Magill J., Galy J. Radioactivity Radionuclides Radiation

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6. Archaeology and Dating

Radioactive Dating

Radioactive dating methods are based on the temporal decrease of the number of

radioactive atoms and/or on the related ingrowth of radioactive or stable daughter

nuclides. These changes are described by the radioactive decay laws and in particular

by the decay constant or half-life. Because the half-life of a given radioisotope is

not affected by temperature, physical or chemical state, or any other inﬂuence of

the environment outside the nucleus (apart, of course, from nuclear reactions), then

radioactive samples continue to decay at a predictable rate. This makes several types

of radioactive dating feasible [1, 2].

Fig. 6.1. The Dead Sea scrolls were dated to 1900 y BP (before present) using

C dating [3].

Comparison of Present and Initial Radioactivity

The simplest form of isotopic age computation is where there are no daughter atoms

present initially and where no mass has been lost from the sample. The equation for

the time-dependence of the parent is given by:

P(t) = P(0)e

−kt

where P(t)is the quantity of parent isotope present at time t,P(0) the initial amount

and k the decay constant k = ln 2/τ . It follows that the age can be obtained from

Age = t =

· ln



P(0)

P(t)



106 6. Archaeology and Dating

C Dating

Carbon-14 is produced at almost a constant rate in the atmosphere by interactions of

cosmic rays with nitrogen i.e.

N(n,p)

C. Following production the carbon atoms are

oxidised to form

which then follows the CO

cycle. Following the death of an

organism, the CO

exchange is terminated and the

C starts to decay. Since the initial

activity is known (activity of

C in the atmosphere), and the present value of

Cinthe

organism can be measured, the age can be determined.

Example: Take the present

C activity to be 900 Bq per gram. In the sample the activity

is 6 Bq per gram. The age of the sample is then

Age =



5730 y

0.693



· ln



900



= 41400 y .

Archaeological dating by radiocarbon is limited to about ten half-lives i.e. to about

50,000 BP (before present). Longer-lived nuclides such as

Be (1.6 million years),

(760,000 years) and

Ca (100,000) can be used to date older samples.

So from a knowledge of the parent concentrations at different times, the age can

be evaluated. This age determination can be applied to many of the radionuclides

produced in the atmosphere by the cosmic radiation (cosmogenic radionuclides). The

best known example is

C (see inset).

Since the parent atoms decay to daughter atoms, the number of daughter atoms

D(t) = P(0) − P(t)or P(0) = P(t)+ D(t), the “age” t can be obtained from

Age = t =

· ln



1 +

D(t)

P(t)



From a measurement of the parent and daughter concentrations, and the time t , the

age can be evaluated (assuming the decay constant is known).

Radioactive Parent and Stable Decay Product

In this case a parent nuclide decays to a stable daughter. In general one has to account

for the fact that the (stable) daughter nuclide is already present such that the following

relation holds:

D(t) + P(t)= D(0) + P(0).

Since this now adds an additional unknown, D(0), additional information is required

before the age can be determined. There are two main assumptions in the dating

process:

• The amount of daughter isotope at the time of formation of the sample is zero (or

known independently and can be compensated for).

• No parent isotope or daughter isotope has entered or left the sample since its time

of formation.

If one of these assumptions has been violated, the simple computation above yields

an incorrect age.

Radioactive Dating 107

Isochron Methodology

Isochron methods avoid the problems which can potentially result from both of the

above assumptions. Such information can be obtained in cases where there are other

stable isotopes of the elements involved in the sample. This stable, non-radiogenic

nuclide can then be used as a reference nuclide. Denoting the concentration of the

stable, non-radiogenic daughter nuclide by D

, then the above equation can be written

in the form of ratios [4, 5] e.g.

D(t) + P(t)

D(0) + P(0)

Substituting P(0) = P(t)e

+kt

, the relation can be expressed as

D(t)

P(t)

− 1]+

D(0)

From which the age is given by

Age =



1 +

(D(t)/D

− D(0)/D

)

P (t)/D



The equation for D(t)/D

above has the form

y = x ·[e

− 1]+y

On a plot of y vs. x, the slope is dy/dx = e

− 1. The age can then be determined

Age =

· ln



1 +



If the samples have the same age, a plot of D/D

against P/D

will give a straight

line with slope (e

− 1) intersecting the ordinate at D(0)/D

. Such a plot is called

an isochron and is particularly useful for age determinations on samples of the same

age.

Rubidium-Strontium Dating

In the Rb/Sr method, determination of the parent (

Rb) and the daughter (

Sr)

are compared to to the stable isotope

Sr which is used as the reference nuclide.

Application of the isochron method to the Rb/Sr system gives









− 1) +





A plot of

Sr/

Sr against

Rb/

Sr for various samples of the same age is

shown in Fig. 6.1. From the relation above, using 1/k = τ/0.693, the age can then

be determined i.e.

