path: root/49070-0.txt

*** START OF THE PROJECT GUTENBERG EBOOK 49070 ***

                             Nuclear Clocks


The Understanding the Atom Series

Nuclear Energy is playing a vital role in the life of every man, woman,
and child in the United States today. In the years ahead it will affect
increasingly all the peoples of the earth. It is essential that all
Americans gain an understanding of this vital force if they are to
discharge thoughtfully their responsibilities as citizens and if they
are to realize fully the myriad benefits that nuclear energy offers
them.

The United States Atomic Energy Commission provides this booklet to help
you achieve such understanding.

           [Illustration: Signature of Edward J. Brunenkant]

                                          Edward J. Brunenkant, Director
                                       Division of Technical Information




  UNITED STATES ATOMIC ENERGY COMMISSION

  Dr. Glenn T. Seaborg, Chairman
  James T. Ramey
  Wilfrid E. Johnson
  Francesco Costagliola

                     [Illustration: NUCLEAR CLOCKS]

                             by Henry Faul




                                CONTENTS


  INTRODUCTION                                                          1
  THEORY OF NUCLEAR AGE DETERMINATION                                   5
  THE CARBON-14 CLOCK                                                   9
      Carbon-14 Counting                                               12
      Carbon-14 Results                                                15
  THE LONG-LIVED CLOCKS                                                19
      The Rubidium-Strontium Clock                                     20
      The Uranium Fission Clock                                        24
      Plumbology                                                       27
  THE AGE OF THE EARTH                                                 27
      Analytical Techniques                                            31
      Minerals That Can Be Dated                                       34
  SOME INTERESTING RESULTS                                             40
      The Old Man From Olduvai                                         40
      The Geologic Time Scale                                          41
      Precambrian Stratigraphy                                         47
  AND WHERE DO WE GO FROM HERE?                                        48
  GLOSSARY                                                             49
  APPENDIX                                                             52
  SUGGESTED REFERENCES                                                 58


                 United States Atomic Energy Commission
                   Division of Technical Information
           Library of Congress Catalog Card Number: 67-60195
                            1966; 1968(Rev.)

[Illustration: _A 14,000-year-old burial site being uncovered in the
area of the Aswan Reservoir in Sudan. To determine the age of such
ancient remains, archaeologists search for every scrap of associated
wood or charcoal that could be used for age measurement of carbon-14,
one of the “nuclear clocks” described in this booklet._]

                     [Illustration: NUCLEAR CLOCKS]

                             By HENRY FAUL




                              INTRODUCTION


_How old is a rock?_

_How old is man?_

_How old is the earth?_

It would be difficult to find a reason why anyone would really have to
know the answers to these questions, yet they have been asked over and
over again since the dawn of human society. The records of every
civilization disclose attempts to delve into the past beyond the memory
of the oldest man, beyond recorded history, beyond earliest legend.

Curiosity about the remote past may be very ancient, but the only
reliable method of measuring very long intervals of time is new. The
possibility of doing so became apparent only after the discovery of
RADIOACTIVITY[1] in 1896 by Henri Becquerel, when Marie and Pierre Curie
in 1898 recognized that some atoms are radioactive and change by
themselves into other atoms at regular and constant rates. If something
gradually transforms itself into something else, if this transformation
goes on at a known pace, and if all the products of the activity are
preserved in some kind of a CLOSED SYSTEM, then it is theoretically
possible to calculate the time that has elapsed since the process
started. The theory was clear for years; the only problem was how to
satisfy all those ifs.

By 1910 it was well established that the earth must be extremely
ancient. Analyses of some minerals containing uranium showed them to be
hundreds of millions of years old, even though the uranium came from
rocks that were known to be relatively young among geologic STRATA.
Measurements still were inaccurate, however, and only a few rare and
unusually rich radioactive minerals contained enough of the products of
RADIOACTIVE DECAY[2] to allow analysis of their age by the crude methods
then available.

Not much progress was made for about 30 years until A. O. C. Nier, a
Harvard University physicist, perfected an instrument called a MASS
SPECTROMETER (to be described later) just before World War II. The rapid
technological advances of the war years followed. The Manhattan
Project[3] made the atomic bombs that ended the fighting; it also
developed new scientific techniques that could be applied, when peace
returned, to the measurement of geologic time.

The next important advance was contributed in 1946 by Arthur Holmes in
England and by F. G. Houtermans in Germany. Each of these scientists had
seen Nier’s reports before the war and had realized that Nier’s
mass-spectrometer analyses of lead made it possible, for the first time,
to make rational calculations about the age of the earth. The two
scientists independently calculated that age at about 2 to 3 billion
years, using the handful of data available to them from Nier’s
measurements. It is interesting that today, thousands of analyses later,
our planet’s age usually is given as 4.5 billion years. The early
estimates were not far off.

Development of various methods for measuring the age of minerals
followed rapidly, and by 1955 many fundamental studies needed for
measuring the age of very old substances were complete. The basic
techniques are summarized in Table I. They will be explained later. The
new methods produced broad confirmation of the early rough estimates and
they also brought a few surprises.

Before we go into these discoveries, let us look at some theoretical
foundations.

                   Table I    BASIC MEASUREMENT METHODS
  Method              Material      Time Dated         Useful Time Span
                                                       (years)
  Carbon-14           Wood, peat,   When plant died    1000-50,000
                      charcoal
                      Bone, shell   Slightly before    2000-35,000
                                    animal died
  Potassium-argon     Mica, some    When rock last     100,000 and up
                      whole rocks   cooled to about
                                    300°C
                      Hornblende    When rock last     10,000,000 and up
                      Sanidine      cooled to about
                                    500°C
  Rubidium-strontium  Mica          When rock last     5,000,000 and up
                                    cooled to about
                                    300°C
                      Potash        When rock last     50,000,000 and up
                      feldspar      cooled to about
                                    500°C
                      Whole rock    Time of            100,000,000 and up
                                    separation of
                                    the rock as a
                                    closed unit
  Uranium-lead        Zircon        When crystals      200,000,000 and up
                                    formed
  Uranium-238         Many          When rock last     100-1,000,000,000
  fission                           cooled             (Depending on
                                                       material)

[Illustration: _Time scale of the Earth, drawn to scale. See also the
Holmes time scale on page 46._]

  Event    Geologic Time                      Period           Era
  Man appears[4] (2 million years ago)
                                              Quaternary       CENOZOIC
                                              Tertiary
  Extinction of the dinosaurs (70 million
  years ago)
                                              Cretaceous       MESOZOIC
  Mammals appear (130 million years ago)      Jurassic
                                              Triassic
  Oldest known reptiles (300 million years    Permian          PALEOZOIC
  ago)
                                              Pennsylvanian
                                              Mississippian
                                              Devonian
                                              Silurian
                                              Ordovician
                                              Cambrian
  First abundant life in the sea (animals
  without backbones) (550 million years ago)
  Algae and other microorganisms (1,900       Proterozoic      PRECAMBRIAN
  million years ago)
                                              Archean
  Oldest rocks in North America (2,800
  million years ago)
  First hint of life (bacteria?) (3,100
  million years ago)
  Oldest rocks (3,300 million years old)
  Formation of Earth’s core (4,500 million
  years ago)




                  THEORY OF NUCLEAR AGE DETERMINATION


We can think of the nucleus of an atom as a sort of drop—a bunch of
NEUTRONS and PROTONS held together by very strong short-range forces.
These elementary particles within a nucleus are not arranged in any
fixed or rigid array, but are free to move about within the grip of
these forces. These motions may be quite violent, but for most NUCLIDES
found in nature, the nuclear forces are powerful enough to keep
everything confined; thus the nuclei of these atoms hold together, and
are said to be stable. If any one nucleus of a given ISOTOPE is stable,
then all others are also stable, because what is true for one atom of a
given kind is true for all others of the same kind.[5]

Some nuclides, both man-made and natural, are unstable, however. Their
nuclei are in such violent turmoil that the nuclear forces cannot always
hold them together, and various bits and pieces fly off. If we were to
try to predict when one particular unstable nucleus would thus
disintegrate, however, we could not succeed, because the instant any
specific decay (or disintegration) event will occur is a matter of
chance. Only if a large number of unstable nuclei of one kind are
collected together can we say with certainty that, out of that number, a
certain proportion will decay in a given time. It turns out that this
proportion is the same regardless of any external conditions.

This property of nuclei to decay by themselves is called radioactivity.
Radioactive nuclei decay at constant rates regardless of temperature,
pressure, chemical combination, or physical state. The process goes on
no matter what happens to the atom. In other words, the activity inside
the nucleus is in no way affected by what happens to the ELECTRONS
circling around it. (Only in very special cases can outside disturbances
affect the radioactivity of a nucleus and then only slightly. For all
practical purposes, rates of radioactive decay are constant.)

Most radioactive nuclides have rapid rates of decay (and lose their
radioactivity in a few days, or a few years, at most); most of these are
known today only because they are produced artificially. Some of them
may have been present at the time the solar system was formed, but they
have since decayed to such insignificant fractions of their original
amounts that they can no longer be detected. Only a few radioactive
nuclides decay slowly enough to have been preserved to this day, and so
are present in nature. They are listed in Table II.

