The Uranium-Lead Clock

We can illustrate the method with the first radioactive clock devised, the one based on the decay of uranium to lead. Radioactive decay goes strictly according to a law of statistical probability. The amount of uranium decaying in a unit of time is always proportional to the amount left. This results in a curve like that in the drawing (page 19), which shows the amount left after any given time. The time it takes for half the uranium to decay is called its half-life. One half of the remaining half will decay in the next half-life, leaving one quarter of the original amount. After three half-lives, one eighth will be left, and so on. The half-life of uranium is 4.5 billion years.

Since the uranium is transformed into lead, the amount of lead is increasing all the time. The amount accumulated up to any given time is shown by the broken curve. The lead curve is the complement of the uranium curve, so that the total number of lead atoms and uranium atoms is always the same, equal to the number we started with.

Now suppose we have a rock containing uranium but no lead, and we seal it up tight so that nothing can get into or out of the rock. Then, some time later we open it up and measure the amounts of both elements. We can tell from that how long the rock has been sealed. For example, if we find equal amounts of lead and uranium, we know that one half-life, that is, 4.5 billion years, has passed. If we find that just 1 percent of the uranium has decayed to lead, we can use the mathematical formula for the curve to figure that 65 million years have elapsed.

Note that we do not have to know how much uranium was in the rock to start with because all we have to measure is the proportion of lead to uranium at the end of the period​—which is just as well because none of us were around to measure anything at the beginning of the experiment.

Now you may be thinking that these are immense periods of time we are talking about, millions and billions of years. What is the possible use of a clock that runs so slowly? Well, we learn that the earth itself has been in existence for a few billion years, and there are rocks in a few places that appear to have been there for a good part of that time. So geologists find such a clock quite useful in studying the history of the earth.

How Certain Are They?

We must admit that the dating process isn’t quite as simple as we have described it. We mentioned that the rock has to be free from lead at the beginning. This is usually not the case; there is some lead to start with. This gives the rock what is called a built-in age, something more than zero. Also, we assumed that the uranium was tightly sealed in the rock so that nothing could get in or out. Sometimes this may be true but not always. Over long periods of time, some of the lead or the uranium might seep out into groundwater. Or more uranium or lead might get in, especially if it is a sedimentary rock. For this reason, the uranium-lead clock works best on igneous rocks.

Other complications arise from the fact that another element, thorium, which may be in the mineral, is also radioactive and slowly disintegrates into lead. Besides that, uranium has a second isotope​—the same chemically but different in mass—​that decays at a different rate, also forming lead. Each of these ends up in a different isotope of lead, so we need not only a chemist with his test tubes but also a physicist with a special instrument to sort out the various isotopes, leads of different mass.

Without going into detail on these problems, we can understand that the geologists using the uranium-lead clock have to look out for a number of pitfalls if they are to get a reasonably trustworthy answer. They are glad to have other radiometric methods to verify their age measurements. Two others have been developed that can often be used on the same rock.

[Graph on page 19]

(For fully formatted text, see publication)

The decrease in uranium is directly proportionate to the increase in lead

100%

50%

25%

12.5%

Half-lives 1 2 3

lead (argon)

(potassium) uranium

[Diagram on page 18]

(For fully formatted text, see publication)

Uranium

Lead

How much uranium (or lead) did this rock originally have?

How much uranium (or lead) leached into the rock later?

How much lead derived from the decay of thorium?