Age =

47.5Gy

(0.693)

· ln



1 +

0.3

4.51



= 4.41 Gy

108 6. Archaeology and Dating

Fig. 6.2. Rb/Sr dating method [2],

HyperPhysics, © C. R. Nave, 2003

Radioactive Disequilibrium

Radioactive disequilbria may arise in a variety of situations in which the parent

and daughter nuclides do not remain together. Following chemical processing, it is

possible to separate the parent and daughter nuclides. Following this separation, the

daughter nuclide will start to grow in again. Information on the time of this processing

or separation may be obtained by comparing the ratio of the parent to daughter

nuclides. An example of this is given later in this chapter for the determination of

the age of plutonium particles. Fresh plutonium particles will, in general, contain the

isotopes

238

Pu,

239

Pu,

240

Pu,

241

Pu, and

242

Pu depending on the production route.

With time, these nuclides decay to

234

235

236

241

Am, and

238

U, respectively.

From the ratios of the parent to daughter nuclides, one can deduce the elapsed time

and hence the age of the particle.

Fission Tracks

Fission tracks, which result from spontaneous ﬁssion or by neutron induced ﬁssion,

can be used for dating purposes. The method is really only applicable to

238

U where

there is a measurable density of tracks. In a ﬁrst step, the tracks naturally produced in

minerals by

238

U spontaneous ﬁssion are counted. In the second step, the uranium in

the sample is determined by

235

U ﬁssion tracks in a reactor with a well characterised

thermal ﬂux. The age of the sample is obtained from the ratios of the tracks, the

reactor neutron ﬂux, etc.

In the following sections, various examples of dating techniques based on ra-

dioactive decay are described in more detail.

An Astrophysical Clock

Heavy elements such as uranium formed in a supernova more than 6000 million

years ago. From the supernova remnants, the solar system was born around 4600

Age of the Earth 109

Fig. 6.3. The Astrophysical Clock

million years ago. Assuming uranium isotopes were produced in equal amounts in

the supernova the ratios of uranium isotopes can be used as an astrophysical clock.

Today, the natural abundance of

235

U ratio is 0.71%. The natural reactors at Oklo in

Africa occurred around 2000 million years ago at which time the natural abundance of

235

U was around 3%. Evidence indicates that the natural uranium deposits achieved

nuclear criticality and operated for tens of thousands of years or longer. The absence

236

U, which has a half-life of 2.342 × 10

y indicates that induced ﬁssion stopped

at least 10

years ago. The recently discovered “Toumai” has been dated to around

7 million years. In the above diagram this time is almost indistinguishable from the

present time.

Age of the Earth

Towards the end of the 19th century, the age of the Earth was of great scientiﬁc

controversy [6]. Lord Kelvin had estimated the age to be around 20 million years

based on the rate of cooling assuming that the Earth was originally in a molten

state. Already by 1840, from the work of Hutton and Lyell, it was known that rocks

were laid down on top of one another in an orderly manner. This gave rise to age

estimates based on sedimentation geology. Darwin had estimated the age of the Earth

at 300 million years from cliff erosion assuming an erosion rate of 1 inch per century.

110 6. Archaeology and Dating

Fig. 6.4. Portrait of Lord Kelvin (1824–1907) by

W. Rothenstein. © Hunterian Art Gallery, University

of Glasgow

Shortly after the discovery of radioactivity by Becquerel in 1896, Rutherford and

Soddy showed that through radioactive decay, one element could be transformed into

another (see page 43), e.g. radium (a metal) became radon (a gas).They suggested also

that the observed presence of helium in rocks might be due to radioactive “decay”.

The same authors ﬁrst established the “decay chain” of the unstable “parent” uranium.

They identiﬁed the 14 stages in the decay of uranium, shown in Fig. 6.5, producing

8 atoms of helium.

Based on these observations, Rutherford and Soddy concluded that if the amount

of helium in a rock could be measured, one could estimate how long this process

Fig. 6.5. Decay chain of uranium with the 14 stages established by Rutherford (from the

“Universal Nuclide Chart”, Appendix E)

Prehistoric Cave Art at Altamira, Northern Spain 111

took i.e. the age of the rock. In particular, by measuring the amount of radium and

helium, Rutherford dated the age of a rock at 500 million years. The problem with

this method was, however, that helium gas could escape from the rock and that

an age determination would result in a minimum age. From these results, Kelvin’s

age determination was clearly too low. In 1907, Boltwood had observed that along

with helium, large amounts of lead were found in rocks containing radioactivity. He

postulated that lead was the stable product in the decay of uranium. Based on this,

Arthur Holmes proposed that the age could be determined by measuring the amount

of lead, rather than helium i.e. on a uranium/lead technique. The basic assumption

here was that the “ordinary” lead in a rock was present in much smaller quantities

than the amount produced by the decay of uranium.