  Table II    RADIOACTIVE NUCLIDES WITH HALF-LIVES LARGE ENOUGH TO BE STILL
                  PRESENT IN USEFUL AMOUNTS ON THE EARTH[6]
  PARENT Element   DAUGHTER         HALF-LIFE (years)    Type of Decay
                   Product
  Potassium-40     Argon-40         1.3 × 10⁹ (total)    ELECTRON CAPTURE
                   Calcium-40                            BETA DECAY
  Vanadium-50      Titanium-50      ~6 × 10¹⁵ (total)    Electron capture
                   Chromium-50                           Beta decay
  Rubidium-87      Strontium-87     4.7 × 10¹⁰           Beta decay
  Indium-115       Tin-115          5 × 10¹⁴             Beta decay
  Tellurium-123    Antimony-123     1.2 × 10¹³           Electron capture
  Lanthanum-138    Barium-138       1.1 × 10¹¹ (total)   Electron capture
                   Cerium-138                            Beta decay
  Cerium-142       Barium-138       5 × 10¹⁵             ALPHA DECAY
  Neodymium-144    Cerium-140       2.4 × 10¹⁵           Alpha decay
  Samarium-147     Neodymium-143    1.06 × 10¹¹          Alpha decay
  Samarium-148     Neodymium-144    1.2 × 10¹³           Alpha decay
  Samarium-149     Neodymium-145    ~4 × 10¹⁴?           Alpha decay
  Gadolinium-152   Samarium-148     1.1 × 10¹⁴           Alpha decay
  Dysprosium-156   Gadolinium-152   2 × 10¹⁴             Alpha decay
  Hafnium-174      Ytterbium-170    4.3 × 10¹⁵           Alpha decay
  Lutetium-176     Hafnium-176      2.2 × 10¹⁰           Beta decay
  Rhenium-187      Osmium-187       4 × 10¹⁰             Beta decay
  Platinum-190     Osmium-186       7 × 10¹¹             Alpha decay
  Lead-204         Mercury-200      1.4 × 10¹⁷           Alpha decay
  Thorium-232      Lead-208         1.41 × 10¹⁰          6 Alpha + 4
                                                         beta[7]
  Uranium-235      Lead-207         7.13 × 10⁸           7 Alpha + 4 beta
  Uranium-238      Lead-206         4.51 × 10⁸           8 Alpha + 6 beta

In a large number of radioactive nuclei of a given kind, a certain
fraction will decay in a specific length of time. Let’s take this
fraction as one-half and measure the time it takes for half the nuclei
to decay. This time it is called the HALF-LIFE of that particular
nucleus and there are various accurate physical ways of measuring it.
During the interval of one half-life, one-half of the nuclei will decay,
during the next half-life half of what’s left will decay, and so on. We
may tabulate it like this:

  Elapsed time     Amount left of
  (Number of       what was
  half-lives)      originally
                   present
  1                ½
  2                ¼
  3                ⅛
  4                ¹/₁₆
  5                ¹/₃₂
  6                ¹/₆₄
  7                ¹/₁₂₈
  ...              ...

In other words, after seven half-lives, less than 1% of the original
amount of material will still be radioactive and the remaining 99%+ of
its atoms will have been converted to atoms of another nuclide. This
kind of process can be made the basis of a clock. It works, in effect,
like the upper chamber of an hourglass. Mathematically it is written:

                             N = N₀e^{-λt}

  where

    N = the number of radioactive atoms present in the system now,

    N₀ = the number that was present when t = 0, (in other words, at the
          time the clock started),

    e = the base of natural (or Napierian[8]) logarithms (the numerical
          value of e = 2.718 ...),

    λ (lambda) = the decay rate of the radioactive material, expressed
          in atoms decaying per atom per unit of time,

    t = the time that has elapsed since the origin of system, expressed
          in the same units.

Obviously, in ordinary computations that would not be enough information
to calculate the time, because there still are two unknowns, _N₀_ and
_t_. In a closed system, however, the atoms that have decayed do not
disappear into thin air. They merely change into other atoms, called
daughter atoms, and remain in the system.

And at any point in time, there will be both PARENT and DAUGHTER atoms
mixed together in the material. The older the material, the more
daughters and the fewer parents. Some daughters are also radioactive,
but this does not change the basic situation. Thus it follows that

                               N₀ = N + D

where D = the number of daughter (decayed) atoms. We may then substitute
into the first equation

                          N = (N + D) e^{-λt}

and solve

                         t = 1/λ · ln(1 + D/N)

where ln = the natural logarithm, the logarithm to base e.

This kind of system can be represented crudely by an old-fashioned
hourglass, as shown in the figure, which has the parameters of these
equations marked. (Keep in mind, however, that this is only a gross
analogy. Nuclear clocks run at logarithmically decreasing rates, but the
speed of a good hourglass is roughly constant.)

[Illustration: _An hourglass illustrates an ideal closed system. Nothing
is added and nothing is removed—the sand just runs from the top bulb to
the bottom._]

Remember that the decaying nucleus does not disappear. It changes into
another nucleus, and this new nucleus forms an atom that may be captured
and held fixed by natural processes. The decayed nuclei are thus
collected, so that here we have the bottom chamber of the hourglass.

But sometimes we need only the top chamber of an hourglass.




                          THE CARBON-14 CLOCK


Carbon-14 decay is the best example of a top-only hourglass. Carbon-14
is constantly being produced in the upper atmosphere from atoms of
nitrogen-14 being struck by neutrons that had their origin in COSMIC
RAYS. The reaction is written:

                      ¹⁴N + neutron → ¹⁴C + proton

Radioactive decay then follows, with a half-life of 5800 years[9] for
the ¹⁴C.

                  ¹⁴C → ¹⁴N + electron (BETA PARTICLE)

The radiocarbon emits an electron and changes back into nitrogen.

As far as anyone can tell, ¹⁴C was produced at a constant rate above the
earth for at least 50,000 years before the first atomic bomb was
exploded. In other words, the ¹⁴C cycle is like an hourglass in which
the sand in the upper part is replenished as fast as it runs out through
the hole in the waist. A process of this sort, where production equals
decay, is called a SECULAR EQUILIBRIUM.

The newly produced ¹⁴C soon is evenly mixed with the carbon dioxide in
the air, is taken up by all living plants, and then finds its way into
all living animals. In effect, all carbon in living organisms contains a
constant proportion of ¹⁴C. If any of this carbon is taken out of
circulation—when a tree branch is broken off, for instance, or when a
shellfish dies in the ocean—no more new ¹⁴C is added to that particular
system, but the old ¹⁴C continues to run out. In effect it now starts
measuring time as an hourglass should.

[Illustration: _To illustrate secular equilibrium, one must imagine an
hourglass in which the sand in the top bulb is continuously
replenished—as fast as it runs out through the hole in the waist and
disappears._]

When we find a piece of charcoal in a cave or a piece of wood in some
ancient structure, for example, we can measure the amount of carbon in
it, determine how much of it is ¹⁴C, and then calculate back to the time
when the radioactivity from the ¹⁴C was the same as we now find in
living wood. In other words, if we assume that we know from the observed
secular equilibrium how much ¹⁴C originally was present in living
material, then we can calculate the time of death of any similar but
ancient material. That is the basis of the ¹⁴C method of age
determination.

[Illustration: _Dinosaur tracks imprinted in rock in Navajo Canyon,
Arizona, arouse the professional interest of this scientist. Fossil
traces of extinct prehistoric creatures were for a long time the best
clues to the age of rock formations._]

[Illustration: _A scientist using liquid nitrogen to freeze carbon
dioxide gas made from a sample of ancient material that he is preparing
for age determination by the carbon-14 technique._]

For example, a bit of a rafter from a prehistoric cliff-dwelling or a
remnant of charcoal from an ancient fire may be analyzed for its
remaining ¹⁴C content, and its age determined accurately within the
margin of a few hundred years. This fixes the time at which the wood for
the rafter or the firewood was broken or cut from the living tree, and
hence the period in which the men lived who used the wood.

[Illustration: _The most useful samples for carbon-14 age determination
are charcoal, wood, and shells._]


Carbon-14 Counting

Carbon-14 measurements are made by taking a known amount of carbon,
reducing it to a gas, and then counting the ¹⁴C disintegrations in the
gas. This may sound simple, but in reality the measurement process is a
formidable undertaking, because the amount of the ¹⁴C isotope in the
carbon is so extremely small. (The remainder of the carbon, of course,
consists of other isotopes—¹²C or ¹³C, which are stable.)

There are two basic techniques. The carbon can be:

  1. Burned with oxygen to form carbon dioxide, or

  2. Reduced chemically to methane or ethane, or to a carbide from which
  acetylene can be evolved by adding water. (See booklet cover and
  description on page 59.)

The first technique is the simpler, but carbon dioxide (CO₂) contains
only one atom of carbon per molecule, whereas acetylene (C₂H₂) and
ethane (C₂H₆) each contain two. Consequently, the SPECIFIC ACTIVITY of
acetylene or ethane is twice that of carbon dioxide, other things being
equal. For that reason acetylene or ethane are the preferred gases in
some laboratories. On the other hand, they are explosive, and that
cautions other scientists into using the carbon dioxide method.

Whichever gas is used, it is first purified and then stored in a bottle
for a month or so. This storage allows for decay (disappearance) of any
radon, the gaseous radioactive product of uranium decay. Uranium
contamination is difficult to avoid at the low radioactivity levels of
¹⁴C, but the half-life of radon is only 3.82 days, so that it will decay
to an insignificant level in a month. After the storage period, the gas
is pumped into an array of instruments known as a low-background
PROPORTIONAL COUNTER, and its radioactivity is determined. This is an
involved process. First there is the matter of the BACKGROUND COUNT.

