All?gre Claude J. Isotope Geology

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The

Rb^

Sr age is thought to markthe intrusion of the magma beneath the volcano and

the creation ofa magma chamber.The

230

Th^

238

Uages supposedlydatethe crystallization

of zircon in the same magma chamber.The

Ar^

Ar ages date the eruptions.This exam-

ple raises n ot the question of uncertaintybutof identi¢cation.What age is the radiometric

phenomenon associatedwith? W hatexactly is itthatwe date?

In the previ ous examples webarely posedthe questionjust raised for LongValley (except

for the Eldora gneiss). For th e komatiites the answer is clear enough: we want to date the

magmaintrusion.For Greenland, itis alittlefuzzier. Is itth e emplacementofgranitebefore

metamorphism? Is itthe metamorphic episode?It is not absolutelyclear.

Here, with the LongVall ey rhyolite, there is no getting round the question.The ages can

only be interpreted in the context of a ge olog ical sc enar io,ageneralmodel.Atthesame

time, itc anbeseenthatthe di¡erentchronometersarenotusedfordatingthesamephenom-

ena.The very idea of concordance of ages obtaine d by the various methods, so far consid-

ered as the criterion of absolute reliability, mu st be re¢ned. Perhaps the uncertainty that

can be estimated by the various methods re£ects merely a p roblem of identi¢cation. Let us

try toextend thistypeof interpretation.

Thus,wh enweobser vethat

Rb^

S r ages on whole rock measured in granite are gen-

erallya littleyounger than the ages obtained on zirconby the concordia method, we ques-

tion what this di¡erence means. It may arise because zircon is the ¢rst mineral to

crystall i z e wh ereas

Rb^

S r is re-homogenized by the circulati on of hydrothermal

£uid which is driven o¡ towards the end of granite crystall ization and gives rise to the

aplite and pegmatite seams. This is not the only interpretation.We might also consi der

thatthe zircon is aged because it has inherited older zircon. Ion microprobe examination

Ar/

Mammoth Knolls IC-42

Plateau age = 101

± 8 ka

0.003

4 6 8 10

0.002

0.001

Ar/

LSR Flow IC-24

Ar/

Ar = 296.5 ± 2.4 ka

Age = 151

± 4 ka

PA = 152 5

0.003

2 3 4 5

0.002

0.001

T = 202.6 ± 0.9 ka

glass

230

Th/

232

238

232

IC-24

2 3 4 5

zircon

T = 235.6

± 1.2 ka

230

Th/

232

238

232

IC-42

1 2 3 4

zircon

Mammoth

Knolls

Deer

Mountain

Age = 257

± 39 ka

Rb/

= 0.70628 ± 2

Sr/

Rb/

10 20 30

0.706 28

0.706 32

0.706 36

0.706 40

Figure 5.21 Results obtained by various methods for the rhyolite of Long Valley, California. After Reid

.(1997).

187 Geological interpretations

of zircon minerals has now provided an answer but before we were in a position of

indeter minacy!

Conclusions

There are two conclusions to be drawn from these studies (whichwe could have multiplied

inde¢nitely). First, it has be en seen that the quantitative methods of interpreting isotope

measurements actuallygavevery coherent ages (despitethe slight uncertainties with de cay

constants).Second,wehavejustobservedthatbetter u nderstandi ngofthese measurements

requi re s t h em tob e i ncl u de d in geolo g ical s c h emas of inter pretat ion.Thegeological inter-

p retation bene¢ts on the one hand from the results of radiometric dating but in exchange it

alone can make the ¢guresyieldedbythevarious methodsfully meaningful.

Let us repeat, there i s n oth ing automatic about i nterpreting radiometric ages. Age

is m ean ing ful o nly i n a g iven ge olog ical context. I n ad dition , i n retu rn , i ncl us ion in a

geolo gical co ntext e nl ighten s th e ge och em ical b ehavior of t he vario us c h ronometers .

