Some chemical elements have isotopes that are inherently unstable and undergo radioactive decay. (Isotopes of the same element always have the same number of charged protons in each atomic nucleus, but have different numbers of noncharged neutrons. Isotopes of a single element act the same

"Simple" radioactive dating can be visualized as using a kind of atomic hourglass. The radioactive "parent" decays into a "daughter" isotope (often of a different element, since radioactive decays usually involve charged particles). So, if both parent and daughter elements are present, the ratio of parent isotope to daughter isotope can give a clue to the age of the sample. If there is more parent than daughter, the sample is still young (the top of the hourglass is still mostly full). If there is less parent than daughter, the sample is old (most of the sand is at the bottom of the hourglass).

But simple dating techniques can be distorted in several ways. What if there were some of the daughter isotope in the sample

To give a concrete example, suppose that we examine 3 different minerals from a rock, labeled A, B, and C, and that isotopic tests revealed the relative amounts of 3 chemical isotopes in these minerals. The parent isotope is rubidium-87 (

The present-day relative amounts of the isotopes in our fictitious example are:

Mineral | ^{87}Rb |
^{87}Sr |
^{86}Sr |

A | 60 | 80 | 40 |

B | 30 | 60 | 60 |

C | 10 | 60 | 100 |

These numbers are purely hypothetical — they were chosen so the explanation would be easy to understand. I decided to make the rock 49 billion years old, one half-life of rubidium. (Yes, that is much older than the universe, but this is merely an example.)

If we were to apply the "simple" dating method to A, B, and C, we would arrive at 3 different ages, assuming that there was no initial daughter isotope (

There are 3 important questions to consider when choosing a mineral sample for radiometric dating: (1) Is the rock a good sample for radioactive dating? (2) What was the initial amount of daughter product (87Sr) in the rock at the time it formed out of a melt? (3) How old is the rock? The isochron technique provides a way to answer these questions.

Imagine going back in time 49 billion years to observe the rock as it is crystallizing from a melt. The rock has both isotopes of strontium: the daughter product

The rubidium-heavy mineral A has the highest ratio; A’s ratio of parent isotope to non-radiogenic isotope is 120 / 40 = 3.0. In contrast, the rubidium-poor mineral C has the lowest ratio; C’s ratio of parent isotope to non-radiogenic isotope is 20 / 100 = 0.2. Note that

Now let us return to the present and see what has happened to our rock. The next table shows the present-day amounts and ratios of the isotopes.

Because the time elapsed since the rock solidified is one half-life of

So what is an

The lines with arrows represent the changes in those single minerals over time. For example, A’s

How is the isochron’s slope related to the age of the rock? Let us consider one more example — that of the same rock, 49 BY in the future (long after our sun has turned into a smoldering dwarf star).

The slope of the far-future isochron is (2.75 - 0.65) / (0.75 - 0.05) = 2.1 / 0.7 = 3.0. The age is obtained by adding 1.0 to the slope, and then stating the sum as a power of two; that power is the age, in half-lives. For a slope of 3, 3 + 1 = 4 = 2

When applied correctly, the isochron method provides a powerful way to tackle some of the problems encountered with "simple" dating techniques. For one thing, if the sample minerals did not solidify at the same time but were mashed together, the points will generally

But the method is not infallible. For example cases of non-uniform mixing, or conglomeration of certain types of rocks, can sometimes lead to "false" or "fictitious" isochrons — isochrons that do not represent the true age of the rock. These possible pitfalls are discussed in Bernard-Griffiths (1989) and Faure (1986). There are methods to counteract these problems, such as taking more mineral samples, performing mixture analyses on more than one element, and by checking dates by independent means (such as looking at different parent/daughter pairs). (For more details on this and other methods, see the chapter on dating techniques in Dalrymple [1991] and York and Dalrymple [2000].) When such checks are made, confidence in the results is greatly increased. For example, the St Severin meteorite was dated with three different methods (Rb-Sr, Sm-Nd, and Ar-Ar) as being between 4.4 and 4.6 billion years old (Dalrymple 1991, 288).

Creationists love to attack such methods by claiming that we do not really know if radioactive decay rates are constant over time. They point out no human was around back then, so who knows for sure? They also hypothesize that decay rates varied during supernatural events (the Creation, the Flood), but of course they do not test these hypotheses. One interesting point against the creationists is the fact that, if decay rates

Dalrymple GB. The Age of the Earth. Stanford (CA): Stanford University Press 1991.

Faure G. Principles of Isotope Geology>. 2nd ed. NY: John Wiley and Sons, 1989.

York D, Dalrymple GB. Comments on a creationist’s irrelevant discussion of isochrons. Reports of the National Center for Science Education> 2000 May/Jun; 20 [3]: xx–xx.