The background count of an instrument is the number of pulses (counts)
it will give per unit time when there is _no_ radioactive sample in it.
These counts are caused by cosmic rays, by radioactive contamination
always found in the vicinity of the counter, or by any contamination
inside the instrument. In ¹⁴C counting, all these sources of background
must be reduced to negligible levels. This is done in a number of ways.

For one thing, the whole assembly is constructed with surrounding walls
of lead or iron more than a foot thick. Such a shield will stop all the
GAMMA RAYS coming from radioactive contamination in the laboratory and
much of the cosmic radiation; high-energy cosmic rays and all neutrons
still will get through. Therefore, there is an ANTICOINCIDENCE RING
inside the lead shield. This is a cylindrical space completely
surrounded by GEIGER COUNTERS that are connected to each other and to
the SAMPLE COUNTER in the middle. With this arrangement, when the sample
counter and any ring counter discharge simultaneously, it is a signal
that the pulse triggering this response was caused by some energetic
particles, such as a cosmic ray, passing through the whole assembly. A
pulse recorded simultaneously on two counters is automatically rejected
from the counting mechanisms. Some instruments have been designed with a
cylinder of paraffin immediately inside the anticoincidence ring, to
slow down neutrons so that they can be captured, and with a final shield
of highly purified mercury between two cylinders of selected steel to
hold out even more unwanted radiation.

[Illustration: ]

[Illustration: _A carbon-14 counter. Sketch (above) shows arrangement of
components in photo (left)._]

Finally, the sample counters are made of specially selected metal tubing
that is extremely low in radioactive content, with a fine wire stretched
down the middle. (In some recent designs, the anticoincidence ring and
sample counter are combined in a single cylindrical housing with a thin
foil of metallized plastic between them.) A thin glass filling tube
connects the sample counter with the outside world.

[Illustration: _Detail of one type of sample-counting tube for carbon-14
work. Carbon-14 in benzene gas molecules is placed in the central cell
and mixed with a fluid that scintillates, or emits light flashes, when
exposed to radiation. Photomultiplier tubes convert the flashes to
electric signals._]

The radiocarbon-bearing gas is pumped into the sample counter through
the filling tube, and all the counts resulting from its disintegrations
are recorded electronically. The age of the sample is calculated from
the NET COUNTING RATE (the sample counting rate minus the background);
the lower the counting rate the higher the age. The upper limit of the
age that can be measured is determined by the STATISTICAL ERROR (that
is, by the measure of the instrument accuracy) in the net count. In very
old samples this error may be great enough so that the calculated age of
the sample may have little or no meaning.


Carbon-14 Results

OBJECTS DATED BY RADIOCARBON

[Illustration: _Hair of an Egyptian woman. 5020 ± 290 years old._]

[Illustration: _Linen wrapping from the Dead Sea Scroll containing the
Book of Isaiah. 1917 ± 200 years old._]

[Illustration: _Peruvian rope. 2632 ± 200 years old._]

[Illustration: _Preglacial wood found in Ohio. More than 20,000 years
old._]

[Illustration: _Rope sandal found in an eastern Oregon cave. One of a
pair of 300 pairs found in this cave. 9035 ± 325 years old._]

Carbon-14 is by far the most widely used method of measuring geologic
time. It has become the mainstay of archeology and geology for studies
of events of the past 50,000 years or so, and also has wide applications
in climatology, ecology, and geography. It would be difficult to pick
out the most significant example of the use of this method, but one
important contribution has been in study of the early inhabitants of
North America. With the aid of ¹⁴C it has been possible to date human
living sites from many points in the western United States. The first
appearance of these sites, about 11,500 years ago, apparently coincided
with the time when a land bridge was open from Asia to America over what
is now the Bering Strait. An ice-free passage extended from this bridge
through present-day Alaska and western Canada to the United States. This
may have been the route taken by the first immigrants to America—a
population of mammoth-hunters, who made the characteristic flint
_Clovis_ arrow and spear points.

[Illustration: _A Clovis arrow point chipped from flint by the earliest
men on the American continent. The photograph is actual size._]

By about 11,000 years ago, these Clovis people had spread across the
area of the United States and into Mexico. It may have been they who
killed off the mammoths and then gradually assumed the characteristics
of the _Folsom_ culture. The Folsom people were bison-hunters, and long
were thought to have been the first population in America. It was with
the use of ¹⁴C that it finally was possible to place these two cultures
in proper sequence—the Clovis first—and to correlate them with major
natural changes, especially the advance and retreat of glaciers across
the continent.




                         THE LONG-LIVED CLOCKS


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.


The Rubidium-Strontium Clock

The decay of rubidium-87 (⁸⁷Rb) into strontium-87 (⁸⁷Sr) is perhaps the
most useful scheme for geologic age determination. The same problem
shows up here, but at least there is a way out of the wilderness. It is
not exactly simple, but a consideration of it is fundamental to
understanding the process of nuclear dating. The figure shows patterns
from mass spectrometer charts; each peak represents an isotope of
strontium, and the height of every peak is proportional to the relative
abundance of that isotope. In the figure, A shows the mass-spectrum of a
rock or mineral containing COMMON strontium (which is a mixture of
several isotopes). The peak of ⁸⁷Sr is small compared to the others. B
shows the mass-spectrum of strontium from an old rubidium-rich mineral
CRYSTAL, drawn to the same scale, as far as the nonradiogenic isotopes,
⁸⁴Sr, ⁸⁶Sr, and ⁸⁸Sr, are concerned. The ⁸⁷Sr peak in this spectrum is
obviously larger than in the common strontium in A. This is because this
isotope is radiogenic and has been accumulating from the decay of
rubidium since this crystal was formed.

The question we must answer is: How much of this ⁸⁷Sr was formed from
⁸⁷Rb decay and how much originally was present in the crystal as an
impurity? If the amount of this ORIGINAL strontium is not too large, the
problem can be solved by simple arithmetic.

First, we must find a good sample of common strontium—that is, ordinary
strontium, the kind shown at left in the figure. We cannot require that
this strontium be entirely uncontaminated by radiogenic strontium,
because all strontium is more or less contaminated. What we need is
strontium contaminated to _just the same extent_ as the strontium that
was taken as an impurity into the closed system when it first formed. In
geological specimens such a material is usually available.

[Illustration: _Drawings of mass-spectrometer charts showing the
isotopic spectra of two kinds of strontium: (A) common strontium and (B)
strontium from an old mineral rich in rubidium._ (_See page 32 for photo
of a mass spectrometer._)]

[Illustration: _Rubidium-87 and strontium-87 fall on the same spot in
the mass spectrum. Therefore, rubidium must be separated chemically from
strontium before the strontium can be analyzed in a mass spectrometer.
It is done with ion-exchange columns. Four of them are shown in this
photograph. The author of this booklet is adding a sample, dissolved in
a few drops of hydrochloric acid, to the second column._]

Let us take as our closed system a mica crystal in a mass of granite.
Mica contains a fair amount of rubidium, and it retains its radiogenic
strontium very well. Furthermore, mica crystals are often associated or
even intergrown with the slender, rod-shaped crystals of a mineral
called apatite—a phosphate of calcium. It is justifiable, on the basis
of geological knowledge, to say that the mica and the apatite grew at
roughly the same time and thus presumably from the same liquid medium
that became granite when it later solidified. Now strontium is
geochemically similar to calcium, and some strontium will have gone into
the apatite crystal in place of calcium. Apatite contains no
alkalis—hence apatite will have virtually no rubidium (which is an
alkali) in it to contaminate the ⁸⁷Sr. Consequently, when we find
apatite in an old granite, we know the apatite will still contain the
kind of common strontium that was taken into the mica crystal when it
grew originally.

We can separate the apatite from the granite by standard mineralogical
techniques, extract the strontium from the apatite chemically, and
analyze it on a mass spectrometer to obtain the isotopic spectrum—the
relative amount of each isotope that is present. We can then perform the
same isotopic analysis on the strontium extracted from the mica, and
subtract the original (apatite) strontium from the total (mica)
strontium, to obtain the radiogenic component or daughter product. (See
page 32 for details of this method.)

Obviously, there is a certain error associated with every isotopic
analysis, so such a calculation is meaningful only when the radiogenic
component is large compared with the error in the measurement of
isotopic abundance. When one large quantity must be subtracted from
another large quantity to obtain a small difference, there is an obvious
limit to how much one can trust the result. The absolute accuracy in
measuring strontium isotope abundance is a few tenths of 1%, using the
best mass spectrometers now available. In practice, one can trust a
calculated age for a specimen only when the ⁸⁷Sr is as little as about
5% radiogenic. The results do not mean much when only 1 or 2% is
radiogenic.

[Illustration: _A sample of granite being made ready for crushing and
mineral separation._]


The Uranium Fission Clock

When a neutron strikes the nucleus of uranium-235 (²³⁵U) or
plutonium-239 (²³⁹Pu), it may cause the nucleus to split into two
roughly equal fragments, releasing neutrons and energy. This is the
well-known process of neutron-induced fission, the method in which
nuclear energy is produced in both reactors and bombs.[14] The most
common uranium isotope, ²³⁸U, also breaks up by fission, but does so all
by itself, without the need for any external neutrons. That process is
_spontaneous fission_ and it goes on at random, very much like
radioactive decay. It is a relatively rare process and the fission
half-life is long—about 10 million aeons (10¹⁶ years). That means that
only about one spontaneous fission occurs in uranium-238 for every 2
million alpha decays. That is enough to make a useful clock, however,
because ²³⁸U is present almost everywhere. (See Table III on page 19.)

