The Project Gutenberg eBook ofNuclear Clocks

The Project Gutenberg eBook ofNuclear ClocksThis ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.Title: Nuclear ClocksAuthor: Henry FaulRelease date: May 29, 2015 [eBook #49070]Most recently updated: October 24, 2024Language: EnglishCredits: Produced by Stephen Hutcheson, Dave Morgan and the OnlineDistributed Proofreading Team at http://www.pgdp.net*** START OF THE PROJECT GUTENBERG EBOOK NUCLEAR CLOCKS ***

This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

Title: Nuclear ClocksAuthor: Henry FaulRelease date: May 29, 2015 [eBook #49070]Most recently updated: October 24, 2024Language: EnglishCredits: Produced by Stephen Hutcheson, Dave Morgan and the OnlineDistributed Proofreading Team at http://www.pgdp.net

Title: Nuclear Clocks

Author: Henry Faul

Release date: May 29, 2015 [eBook #49070]Most recently updated: October 24, 2024

Language: English

Credits: Produced by Stephen Hutcheson, Dave Morgan and the OnlineDistributed Proofreading Team at http://www.pgdp.net

*** START OF THE PROJECT GUTENBERG EBOOK 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.

Signature of Edward J. Brunenkant

Edward J. Brunenkant, DirectorDivision of Technical Information

UNITED STATES ATOMIC ENERGY COMMISSIONDr. Glenn T. Seaborg, ChairmanJames T. RameyWilfrid E. JohnsonFrancesco Costagliola

UNITED STATES ATOMIC ENERGY COMMISSION

Dr. Glenn T. Seaborg, ChairmanJames T. RameyWilfrid E. JohnsonFrancesco Costagliola

Dr. Glenn T. Seaborg, Chairman

James T. Ramey

Wilfrid E. Johnson

Francesco Costagliola

NUCLEAR CLOCKS

by Henry Faul

United States Atomic Energy CommissionDivision of Technical InformationLibrary of Congress Catalog Card Number: 67-601951966; 1968(Rev.)

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.

NUCLEAR CLOCKS

By HENRY FAUL

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 ofRADIOACTIVITY[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 aCLOSED 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 geologicSTRATA. Measurements still were inaccurate, however, and only a few rare and unusually rich radioactive minerals contained enough of the products ofRADIOACTIVE 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 aMASS 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.

Time scale of the Earth, drawn to scale. See also the Holmes time scale onpage 46.

We can think of the nucleus of an atom as a sort of drop—a bunch ofNEUTRONSandPROTONSheld 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 mostNUCLIDESfound 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 givenISOTOPEis 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 theELECTRONScircling 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.

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 theHALF-LIFEof 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:

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

Obviously, in ordinary computations that would not be enough information to calculate the time, because there still are two unknowns,N₀andt. 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 bothPARENTandDAUGHTERatoms 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.)

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.

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 inCOSMIC 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 aSECULAR 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.

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.

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.

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.

The most useful samples for carbon-14 age determination are charcoal, wood, and shells.

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, or2. Reduced chemically to methane or ethane, or to a carbide from which acetylene can be evolved by adding water. (See booklet cover and description onpage 59.)

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 onpage 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, theSPECIFIC ACTIVITYof acetylene orethane 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-backgroundPROPORTIONAL COUNTER, and its radioactivity is determined. This is an involved process. First there is the matter of theBACKGROUND COUNT.

The background count of an instrument is the number of pulses (counts) it will give per unit time when there isnoradioactive 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 theGAMMA RAYScoming 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 anANTICOINCIDENCE RINGinside the lead shield. This is a cylindrical space completely surrounded byGEIGER COUNTERSthat are connected to each other and to theSAMPLE COUNTERin 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 immediatelyinside 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.

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 radioactivecontent, 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.

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 theNET 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 theSTATISTICAL 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.

Hair of an Egyptian woman. 5020 ± 290 years old.

Linen wrapping from the Dead Sea Scroll containing the Book of Isaiah. 1917 ± 200 years old.

Peruvian rope. 2632 ± 200 years old.

Preglacial wood found in Ohio. More than 20,000 years old.

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 flintClovisarrow and spear points.

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 theFolsomculture. 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.

All other practical age-determination schemes are based on a few long-lived isotopes, with half-lives relatively near the age of the earth (4.5AEONS). They are:

It is apparent that Table II onpage 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 theRADIOGENICdaughter 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 theRARE EARTHelements 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 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 containingCOMMONstrontium (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 mineralCRYSTAL, 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 thisORIGINALstrontium 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 tojust the same extentas 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.

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