The greatest achievement of the “plumbologists” has been the calculation
of the age of the earth, first proposed by Houtermans, a German
physicist, and independently by Arthur Holmes, a British geologist, in
1946 and finally perfected by C. C. Patterson in 1953. It is actually a
rather simple calculation, although the way to discovering it was far
from easy. Before we look at it in detail, however, let’s consider some
basic assumptions and explain what is meant by “the age of the earth”.
From studying the mechanics of the solar system, scientists have become
reasonably certain that the earth and the other planets and their
satellites all were formed in a common process in a relatively short
period of time, geologically speaking. Perhaps it took a dozen million
years or so, but compared to the time that has elapsed since, that is a
twinkling. At some time soon afterwards, the earth became molten, or at
any rate fluid enough to allow much of its iron to settle toward the
center to form the earth’s core. Similar cores presumably formed in
other planets. As the iron went down, it took some lead with it, and as
the silica went up, uranium followed it toward the surface, because of
the chemical affinity between these kinds of elements. In the present
earth, we have found, almost all the uranium is concentrated in the top
layer, or crust, which is only about 25 miles thick under the continents
and even thinner under the oceans.
[Illustration: _Internal structure of the earth. The central core is
probably an alloy of iron and nickel, surrounded by a mantle of less
dense silicate material, with a thin crust of still lighter silicates._]
The time of this early and relatively rapid separation of uranium and
lead on a worldwide scale is the event that plumbologists can determine,
and the period since then is what they mean by “the age of the earth”.
When Houtermans first wrote about it, he called it “the age of uranium”.
How is this done? We have said that one of the isotopes of uranium,
²³⁵U, decays faster—about 6.3 times faster—than the other, ²³⁸U. They
decay into two different isotopes of lead. Therefore, if we can
determine the isotopic composition of average ordinary lead in the
earth’s crust today, and if we can somehow obtain a sample of the kind
of lead that is locked in the earth’s core, we can calculate how long it
took to change the PRIMORDIAL lead (like that in the core) into
present-day lead in the crust by the gradual addition of radiogenic
lead—lead that has resulted from the decay of uranium. Now, someone
might logically ask, “Isn’t it necessary to know also the actual amount
of uranium involved in the process, and isn’t this difficult to
determine?” It turns out to be a remarkable aspect of the
Holmes-Houtermans calculation that the uranium-concentration terms
cancel out in the equations and only the _ratio_ of the isotopes and
their decay constants need be considered. These are all known
accurately.
Next, we must decide just what is average present-day lead? It isn’t
enough to go to a lead mine and get a sample, because, unfortunately,
leads from different mines have widely varied isotopic composition—that
is, a different mixture of four natural isotopes, ²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb,
and ²⁰⁸Pb—as a result of their geologic histories. No, lead samples from
a mine won’t do. However, geologists have been able to separate lead
from recent marine sediments, obtained from the ocean bottom, far from
land. These are of uniform composition, and are good samples of what the
world’s rivers bring into the ocean. Other useful samples can be found
in plateau basalts, which are enormous bodies of dark volcanic rock that
make up the bedrock in many parts of the world. The lead from these
basalts is isotopically very much like the lead in the oceans.
Very well, but how about the lead from the core? Where can we hope to
find a sample of it? It turns out to be easier than you might think.
Astronomers believe it highly probable that most meteorites are
fragments of a former planet that broke up for reasons that are not
entirely clear. It is pretty definite, however, that this protoplanet
(or these protoplanets, for there may have been more than one) had an
iron core, and this core (or these cores) is the source of the iron
meteorites sailing around in space. A large meteorite hit the earth not
too long ago (geologically speaking) and caused the Meteor Crater near
Canyon Diablo in Arizona.
[Illustration: _Examining ocean-bottom sediments obtained by lowering a
tube-like instrument that brings up a long rod-shaped “core”, prior to
nuclear age determination of the sample._]
Many fragments of the meteorite iron have been found around the crater,
and it is reasonable to assume that this is the kind of iron we would
expect to find in the core of the earth. Like the core iron, it is mixed
with a little lead, which can be isolated and analyzed in a mass
spectrometer for its isotopic composition. This lead is found to be much
less contaminated with radiogenic lead, and hence is much more primitive
than the oldest leads found on earth. Thus, meteorites presumably are as
close as we can get to true primordial lead—the lead of the time when
the earth (and the protoplanet) first formed.
Once these measurements were available, it was easy to write the
Houtermans equation for present-day and primordial leads in this way:
((²⁰⁶Pb)/(²⁰⁴Pb)) present - ((²⁰⁶Pb)/(²⁰⁴Pb)) primordial
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((²⁰⁷Pb)/(²⁰⁴Pb)) present - ((²⁰⁷Pb)/(²⁰⁴Pb)) primordial
= 137.7 ((e^{λ}238^{t} - 1))/((e^{λ}235^{t} - 1))
The present ratio of ²³⁸U to ²³⁵U is 137.7.
e = the base of natural logarithms
λ = the DECAY CONSTANT of each isotope of uranium
t = the age of the earth.
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.