Imagine an atom of ²³⁸U in some mineral. When the atom suddenly
fissions, it breaks in two with considerable energy, and the two fission
fragments rip like cannon balls through the surrounding crystalline
structure in opposite directions, creating havoc along the way. They
travel a distance something like 10 microns (4 millionths of an inch)
before they are finally slowed down and stopped by all their collisions
with other atoms. Each fragment’s path remains behind as an intensely
damaged tube through the crystal.

The process was known for a long time before anyone was able to find
these fission tracks (the damaged tubes) in the crystals. Finally, about
1960, three young physicists, R. L. Fleischer, P. B. Price, and R. M.
Walker, working at the General Electric Research Laboratory, fell upon
the idea of etching freshly broken surfaces of crystals with acid. They
reasoned that a region so intensely disturbed by the passage of a
fission fragment should be etched more easily and deeply than the
undisturbed surrounding crystal. That idea turned out to be correct, and
fission tracks have now been found in almost every common mineral (since
almost all minerals contain small amounts of uranium).

[Illustration: _Tracks of uranium fission from a fossil antelope bone
fragment from Hopefield, Cape Province, South Africa._]

The fission clock method works this way: A cleavage face or a polished
surface of a crystal or glass fragment is etched with a suitable
solvent. Different acids work best for different materials, and a
suitable procedure must be developed especially for each substance. The
etching brings out the fission tracks so they can be seen (usually as
little conical pits) and counted under a microscope.

After this, the sample is exposed to a known amount of slow neutrons[15]
in a nuclear reactor. New fissions are produced, but this time only in
²³⁵U (which is present in all natural uranium in the proportion of 1
atom of ²³⁵U to 137.7 atoms of ²³⁸U), because slow neutrons do not
produce fissions in ²³⁸U. After the neutron irradiation, the same
surface is etched again, and the new tracks counted. The old tracks,
having been etched twice, now appear larger and thus can be
distinguished from the new ones that were caused by ²³⁵U fission.

The rate at which ²³⁸U decays by fission, λ_{f}, is known, as are the
rate it decays by alpha decay, λ_{α}, and the total number of slow
neutrons, _n_, to which the sample was exposed in the reactor. The age
of the crystal or glass can then be calculated:

         t = (1)/(λ_{α}) ln (1 + (_n_N_{s})/(N_{i}) × constant)

  where

    ln = the natural logarithm (log to the base _e_),

    N_{s} = the number of atoms in the sample.

    N_{i} = the number of atoms of ²³⁵U in the irradiated sample,

and the constant has the value:

         ½ (λ_{α} × 582 × 10⁻²⁴)/(λ_{f} × 137.7) = 4.25 × 10⁻¹⁸

Fission-track dating is a brand new technique, still only partly
developed. It has enormous range and is applicable to numerous minerals;
these advantages imply that it is likely to become very useful.

[Illustration: _An atomic absorption spectrophotometer is used to
measure the amount of potassium in samples of mica dissolved in acid._]


Plumbology

The most complicated and therefore probably the most interesting decay
scheme of all is the decay of uranium to lead, discovered well over half
a century ago and still intensively studied. There are several reasons
for the interest.

First, uranium and lead are geochemically separated to a high degree,
not only on the small scale of an ore deposit but also on the scale of
the earth as a whole. Second, natural uranium has two isotopes with
half-lives that are neither too long nor too short to be useful (the
greater half-life almost exactly equaling the age of the earth), and
these half-lives differ from each other by a factor of about 6.3. That
leads to very important consequences, as we shall see. Third, uranium
and lead are both common, and techniques are available for extracting
them in measurable quantities from almost any natural material.

As a consequence of these happy circumstances, the study of uranium and
lead has contributed a great deal to understanding the earth’s history
and the processes that go on inside it. F. G. Houtermans, one of the
great pioneers in this study, jokingly called the method PLUMBOLOGY, and
it seems a useful name.




                          THE AGE OF THE EARTH


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
         ------------------------   --------------------------
         ((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.


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.

[Illustration: _A large (12-inch) mass spectrometer (at left) in use.
Electronic equipment (right) charts results (see page 21)._]

[Illustration: _Essential parts of a mass spectrometer. Atoms to be
analyzed are changed to ions in the source. Then the ions are
accelerated by high voltage, deflected in a magnetic field according to
their mass, and the intensity of the separated beams is measured in the
collector._]

Mass Spectrometry

The mass spectrometer measures isotopic abundances using a magnetic
field to sort electrically charged particles into groups according to
their masses. It works this way: A small drop of material to be analyzed
is placed on a metal filament and dried. The filament, in its holder, is
placed inside the mass spectrometer, and heated electrically in a
vacuum, like the filament in a light bulb. As the wire begins to glow,
some of the sample begins to radiate, or “boil off”, losing an electron
or two in the process. In other words, some of the atoms will be changed
into positive IONS.

An alternative method is to introduce the sample material into the
vacuum chamber in the form of a gas (like argon, for example), and then
bombard the gas with electrons streaming from a hot filament. The
electron stream will knock some electrons off the gas molecules and this
also will produce positive ions. Either process of ion production is
satisfactory, depending on the problem to be tackled, but the mass
spectrometers for the two methods are naturally quite different.

Whichever way the ions were produced, they are next exposed to a strong
electric field, accelerated, and electrostatically focused into a beam.
These charged particles are directed into a magnetic field between the
pole faces of an electromagnet. The magnet does the analyzing by the
principle of magnetic deflection that was known to André Ampere and
Michael Faraday more than a century ago. Any moving electric charge has
a magnetic field associated with it. This field interacts with the field
of the analyzing magnet to impress a deflecting force on the charge. The
force acts at right angles to the direction the charge travels and also
at right angles to the direction of the impressed magnetic field. The
pull of this force depends only on the electric charge and the speed of
each particle: A light single-charged particle will be deflected more
than a heavier particle with the same charge. In this way, the ions in
the beam are sorted out into a number of separate beams, each made up of
particles of the same charge/mass ratio. Each beam contains one isotope
of the original material, because isotopes differ on the basis of their
mass. By adjusting the current in the electromagnet we can direct these
separate beams into a “collector” and electrically measure their
intensity one by one. This gives the relative abundance of the separate
isotopes in the sample.


Minerals That Can Be Dated

Measuring age by one of the long-lived radioisotopes requires a closed
system. Usually this is some kind of crystal formed in a period of time
that is short, compared to the time that has elapsed since, and that has
remained unchanged since it formed. Specifically, neither the parent
isotopes can have been added nor the daughter isotopes removed by any
process other than radioactive decay.

The earth is a dynamic system, however. Things are always changing and
moving—not very rapidly, perhaps, but fast enough, in geologic time, to
raise mountains and shift oceans. Solutions are moving around,
dissolving something here and depositing it again somewhere else.
Temperatures are changing as one place is denuded by erosion and another
area buried under layers of sediment. Under such conditions, few systems
remain closed. It is perhaps surprising that we find any closed systems
at all. Let us look at a few that are known to be reliable. (They are
listed in Table I on page 4.)

Potash Feldspar

In the early 1950s, when the potassium-argon (parent-daughter) method
was being developed by scientists at the University of Chicago, it was
thought that the potash-bearing variety of the mineral feldspar would be
an ideal closed system, because it was usually optically clear and free
of flaws. This widely shared, logical, and perfectly scientific
deduction soon turned out to be quite wrong. The scientific workers
discovered that when feldspar and mica from the same rock (and thus of
the same age) were analyzed side by side, the mica always came out
older! Investigation showed that feldspar “leaked” argon (lost some of
its radiogenic argon) even at room temperature, but the mica retained
all or nearly all of the argon that had been generated in it.

Mica

With the development of the rubidium-strontium (parent-daughter) method
by L. T. Aldrich and his co-workers at the Carnegie Institution of
Washington, came the realization that mica was also very useful for this
analysis, for it usually contains ample rubidium and not much original
strontium that would mask the presence of the radiogenic strontium. As a
result, mica, especially black mica (the mineral biotite), has enjoyed
great popularity as a good and easy-to-find closed system.

[Illustration: _A scientist making adjustments on an “argon train”, a
maze of glass tubing in which argon is released from minerals and
purified for analysis._]

Everything has its limits, and mica is no exception: Even mica tends to
leak argon at elevated, but still relatively low (geologically
speaking), temperatures. These effects also depend on pressure and other
factors, not all of which are well known; these elevated temperatures,
pressures and other conditions of course act to some extent on all rocks
buried in the earth’s crust. It is known that at only about 300°C at
moderate pressures argon is leaked from mica faster than it is being
generated in it by the decay of radioactive potassium. The temperature
needed to cause the rapid loss of strontium from mica is not much
higher. Mica, especially biotite, will recrystallize and lose all its
radiogenic constituents (argon and strontium) at temperatures where many
other minerals show little or no change.

