Nuclear Clocks Revised — Themes and Context

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.

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

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.)

_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)

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 = 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

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

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.)

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.

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.

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.

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.

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.

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.

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.

OBJECTS DATED BY RADIOCARBON

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.

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