All other practical age-determination schemes are based on a few
long-lived isotopes, with half-lives relatively near the age of the
earth (4.5 AEONS). They are:
Table III
Isotope Emits Decays to Half-life
Uranium-238 8 ALPHA PARTICLES[10] Lead-206 4.51 aeons
Uranium-238 Spontaneous fission 2 Fragments 10 million
aeons[11]
Uranium-235 7 Alpha particles Lead-207 0.713 aeons
Thorium-232 6 Alpha particles Lead-208 14.1 aeons
Rubidium-87 Beta particle Strontium-87 4.7 aeons
Potassium-40 Electron capture Argon-40 1.3 aeons
...... ...... ...... ......
Rhenium-187[12] Beta particle Osmium-187 40 aeons
It is apparent that Table II on page 6, showing the long-lived
radioactive nuclides, is much longer than the list of the seven shown
here that are actually useful in practice. Some of the nuclides that are
theoretically available are useless on a practical basis, because they
are so rare in nature. Many others cannot be used for reasons that are
fundamental to the whole process of nuclear age determination by “whole
hourglass” (that is, parent-daughter) methods. Let’s look at these
reasons.
These methods are based on closed systems in which the daughter products
of the radioactive decay are locked with the parent material from the
beginning of the system, and nothing is added or removed thereafter. To
state it in terms of our analogy, the hourglass must be in perfect
working order—no leaks or cracks permitted.
There is another fundamental requirement: At the beginning, the bottom
part of the hourglass must be empty. If some sand were already in the
bottom at the start, we would mistakenly be led to conclude that the
time elapsed was longer than it actually was. That necessity places a
severe limitation on the type of system we can use.
Consider, for example, the decay of potassium-40 into calcium-40.
Measuring this process is perfectly suitable from the point of view of
half-life, but the daughter product is identical with the most common
isotope of ordinary calcium. And calcium is present everywhere in
nature! Even the purest mineral of potassium, sylvite (the salt,
potassium chloride), contains so much calcium impurity that the
RADIOGENIC daughter calcium, produced by the decay of potassium in
geologic time, is negligible in comparison. We can say that the bottom
of this potassium-40 hourglass has been stuffed with so much sand from
the very beginning that the few grains that fall through the waist are
lost in the overall mass. This demonstrates that schemes involving the
decay of a relatively rare nuclide into a relatively common one are not
usable. Natural geochemical separations of elements are never perfect,
anyway.
Similarly, the decay of any of the RARE EARTH elements into other rare
earth elements is not particularly helpful, because the rare earths are
so similar chemically they tend to travel together when they move in
nature.[13] Wherever the parent isotope goes, the daughter tags along.