That means that we cannot always rely on mica to give the date of the
_original_ crystallization of a rock—the time when it cooled from a
molten state. Instead, mica will tell us when the rock _last_ cooled
from, say, several hundred degrees centigrade, regardless of what may
have happened to the rock before that. The mica may have been reheated
as a result of being buried under a few miles of sediment, for example.
The mica will show when the rock last cooled—in other words, when it
came up again.

Low-Strontium Feldspar

In spite of early disappointments with potash feldspar for argon dating,
some of it is useful for rubidium-strontium procedures. It all depends
on how much original strontium the potash feldspar contains. Most
feldspars, unfortunately, contain far too much, but rapid screening by
X-ray fluorescence or flame photometry methods can weed these out and
identify specimens low enough in original strontium to be useful.
Otherwise, feldspar is an excellent closed system for rubidium and
strontium; it remains closed even at temperatures high enough to melt
many other minerals. It is not affected at all by the same degree of
heating that will drive argon out of biotite. The rubidium-strontium age
of feldspar usually comes close to the time of original crystallization
of the rock.

Obviously, here is a geologically important tool. If we find feldspar
and biotite in one rock, and if feldspar, tested by the
rubidium-strontium method gives the same age as biotite tested by
potassium-argon decay, then we can say with confidence that the rock has
not been reheated since shortly after it crystallized. Conversely, if
the biotite comes out much younger than the feldspar, we can be sure
that something _has_ happened to this rock long after it first
crystallized. Such information is not only valuable to pure science—it
can also be useful in locating areas favorable for ore prospecting and
in other practical ways.

Zircon

Another very interesting mineral is zircon (a silicate of zirconium),
one of the accessory minerals found in small quantities in many
crystalline rocks. Zircon usually occurs in very small grains and is
heavy and hard, so that it can be separated from the other rock without
much difficulty, even though it may take 100 pounds of rock to supply a
gram of zircon.

Zircon usually contains a fair amount of uranium and very little lead.
It holds radiogenically produced lead well, even at relatively high
temperatures. But that is not all. Even if some of the lead is lost,
there is a mathematical way of correcting for it. This technique is
called CONCORDIA ANALYSIS and was developed by G. W. Wetherill, a
physicist then at the Carnegie Institution of Washington. It is based,
again, on the fact that natural uranium has two long-lived isotopes—²³⁸U
and ²³⁵U—and that the lighter one, ²³⁵U, decays faster than the heavier.
The daughter products of both uranium decay processes are isotopes of
the same element, lead—²⁰⁸Pb and ²⁰⁷Pb, respectively. Heavy isotopes are
not separated to any significant degree by chemical processes, so that
if radiogenic lead has been lost from a system for any reason, the other
lead isotopes also will have been lost in whatever proportion they were
present originally.

If we plot a graph of the radiogenic ²⁰⁶Pb/²³⁸U ratio against the
radiogenic ²⁰⁷Pb/²³⁵U ratio for concordant (closed) systems _of all
ages_, we obtain the curved line shown in the figure below. The curve is
the locus of _all_ concordant U-Pb ages and is called _Concordia_. Then
if we test two or more particular zircons of the same age that have lost
different amounts of lead, at about the same time, the plot of their
²⁰⁶Pb/²³⁸U ratios against their ²⁰⁷Pb/²³⁵U ratios will fall on a
straight line that is a chord of the Concordia curve. The upper
intersection of this chord with the curve then will mark the true age of
the zircons. This is an elaborate technique utilizing difficult chemical
procedures, but it has proved invaluable in solving some important
geologic problems.

[Illustration: _The Concordia curve offers a useful way of analyzing
results of age determinations on the mineral zircon._]

Hornblende

The mineral hornblende provides another useful system. Hornblende is a
complex silicate of sodium, calcium, iron, magnesium, and aluminum, and
usually contains a few tenths of 1% of potassium. It is unusual in that
it tenaciously retains its radiogenic argon, even at relatively high
temperatures.

Sanidine

Still another good system is the rare feldspar, sanidine, which is
excellent for both potassium-argon and rubidium-strontium age
determination. Sanidine usually is found in volcanic ash falls and has
been important in the establishment of the geologic time scale, as we
shall see.

Whole Rocks

Finally there is still another way of obtaining a closed system by using
the whole rock, not just a crystal of a single mineral within it. A
large body of granite or similar rock may contain a number of minerals,
some or none of which may be closed systems. Yet as long as this body of
rock remains impermeable to solutions (which in nature means mostly to
water), no substance will be able to move very far in it because
diffusion in solids is so slow. Consequently it will remain a closed
system, as a whole, regardless of what happens to the individual mineral
grains.

If we take a piece from near the middle of this body of rock and if this
piece is much larger than the largest constituent grain in it, then we
have a fair sample of a closed system—the whole rock. The only
difficulty arises from the fact that few rocks are sufficiently
impermeable to solutions to retain argon, and many rocks contain so much
common strontium that rubidium-strontium analysis is impractical. Still,
we can use the rapid survey methods as for feldspar, selecting the few
rocks that would be useful. This work has been done frequently, and the
results have been fruitful for rubidium-strontium analysis. The
whole-rock rubidium-strontium age dates the time when the rock became
impermeable.




                        SOME INTERESTING RESULTS


The Old Man from Olduvai

[Illustration: _Fossil skull of Zinjanthropus, nearly 2,000,000 years
old, discovered in 1959 by Dr. L. S. B. Leakey in Olduvai Gorge.
Accurate dating of this earliest human ancestor was possible by using
the potassium-argon method._]

One of the most talked-about age measurements in recent years was the
determination of the unexpectedly great age of fossil ancestors of man,
found by the British anthropologist, Dr. L. S. B. Leakey, in Olduvai
Gorge in Tanzania. The measurements were made by Garniss H. Curtis and
Jack F. Evernden at the University of California in Berkeley by the
potassium-argon method. The age came out a little less than 2 million
years, about twice as old as it “should be” in the view of many
scientists. Human remains of such great antiquity had never been found
before, and much doubt was raised about the validity of the figures.

Time periods as short as two million years are not easy to measure by
potassium-argon. The amount of argon produced in that time is extremely
small, and contamination by argon from the air is a serious problem.
Still, the measurements were repeated, the rocks were studied again, and
the result did not change: The fossils were still about 2 million years
old.

In cases like this, one tries to find some other method to check the
results in an independent way. After many attempts it was discovered
that the same rock strata dated by potassium-argon also contained some
pumice—a porous volcanic glass—and that this glass was suitable for
uranium fission-track dating. The measurements were made in the General
Electric Research Laboratory. What was the result? Just about 2 million
years!

When such altogether different techniques give the same number, one can
have some confidence that the number is exact. It would be difficult to
imagine a disturbance in nature that would cause these unrelated methods
to give the same wrong number—in both cases by a factor of two. The
double check simply means the Olduvai man is 2 million years old. There
is not much doubt about it.


The Geologic Time Scale

Much of historical geology is based on a relationship called the LAW OF
SUPERPOSITION. This simply means that when some rock formation was
placed on top of some other formation by natural processes
(sedimentation or volcanic eruption, for example), the layer on top must
be younger than the one on the bottom. Such a conclusion may now seem
obvious, but the concept was not even expressed until the very end of
the eighteenth century and was still a matter of scientific controversy
when Abraham Lincoln was a boy. It was the law of superposition,
however, that led the early geologists to establish the first geologic
time scales and to realize the enormous extent of geologic time.

[Illustration: _Diagram illustrating the law of superposition. Each rock
bed is younger than the strata under it._]

In essence the system of establishing age by this concept is this:
Somewhere a large and easily recognized layer of sedimentary rock was
known. It had a characteristic color, texture, gross composition, and
overall appearance. Let us call it _bed M_. This bed could be traced
across the countryside until a place was reached where it could be seen
that _bed M_ rested on another, different layer of rock, which we might
call _bed L_. _Bed L_ could also be traced some distance and ultimately
could be observed resting on a still different stratum, which we shall
call _bed K_. Some of these beds had fossils in them, and it was
eventually realized that rocks with the same kinds of fossils are of the
same age, even though they may differ in other respects—in color or
composition, for instance.

If _bed M_ was followed in another direction, perhaps a point was
reached where it dipped down a little, and here, was found still another
layer—call it _bed N_—on top of _M_. Obviously, the sequence of beds
from oldest to youngest was _K-L-M-N_. Their relative ages were now
established. Over the years, hundreds of geologists described various
rock layers and identified the fossils in them. By the middle of the
nineteenth century, this “layer-cake” structure of sedimentary rocks was
well-known in western Europe. (One may say, parenthetically, that
America was geologically a vast unknown at that time. Today we know much
more about the geology of Antarctica than anyone a hundred years ago
knew about the geology of the United States.)

A system of nomenclature for the “layer-cake” was developed and refined.
Gradually this nomenclature was accepted internationally. Long-range
correlations between beds of the same age, distant halfway around the
globe from each other, were made possible as the science of PALEONTOLOGY
developed. The relative age of almost any rock containing even poorly
preserved fossils could be determined anywhere in the world with
precision. That is, the age of rock layers in relation to one another
was known. But the real age—the absolute age—remained unknown until
knowledge of radioactivity provided the necessary clocks.

