method. The reader who has not read the article on the Rb-Sr method will find this present article almost completely incomprehensible, and should go back and read it.

The isochron method generalized

I have introduced the isochron method in the context of rubidium and strontium. But is there anything particularly special about those two elements? Not really. For the isochron method to work, what we need are three isotopes with the following properties.

(1) An unstable isotope. This should have a fairly long half-life if it is to be of any use in dating rocks, but not too long, or it will hardly undergo any decay at all. A figure expressible in billions of years is ideal. In the Rb-Sr method, we used ⁸⁷Rb.

(2) A stable daughter isotope of isotope (1). In the Rb-Sr method, we used ⁸⁷Sr.

(3) An isotope which is the same element as isotope (2) and which is neither unstable nor radiogenic, so that in a closed system it remains constant in quantity. In the Rb-Sr method, we used ⁸⁶Sr.

Given a set of three such isotopes, we can apply exactly the same reasoning as we did for ⁸⁷Rb, ⁸⁷Sr and ⁸⁶Sr, and it will be equally valid.

The isotopes

The table below shows some sets of three isotopes which can be treated like rubidium and strontium for the purposes of dating; the table also shows the half-life of the parent and its decay mode. The numbers (1) (2) and (3) are as in the section above.

Method	(1)	half-life	decay mode	(2)	(3)
Rb-Sr	87Rb	48×109 yr	beta minus	87Sr	86Sr
Sm-Nd	147Sm	106×109 yr	alpha	143Nd	144Nd
Lu-Hf	176Lu	36×109 yr	beta minus	176Hf	177Hf
Re-Os	187Re	43×109 yr	beta minus	187Os	186Os
La-Ba	138La	105×109 yr	electron capture	138Ba	137Ba
La-Ce	138La	105×109 yr	beta minus	138Ce	142Ce
K-Ca	40K	1.2×109 yr	beta minus	40Ca	42Ca
U-Pb	238U	4.5×109 yr	decay chain	206Pb	204Pb
U-Pb	235U	0.7×109 yr	decay chain	207Pb	204Pb

Notes

• I said that isotope (3) should be stable. ¹⁸⁶Os is not in fact stable, but as it has a half-life of two quadrillion years, it might as well be.

• In the Lu-Hf method, again, ¹⁴⁴Nd is unstable, but has a half-life even longer than that of ¹⁸⁶Os.

• Similarly in the La-Ce method, neither isotope of cerium used is strictly speaking stable, but their half-lives are so enormously long that for all practical purposes they may be treated as stable.

• In using the K-Ca method, we have to make a slight mathematical adjustment to take into account the fact, mentioned in our article on the K-Ar method, that ⁴⁰K decays to ⁴⁰Ar as well as to ⁴⁰Ca.

• Similarly, ¹³⁸La can decay two ways, to ¹³⁸Ce or ¹³⁸Ba. As you can see from the table, both are susceptible to the isochron method.

• We have noted the peculiarities of the half-life of ¹⁸⁷Re in the article on radioactive decay. As we only have to consider how it behaves in rocks, and not in elaborate equipment in physics laboratories, we may take its half-life to be 43 billion years as given in the table.

• There are two entries for U-Pb because there are two parent isotopes we can use, ²³⁸U and ²³⁵U. Each decays to a (different) final stable element of lead by a complex decay chain.

• In practice, the U-Pb decay chain is usually exploited by methods other than isochron dating, for reasons that will be explained in the next article.