Around this time, Soddy discovered “isotopes” – nuclides which had different

atomic masses. The existence of these isotopes would complicate matters consider-

ably in the development of age techniques – they would, however, ultimately result

in an accurate dating technique. Not only did lead have four such isotopes

208

(parent

232

Th),

207

Pb (parent

235

U),

206

Pb (parent

238

U),

204

Pb (“ordinary” lead) but

natural uranium had also three isotopes (

238

235

234

U with relative abundancies

of 99.28%, 0.72% and 0.0055%, respectively). Following the discovery of the new

isotope of uranium

235

U, which decayed much faster than

238

U, Rutherford in 1929

determined the age of the Earth by assuming that, at formation, equal amounts of

238

U and

235

U were present. The result obtained, 3400 million years, was the ﬁrst

age determination based on isotope ratios.

It also followed from this new isotope of uranium, that the uranium-lead pathways

contained two geological “clocks” that could be used to check one another i.e. the

decay rate of

238

Uto

206

Pb and the decay rate of

235

Uto

207

Pb. In addition, a third

“clock” based on the ratios of the isotopes

206

Pb,

207

Pb relative to the constant value

204

Pb was proposed. This new lead-lead method is still used today in age dating

techniques. The ﬁrst estimates of the age of the Earth based on these lead ratios (the

isochron method) are due to Paterson in the 1950s. The current value of the age of

the Earth is 4550 ± 70 million years.

Prehistoric Cave Art at Altamira, Northern Spain

The most famous of the Altamira paintings are on the plafond–alowceiling in

one of the caves to the left from the entrance [7]. The total area of the ceiling is

about 100 m

. Here the artist skilfully combined pigment painting with the ceiling

relief. The majority of more than 20 animal ﬁgures are bison (though there is also

a horse, a boar and a deer). The most common pigments used in these paintings

were red Fe

, black MnO

and charcoal. Rather than dating the sample by tradi-

tional

C techniques of β activity measurements (where sample requirements would

damage the artwork), accelerator mass spectrometry was used to count individual

carbon isotopes thereby reducing the amount of sample required to a minimum. To

obtain the carbon needed for dating, a scalpel was used to scratch off approximately

20–40 mg from a dark section of the painting. Radiocarbon dating of the charcoal

112 6. Archaeology and Dating

used to draw the bison shown above found the drawing to be 14,000 ± 400 years

old [8].

The Age of Groundwater – The Oasis Ballad Seet

Groundwater provides one of the most important sources of drinking water world-

wide. In dry climates, in deserts, etc., groundwater is often the only permanent

source of water. Important information for the sustainable cultivation of groundwa-

ter resources is the residence time of the water underground i.e. the “age” of the

groundwater. Groundwater is an archive of historical environmental conditions. Fol-

lowing inﬁltration, the water can spend thousands of years in the ground, isolated

from the atmosphere. Valuable information can be obtained from the dissolved noble

gases in the water. Heavy noble gases can give information on the temperature which

existed when the water ﬁrst entered into the ground [9–11].

One of the most reliable methods for dating “young” groundwater (up to ages of

50 y) is based on the rare “stable” isotope

He. This isotope is created in water through

the radioactive decay of the hydrogen isotope tritium

H (half-life 2.34 y) contained

in the water molecules. This tritium is produced in nature in very small amounts by

cosmic radiation through the reaction

N + n →

C +

H. Tritium was produced

in very much larger quantities in the 1950s and 1960s through atmospheric nuclear

explosions. The resulting “tritium peak” in rainfall was used in the following years

as a useful “marker” in hydrology. Today, the tritium levels have almost returned

to their natural constant values. For this reason, little information can be gained on

residence times of water by measuring the tritium content alone.

Of considerably more interest, however, is the combined measurement of

and

He. Following inﬁltration of rainwater, groundwater becomes isolated from the

The Age of Groundwater – The Oasis Ballad Seet 113

Age = t = 1/k · ln



1 +



H →

He + β

−

+ ν

Fig. 6.7. Time evolution of

the concentrations of

and

He in water isolated

from the atmosphere

atmosphere and the concentration of

He increases through the radioactive decay of

H. From the ratio of the

H and

He concentrations, the “age” of the water can be

calculated.

The “age” of the groundwater refers to the time elapsed since the isolation of

the groundwater from the atmosphere. Surface waters, whose dissolved gases are in

solution equilibrium with the atmosphere, have age zero. After isolation from the

atmosphere, for example water at the bottom of lakes or in groundwater, the gas

exchange is no longer possible and helium gas accumulates in the water.

Even the presence of tritium in such water can be useful information since it

establishes that the formation of groundwater inside the previous 50 y. From the

concentrations of the

H and

He, the history of the tritium in groundwater can

Fig. 6.8. The Oasis Ballad Seet in Oman [9] –

how did the irrigation work?