[Illustration: _A geologist carefully maps the layers of soil in which
ancient flint tools have been found. Exact correlation of the
tool-bearing strata with material datable by carbon-14 analysis must be
accomplished before the age of the tools can be determined._]

Even this process wasn’t entirely without problems. The difficulty lay
in the fact that ordinary sedimentary rocks (shale, sandstone, and
limestone) cannot be dated by the usual nuclear methods because they
present no suitable closed systems. Only some volcanic sediments can be
reliably dated by the mica, feldspar, and zircon they contain; but these
ancient ashfalls are rare, usually are only a few inches thick, and are
not easy to identify at the surface because they weather quickly to
clay. Only about a dozen volcanic beds have been accurately dated in
North America. The time points they established are mainstays of the
present geologic time scale, but they have had to be supplemented by
indirect information.

[Illustration: _Steeply dipping sandstone strata from the Cretaceous
Period near Gallup, New Mexico. This photo, taken in 1901 (note the
horse-drawn wagon), was made on an early government survey of Western
lands._]

[Illustration: _Fossils of bird tracks in sandstone in Death Valley,
California._]

The most important of these indirect time points are furnished by what
geologists call BRACKETED INTRUSIVES. It often happens in geologic
history that a mass of rock becomes molten at a great depth and forces
its way up through several layers of sedimentary rocks. The sedimentary
layers are usually bent and twisted (folded) by the upthrust, and where
the cooler rock comes in contact with the molten mass, cooler material
is burned (recrystallized). Geologists call that process CONTACT
METAMORPHISM because the sedimentary rock forms are changed, or
metamorphosed, to have another form or composition.
Contact-metamorphosed rocks, in spite of the damage they have suffered,
may contain recognizable and accurately datable fossils. Thereby the
metamorphic rock establishes a lower limit for the age of the intrusion:
It must be younger than the fossils in the youngest of the metamorphic
rocks it touched.

Now on top of the intrusive rock, we may find another sedimentary rock,
deposited on top of the intrusive after it cooled and was exposed by the
erosion of overlying materials, perhaps millions of years later. This
new sediment may also contain fossils and thus furnish an upper limit
for the age of the intrusion. The measured age of the intrusive rock
thus can be used to set upper and lower limits on the absolute ages of
the two sediments. If we are lucky, the two sediments will bracket a
relatively short interval, making our measurement quite precise.

[Illustration: _Idealized sketch of a bracketed intrusive. The igneous
(molten) rock must be younger than the sedimentary rock (A) it intrudes,
and older than the rock (B) that overlies it. The relative age of the
sedimentary beds is known from their fossils._]

[Illustration: _Facsimile reprint of the famous time scale proposed by
Arthur Holmes in 1959._]

                       Time-scale in millions of years
  PERIODS            Since beginning of period    Duration of period
  PLEISTOCENE                                     _ca_ 1
  ....               _ca_ 1                       ....
  PLIOCENE                                        10
  ....               11                           ....
  MIOCENE                                         14
  ....               25                           ....
  OLIGOCENE                                       15
  ....               40                           ....
  EOCENE                                          20
  ....               60                           ....
  PALEOCENE                                       10
  ....               70 ± 2                       ....
     Upper }
  CRETACEOUS                                      65
     Lower }
  ....               135 ± 5                      ....
     Upper }
  JURASSIC                                        45
     Mid. & Lower }
  ....               180± 5                       ....
  TRIASSIC                                        45
  ....               225 ± 5                      ....
  PERMIAN                                         45
  ....               270 ± 5                      ....
     Upper }
  CARBONIFEROUS                                   80
     Lower }
  ....               350 ± 10                     ....
     Upper }
  DEVONIAN                                        50
     Lower }
  ....               400 ± 10                     ....
  SILURIAN                                        40
  ....               440 ± 10                     ....
  ORDOVICIAN                                      60
  ....               500 ± 15                     ....
  CAMBRIAN                                        100
  ....               600 ± 20                     ....

Using measurements made in many laboratories, and interpolating between
them by using the relative thicknesses of sediments, the great British
geologist, Arthur Holmes, established the time scale that is in general
use today. His original scale is shown on the preceding page. Small
changes can be expected to be made in this scale from time to time, but
major alterations are not likely, except perhaps in the Cambrian Epoch
where the present data are unreliable because they are not complete. (A
scale showing the epochs or periods as often given now is on page 4.)


Precambrian Stratigraphy

So far we have talked only about rocks that are of the Cambrian Epoch or
younger—rocks that may contain fossils. Yet there are vast areas (most
of Canada, for example) that are covered with rocks older than the
Cambrian formation. Some Precambrian fossils have been found, but they
are so rare that they are useless for dating the strata containing them.
Long-range correlation of Precambrian rocks must rely on nuclear
measurements. Therefore it has been only in the last dozen or so years
that some order could be established for the Precambrian rock sequences.
The elaborate Precambrian stratigraphies (arrangements of strata in
sequence) proposed in the past, most of them based on superficial
similarities of the rocks in one place to those in another place, now
have been drastically altered and in some cases completely overturned by
nuclear measurements. We are still far from understanding the sequence
of all the events in that vast span of time we call the Precambrian.
Many thousands of nuclear age determinations will have to be made to
lighten the dark corners of our ignorance.

[Illustration: _Folded strata of Precambrian rocks, including limestones
and shales, in Glacier National Park, Montana._]




                     AND WHERE DO WE GO FROM HERE?


Perhaps we must first realize that we really haven’t come very far yet.
Granted that the age of rocks in many parts of the world is now suddenly
known—and that this was a total mystery some dozen years ago. Granted
that enormous strides forward have been made. It’s only a beginning.

Vast areas of the world are still geologically unexplored. The geologic
time scale is still fragmentary and crude. Thousands of important
geologic questions remain to be defined, explored, and answered by
nuclear age determination. And—as is inevitable in science—many of them
will lead to new questions. It is apparent that dating techniques have
barely begun to be used and understood by geologists.

But apart from geologic work, what else is in store? It is difficult to
predict, but probably the most important advance in the next decade or
two will come when we obtain samples of rock from the moon. Will there
be young rocks there or will they all be 4550 million years old? Or will
they perhaps be some other age? The chemical composition and nuclear
ages of the first moon samples will probably be the most important
information we can hope to obtain from them. These results from the moon
will contribute enormously to our understanding of the processes that
formed the earth, made the continents, and determined the major features
of our world.

We have a long way to go.




                                GLOSSARY


AEON   One billion (10⁹) years.

ALPHA DECAY   Radioactive decay with emission of an alpha particle.

ALPHA PARTICLE   Essentially the nucleus of helium, composed of two
  neutrons and two protons with double positive charge.

ANTICOINCIDENCE RING   A ring of counters connected to exclude outside
  radiation.

BACKGROUND COUNT   The number of impulses per unit time registered on a
  counting instrument when no sample is present.

BETA DECAY   Radioactive decay with emission of a beta particle.

BETA PARTICLE   An electron emitted by a nucleus.

BRACKETED INTRUSIVE   Igneous rock extending into sedimentary rocks that
  are datable by their fossils.

CLOSED SYSTEM   A system in which the parent material radioactively
  decays into its daughter products and nothing is added or removed.

COMMON   (strontium, lead, etc.) The ordinary element present in nature
  at any one time as distinguished from that produced by radioactive
  decay.

CONCORDIA ANALYSIS   A mathematical technique to determine graphically
  the age of a material containing radiogenic lead by comparing its
  uranium-to-lead ratio with the similar ratio in a closed uranium-lead
  system.

CONTACT METAMORPHISM   A metamorphism genetically related to the
  intrusion of molten masses of rock and taking place at or near the
  contact.

COSMIC RAYS   High-energy particles moving in our galaxy.

CRYSTAL   A periodic or regularly repeating arrangement of atoms, formed
  from a single element or compound.

DAUGHTER   A nuclide formed from the radioactive decay of another
  nuclide.

DECAY CONSTANT   The number of atoms decaying per atom per unit of time
  (0.693/half-life).

ELECTRON CAPTURE   A nuclear process in which the nucleus of an atom
  captures an electron from one of the inner shells.

ELECTRONS  Elementary particles with a unit negative electrical charge
  and a mass 1/1837 that of the proton, or 9.12 × 10⁻²⁷ gram. Electrons
  surround the atom’s positively charged nucleus and determine the
  atom’s chemical properties.

GAMMA RAYS  Electromagnetic radiation from an atomic nucleus.

GEIGER COUNTERS  Instruments that count pulses produced by
  radioactivity, consisting of a counting tube with a central wire
  anode, usually filled with a mixture of argon and organic vapor.

HALF-LIFE  The time it takes for half the atoms in a radioactive
  substance to decay.

ION  An atom or molecule that has lost or gained one or more electrons
  and is thus electrically charged.

ISOTOPE DILUTION  An analytical technique involving addition of a known
  amount of an isotopic mixture of abnormal composition to the unknown
  amount of an element of normal or known isotopic composition.

ISOTOPES  Nuclides of the same atomic number but different atomic
  weight. Isotopes of a given element have an identical number of
  protons but different numbers of neutrons in their nuclei.

LAW OF SUPERPOSITION  Statement that overlying strata must be younger
  than underlying strata if there has been no inversion.

MASS SPECTROMETER  An instrument for separation and measurement of
  isotopes by their mass.

NET COUNTING RATE  Sample counting rate minus background counting rate.

NEUTRONS  Elementary particles in the nucleus having no electric charge
  and the mass of one atomic mass unit.

NUCLIDE   A species of atom characterized by the constitution of its
  nucleus.

