Substituting the best experimental lead isotope ratios into the equation and solving for t, Patterson was able to calculate that the earth is 4550 million years (4.55 aeons) old. Subsequent calculations based on other procedures generally have confirmed that result.
Analytical Techniques
Each method of nuclear age determination involves a different sequence of sample preparation. Wood, peat, charcoal, bones, or shells are cleaned for carbon-14 dating in order to remove every trace of possible contamination by modern carbon as well as extraneous old carbon. Rocks are crushed and ground, minerals are separated according to what is needed in any particular study, and the desired elements are extracted and separated by chemical procedures. Often there may be several different ways of doing the same thing; different laboratories use different procedures. In every case, however, long and complicated procedures must be followed before results are obtained from which an age can be calculated. There is no such thing as a black box into which you can throw a rock and read its age on a dial!
Of all the elements that are part of the useful parent-daughter systems, only potassium is common enough to be analyzed by conventional chemical techniques. All the other elements, especially the radiogenic ones, are present in such small quantities that special processes had to be developed to measure them. The most valuable and generally used process is called [ISOTOPE DILUTION].
Isotope Dilution
This is a process for analyzing an unknown material by incorporating uniformly into it a small amount of a radioactive test substance and determining how much the tracer radioactivity is altered by dilution in the original material.
It works like this: Let’s say that we have an unknown number of atoms, x, of a given element. The normal isotopic composition of this element is accurately known, as it is for most elements, and the ratio of two of its isotopes can be expressed as A/B. We now add to x a known (but usually smaller) amount, c, of the same element. This quantity has a drastically different isotopic ratio, A′/B′. We mix x and c thoroughly together. The ratio A′/B′ can have almost any value, but must be different from A/B and we must know exactly what it is. (There are many ways of determining this chemically, or we can use a sample isotope of known composition obtained from the U. S. Atomic Energy Commission’s Oak Ridge National Laboratory at Oak Ridge, Tennessee.) The substance added is known colloquially as the [SPIKE].
After the original material and the spike are thoroughly mixed we have:
x(A/B) + c(A′/B′) = (x + c) (A″B″)
in which A″/B″ will be the ratio of the two isotopes in the mixture. With this information in hand, we can perform any chemical purification or transfer process with the material (see photo on [page 22]), without having to worry about loss. (Even if 90% of the material should be lost in some operation, the isotopic composition would not be changed, and that is all we are interested in.) Now we can place the material containing the isotopic mixture in a [MASS SPECTROMETER], which will determine the ratio A″/B″. When we have that, we may substitute the value of A″/B″ in the equation and quickly calculate x, the unknown concentration of atoms in the original sample.