ORIGINAL   (strontium, lead, etc.) Common strontium, lead, etc., taken
  into a system at the time of its formation.

PALEONTOLOGY   The study of fossil remains.

PARENT   The radioactive element from which a daughter nuclide is
  produced by radioactive decay.

PLUMBOLOGY   The study of the uranium and thorium-lead decay systems.
  The name is derived from the Latin name for lead, _plumbum_.

PRIMORDIAL   Present at the time of the formation of the earth.

PROPORTIONAL COUNTER   An instrument for detecting radiation by
  producing pulses of electrical charge that are proportional to the
  energy of the radiation being measured. The design permits use of
  radiation of a desired energy level (within limits), and
  discrimination against other radiation, especially background
  radiation.

PROTONS   Elementary particles with a single positive electrical charge
  and a mass approximately 1837 times that of the electron. The atomic
  number of an atom is equal to the number of protons in its nucleus.

RADIOACTIVE DECAY   The change of one nuclide to another by the emission
  of charged particles from the nucleus of its atom.

RADIOACTIVITY   The property of some nuclides to decay by themselves
  into others.

RADIOGENIC   Formed as the result of radioactive decay.

RARE EARTH   Any of the elements from atomic number 57 (lanthanum) to 71
  (lutetium).

SAMPLE COUNTER   An instrument into which a sample of material can be
  placed to have its radiation measured.

SECULAR EQUILIBRIUM   The production of a radioactive substance at a
  rate equal to its decay.

SPECIFIC ACTIVITY   The number of atoms decaying per unit time per unit
  weight of the total amount being tested.

SPIKE   A known amount of an element of unusual isotopic composition
  used in isotope-dilution analysis.

STATISTICAL ERROR   The error associated with nuclear measurements and
  arising from the random distribution of nuclear events.

STRATA   Plural of stratum. A sheet or mass of sedimentary rock (formed
  by deposits of sediments, as from ancient seas) of one kind, usually
  in layers between beds or layers of other kinds.




                                APPENDIX
                           Radioactive Decay


When a radioactive nucleus disintegrates or decays, the resultant
  remaining nucleus may still be radioactive, and sooner or later it
  also will disintegrate and become still another kind of atom. This
  process continues through a series of distinct steps until a stable
  atom—one that is not radioactive—is formed. All natural radioactivity
  in the heavy elements proceeds by such a series of steps, and the
  series finally ends with a stable form of lead as its end product. In
  other words, any naturally radioactive heavy element eventually
  becomes nonradioactive lead.

The nucleus of every atom (except hydrogen) contains one or more
  neutrons and one or more protons. The instability of the nuclei of the
  heavy atoms is related to the ratio of the number of neutrons to the
  number of protons in the nuclei. Radioactive decay is, in fact, a way
  of adjusting these ratios. The adjustment can occur in various ways.
  The most common is the emission of alpha particles or beta particles.

An alpha particle is identical with the nucleus of a helium atom and has
  two neutrons and two protons bundled together. Loss of an alpha
  particle from a nucleus lowers the mass number (the total of protons
  and neutrons) of the parent nucleus by four and the atomic number (the
  number of protons) by two; the number of neutrons also is reduced by
  two.

A beta particle is an electron and has a negative electric charge. When
  a beta particle is emitted from a nucleus, the nucleus is changed so
  that it has one more proton (which has a positive charge) and one less
  neutron (which has no charge); in effect, a neutron has changed into a
  proton as the nucleus lost a negative charge. Beta decay occurs in
  nuclei with a greater proportion of neutrons than is normal for the
  number of protons. Since beta emission increases the proportion of
  protons, the process raises the atomic number of the parent nucleus by
  one and leaves the mass number the same.

Gamma rays are a form of electromagnetic radiation. They are emitted
  when a nucleus shifts from one energy state to a lower energy
  state—the energy difference emerging as the gamma radiation. Gamma
  emission often accompanies alpha or beta emission, but the production
  of gamma rays does not itself alter the atomic number nor the mass
  number of the parent.

Nuclei also can decay by emission of a positron, which is a positively
  charged electron. When this occurs, the new nucleus has one more
  neutron and one less proton than its parent; in effect a proton has
  become a neutron as the nucleus loses a positive charge. Positrons
  usually are emitted by nuclei that have a greater proportion of
  protons than is normal for the number of neutrons.

Another process—internal electron conversion—sometimes occurs in
  connection with gamma-ray emission, usually in heavy elements when the
  gamma-ray energy is low. Instead of being emitted directly, the gamma
  ray strikes an orbital electron, knocking the electron out of the
  atom; the gamma ray then disappears. Another electron jumps into the
  “hole” in the orbit from which the first electron was emitted, and
  this jump—from a higher to a lower energy level—results in the
  emission of an X ray (which is similar to a gamma ray, but originates
  in the electron orbit region of the atom, not in the nucleus).

Finally, a nucleus may be altered by electron capture. In a nucleus with
  a low ratio of neutrons to protons, the nucleus captures one of its
  own orbital electrons. This immediately combines with a proton to form
  a new neutron and emit a neutrino (a high-energy particle with neither
  mass nor charge). The process increases the neutron-to-proton ratio of
  the nucleus; the daughter has the same mass number as the parent, but
  has an atomic number one less than the parent.

There are three series by which naturally radioactive nuclei decay to
  stable ones: The Uranium Series, the Thorium Series, and the Actinium
  Series. Man-made radioactive nuclei decay similarly, with bismuth as
  the end product, via the Neptunium Series. These can be illustrated in
  tabular form and diagrammatically. The Actinium Series (Uranium-235
  Series), for example, proceeds like this:

                           THE URANIUM-235 SERIES
  Element            Symbol    Radiation Emitted         Half-life
  Uranium            ²³⁵U      α                         7.13 × 10⁸ years
  Thorium            ²³¹Th     β                         25.6 hours
  Protactinium       ²³¹Pa     α                         3.25 × 10⁴ years
  Actinium[16]       ²²⁷Ac     β (98.8%) and α (1.2%)    21.2 years
     Thorium         ²²⁷Th     α                         18.17 days
     Francium        ²²³Fr     β                         22 minutes
  Radium             ²²³Ra     α                         11.7 days
  Radon              ²¹⁹Rn     α                         4.0 seconds
  Polonium[16]       ²¹⁵Po     α (~100%) and β (~5 ×     1.83 × 10⁻³ second
                               10⁻⁴%)
     Lead            ²¹¹Pb     β                         36.1 minutes
     Astatine        ²¹⁵At     α                         ~10⁻⁴ second
  Bismuth[16]        ²¹¹Bi     α (99.7%) and β (0.3%)    2.15 minutes
     Polonium        ²¹¹Po     α                         0.25 second
     Thallium        ²⁰⁷Tl     β                         4.78 minutes
  Lead               ²⁰⁷Pb     —                         Stable

[Illustration: The Uranium-235 Series]

The Uranium (Uranium-238) Series proceeds like this:

                           THE URANIUM-238 SERIES
  Element            Symbol    Radiation                 Half-life
  Uranium            ²³⁸U      α                         4.51 × 10⁹ years
  Thorium            ²³⁴Th     β                         24.1 days
  Protactinium[17]   ²³⁴Pa     β                         1.18 minutes
  Uranium            ²³⁴U      α                         2.48 × 10⁵ years
  Thorium            ²³⁰Th     α                         7.6 × 10⁴ years
  Radium             ²²⁶Ra     α                         1.62 × 10³ years
  Radon              ²²²Rn     α                         3.82 days
  Polonium[18]       ²¹⁸Po     α (99.98%) and β          3.05 minutes
                               (0.02%)
     Lead            ²¹⁴Pb     β                         26.8 minutes
     Astatine        ²¹⁸At     α                         1.3 seconds
  Bismuth[18]        ²¹⁴Bi     β (99.96%) and α          19.7 minutes
                               (0.04%)
     Polonium        ²¹⁴Po     α                         1.6 × 10⁻⁴ second
     Thallium        ²¹⁰Tl     β                         1.32 minutes
  Lead               ²¹⁰Pb     β                         22 years
  Bismuth[18]        ²¹⁰Bi     β (~100%) and α (~2 ×     5.0 days
                               10⁻⁴%)
     Polonium        ²¹⁰Po     α                         138.4 days
     Thallium        ²⁰⁶Tl     β                         4.30 minutes
     Lead            ²⁰⁶Pb     ...                       Stable

[Illustration: The Uranium-238 Series]




                          SUGGESTED REFERENCES


Books

_How Old Is the Earth?_, Patrick M. Hurley, Doubleday & Company, Inc.,
  Garden City, New York, 1959, 160 pp., $1.25.

_Radiocarbon Dating_ (second edition), Willard F. Libby, University of
  Chicago Press, Chicago, Illinois, 1955, 175 pp., $5.00 (hardback);
  $1.95 (paperback).

_The Birth and Death of the Sun_, George Gamow, The Viking Press, New
  York, 1949, 238 pp., $4.75 (out of print but available through
  libraries), $0.60 (paperback) from the New American Library of World
  Literature, Inc., New York.

_Inside the Nucleus_, Irving Adler, The John Day Company, Inc., New
  York, 1963, 191 pp., $4.95 (hardback); $0.60 (paperback) from the New
  American Library of World Literature, Inc., New York.

_Ages of Rocks, Planets, and Stars_, Henry Faul, McGraw-Hill Book
  Company, New York, 1966, 109 pp., $2.45.

_Principles of Geochemistry_ (second edition), Brian Mason, John Wiley &
  Sons, Inc., New York, 1958, 310 pp., $7.50. (New edition due in 1967.)

_Potassium Argon Dating_, J. H. Zahringer and O. A. Schaeffer,
  Springer-Verlag New York, Inc., New York, 1966, 250 pp., $12.50.


Articles

A Clock for the Ages: Potassium Argon, Garniss H. Curtis, _National
  Geographic Magazine_, 120: 590 (October 1961).

Exploring 1,750,000 Years into Man’s Past, L. S. B. Leakey, _National
  Geographic Magazine_, 120: 564 (October 1961).

Five-Billion-Year Clock, Patrick M. Hurley, _Saturday Evening Post_,
  234: 26 (March 18, 1961).

Geologic Time Scale, J. Laurence Kulp, _Science_, 133: 1105 (April 14,
  1961).

Geology, Reginald A. Daly, _Scientific American_, 183: 36 (September
  1950).

Tracks of Charged Particles in Solids, R. L. Fleischer, P. B. Price, and
  R. M. Walker, _Science_, 149: 383 (July 23, 1965).

How Old Is It?, Lyman J. Briggs and Kenneth F. Weaver, _National
  Geographic Magazine_, 114: 234 (August 1958).

Moving Picture of the Last Ice Age, Richard Foster Flint, _Natural
  History_, 66: 188 (April 1957).

Modern Methods for Measurement of Geologic Time, E. J. Zeller, _Mineral
  Information Service_, 18: 9 (January 1965). Single copies are $0.10
  from Division of Mines and Geology, Ferry-Building, San Francisco,
  California 94111.

Fluted Projectile Points: Their Age and Dispersion, C. Vance Haynes,
  Jr., _Science_, 145: 1408 (September 25, 1964).

Unraveling the Age of Earth and Man, E. L. Simons, _Natural History_,
  76: 52 (February 1967).

Radiocarbon Dating and Archeology in North America, F. Johnson,
  _Science_, 155: 165 (January 13, 1967).

Fission-track Dating of Bed I, Olduvai Gorge, R. L. Fleischer and
  others, _Science_, 146: 72 (April 2, 1965).

Lead Isotopes and the Age of the Earth, G. R. Tilton and R. H. Steiger,
  _Science_, 150: 1805 (December 31, 1965).

Strontium-Rubidium Age of an Iron Meteorite, G. J. Wasserburg and
  others, _Science_, 150: 1814 (December 31, 1965).

[Illustration: THE COVER]

U. S. Geological Survey scientists prepare acetylene gas, made from the
  carbon-14 in a geological specimen, in a vacuum line. This gas will be
  fed into a proportional counter to determine the age of the specimen
  by its ¹⁴C count. (See “Carbon-14 Counting” beginning on page 12.)

[Illustration: THE AUTHOR]

Geophysicist Henry Faul, an authority on nuclear dating, is professor of
  Geophysics and chairman of the Department of Geology at the University
  of Pennsylvania, Philadelphia. He holds a doctoral degree from the
  Massachusetts Institute of Technology, and has taught at the
  Universities of Strasbourg and Bern in Europe. Dr. Faul was a
  geophysicist with the Manhattan Project during World War II, and was
  formerly chief of the Radiation Laboratory, U. S. Geological Survey,
  Denver, Colorado. For many years he was engaged in geological age
  determination work with the Geological Survey and the Carnegie
  Institution of Washington in Washington, D. C.


PHOTO CREDITS

Frontispiece courtesy Anthropology Department, Southern Methodist
University (SMU)

Cover photo courtesy U. S. Geological Survey (USGS)

  Page
  11           USGS
  12           USGS
  14, 16, 17   Willard F. Libby
  18           University of Arizona
  21           Massachusetts Institute of Technology
  22           Graduate Research Center of the Southwest
  23           Graduate Research Center of the Southwest
  25           Robert L. Fleischer
  26           Perkin-Elmer Corporation
  30           University of Texas
  32           Graduate Research Center of the Southwest
  36           Massachusetts Institute of Technology
  40           Des Bartlett, Armand Denis Productions
  43           Anthropology Department, SMU
  44           USGS
  47           USGS
  59           Author’s photo courtesy Graduate Research Center of the
               Southwest




                               Footnotes


[1]Words appearing in SMALL CAPITAL LETTERS are defined in the Glossary
    beginning on page 49.

[2]The process of natural radioactive decay is described in the Appendix
    beginning on page 52.

[3]The U. S. War Department program during World War II that developed
    the first nuclear weapons.

[4]Drawn to scale, the whole age of man is represented by less than the
    width of the line.

[5]For more information on the structure of atoms, see _Our Atomic
    World_, a companion booklet in this series.

[6]From the _Chart of the Nuclides_, prepared by David T. Goldman,
    Knolls Atomic Power Laboratory, August 1964.

[7]This decay process proceeds in a series of steps, during which 6
    alpha particles and 4 beta particles are emitted. (See Appendix.)

[8]Named after their creator, John Napier, a Scottish mathematician
    (1550-1617), who also invented the decimal point.

[9]It is difficult to determine the half-life of ¹⁴C exactly. In the
    early days of ¹⁴C dating, in order not to delay continued work, an
    arbitrary value of 5568 years was chosen and this value is still
    used in calculations.

[10]This means that uranium decays through successive steps in which the
    entire series emits eight alpha particles. (See Appendix.)

[11]Remember, this enormous period of time is a measure of the _rate_ of
    spontaneous fission, _not_ of the age of ²³⁸U.

[12]The rhenium-osmium scheme is shown below the dotted line because the
    method is still in an early experimental stage and its general
    utility is not yet established.

[13]For more on this family of elements, see _Rare Earths, The Fraternal
    Fifteen_, a companion booklet in this series.

[14]For a fuller explanation of the fission process, see _Our Atomic
    World_, another booklet in this series.

[15]Neutrons that have had their speed reduced by passing through a
    moderator (graphite, for example) which is built into every reactor
    to accomplish this very thing. For more about how this is done, see
    _Nuclear Reactors_ and _Research Reactors_, companion booklets in
    this series.

[16]Note that some radionuclides sometimes decay by one method,
    sometimes by another. For example, 98.8% of the nuclei of
    actinium-227 emit a beta particle to form thorium-227; the remaining
    1.2% emit an alpha particle to form francium-223; both of these
    daughter products decay to radium-223.

[17]Some of the protactinium (0.12%) changes by an intermediate step,
    known as isomeric transition, in which its nucleus shifts to a lower
    energy state. The process does not alter the remaining
    parent-daughter progression in the series.

[18]Undergoes both alpha and beta decay, in definite proportion of decay
    events, as shown.


This booklet is one of the “Understanding the Atom” Series. Comments are
invited on this booklet and others in the series; please send them to
the Division of Technical Information, U. S. Atomic Energy Commission,
Washington, D. C. 20545.

Published as part of the AEC’s educational assistance program, the
series includes these titles:

  _Accelerators_
  _Animals in Atomic Research_
  _Atomic Fuel_
  _Atomic Power Safety_
  _Atoms at the Science Fair_
  _Atoms in Agriculture_
  _Atoms, Nature, and Man_
  _Careers in Atomic Energy_
  _Computers_
  _Controlled Nuclear Fusion_
  _Cryogenics, The Uncommon Cold_
  _Direct Conversion of Energy_
  _Fallout From Nuclear Tests_
  _Food Preservation by Irradiation_
  _Genetic Effects of Radiation_
  _Index to the UAS Series_
  _Lasers_
  _Microstructure of Matter_
  _Neutron Activation Analysis_
  _Nondestructive Testing_
  _Nuclear Clocks_
  _Nuclear Energy for Desalting_
  _Nuclear Power and Merchant Shipping_
  _Nuclear Power Plants_
  _Nuclear Propulsion for Space_
  _Nuclear Reactors_
  _Nuclear Terms, A Brief Glossary_
  _Our Atomic World_
  _Plowshare_
  _Plutonium_
  _Power from Radioisotopes_
  _Power Reactors in Small Packages_
  _Radioactive Wastes_
  _Radioisotopes and Life Processes_
  _Radioisotopes in Industry_
  _Radioisotopes in Medicine_
  _Rare Earths_
  _Reading Resources in Atomic Energy_
  _Research Reactors_
  _SNAP, Nuclear Space Reactors_
  _Sources of Nuclear Fuel_
  _Space Radiation_
  _Synthetic Transuranium Elements_
  _The Atom and the Ocean_
  _The Chemistry of the Noble Gases_
  _The First Reactor_
  _Whole Body Counters_
  _Your Body and Radiation_

A single copy of any one booklet, or of no more than three different
booklets, may be obtained free by writing to:

           USAEC, P.O. BOX 62, OAK RIDGE, TENNESSEE    37830

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librarians, and to teachers who can make them available for reference or
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exactly, and the use intended.

In all requests, include “Zip Code” in return address.


                Printed in the United States of America
 USAEC Division of Technical Infection Extension, Oak Ridge, Tennessee




                          Transcriber’s Notes


--Retained publication information from the printed edition: this eBook
  is public-domain in the country of publication.

--In the text versions only, text in italics is delimited by
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--In the text versions only, superscript text is preceded by ^caret.

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End of the Project Gutenberg EBook of Nuclear Clocks, by Henry Faul

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