Each radiochronometer may bear original information, but for it to be credible it must

be matched against other sources of information. It must be consistent with the

other things we know, with the usual behavior of the chronometer in question compared

with other chronometers, and with the speci¢c geological history under study. The

sc ient i ¢c approach i s more li ke dete ct ive work than the applicatio n of automatic

programm ing.

5.5 The geological timescale

5.5.1 History

The making of th e geological timescale, which is the greatest revolution geology has seen,

paradoxically has a long history. It took longer for it to become accepted than for its main

lines tobe established. As stated, th e idea ofusing radioactive decay to measure geological

ages se ems to have occurred independently but at about the same time to Pierre Curie in

France (see Barbo, 1999)andtoErnest Rutherford in Canada (se e Eve, 1939) in the early

twenti eth century.

It was Rutherford who ¢rst attempted to translate this insight into an actual measure-

ment. He had just identi¢e d  p articles as helium atoms. His colleague Ramsay had just

shown how the proportions and abundances of the rare gases could be measured.

Rutherford suggested tohim measuring the amount of helium contained in a uranium ore.

Hedidso. Rutherfordfoundanageofmorethan1billionyears.Thiswasin1906,aboutacen-

turyago. Rutherford’s discovery was abombshell: geological terrains were more than1bil-

lion years old! The second stage took place in 1907 at Yale University, where Rutherford

went to deliver the prestigious Silliman Lecture. Now, at Yale there was a chemist named

Boltwood, whowas interested in chemical transformations related to radioactivity. He sus-

pected that the end product of radioactive chains, which he was analyzing by chemical

methods, was lead. Rutherford suggested he should test out his idea geologically by taking

whatgeologistsreportedtobeyoungandolduraniumoresandanalyzing theirlead content.

The olderones should contain more lead than the youngerones. Boltwood (1907)madethe

corresponding series of m easurements and con¢rmed there was a connection between

188 Uncertainties and results of radiometric dating

leadanduranium chains.Inturn,hethendecide dtousethemethodtodatetheuraniumores

byanalyzing the uranium and lead content of each, and he calculated th e ages by applying

the exponential law for decay. These were purely chemical measurements, not isotope

measurements.

After Boltwood’s discovery, inspired by Rutherford, the chemical dating of lead was

improved by the discovery that thorium toowas the parentofa radioactive chain ending in

lead.The datingformulawas modi¢ed slightlyto read:

Age ¼

ðPbÞ

total

ðUÞþ0:38 ðThÞ

 7400 Ma

where (Pb), (U), and (Th) are th e lead, u ranium, and thorium contents in grams,

respectively.

However, the chemical U^Pb method soon ran into what seemed at the time an insolu-

ble tech nical problem. Uranium ores could be dated, but what of ordinar y rocks?

Chemic al methods of the day were not sensitive enough and could not be used to measure

either uranium or lead contents in ordinary rocks. These contents are measured in parts

per million and at the time such elements could be measured only if their abundances

were of the order of1%.

Thatis why in1908 R. J. Str utt, wholaterbecame thefamous Lord Rayleigh,undertook

to measure the age of ordinary rocks by using the helium method (Strutt,1908).To do this,

he measuredtheradiationproducedbytherock,whichgavehimtheinstantaneous quantity

Heproduced.Henextmeasuredthequantityof

He contained in the rock. It was then

possible to make a simple age calculation. A lthough Strutt was aware from the outset that

helium di¡uses readily from minerals and rocks and so a¡ects the age measured, the

method developed quickly in various parts of the world: in Britain with Strutt himself, in

the United States with Pi g got,andinGermanywithPaneth, who applied it to meteorites

above all. In this race to develop a reliable geochronological method, one of Strutt’s stu-

dents, the Scot Arthur Holmes, made a n ame for himself an d was to play an essential part

in geological age determinations for the next 40 years (see Hol mes,1946). He is one of the

founders of isotope geology.

Althoughgeochronological methodsbasedon leadand helium are subjecttolimitations

and uncertainties, geologists embarked upon the adventu re of constructing an absolute

geological timescale to attribute durations to the geological e ras and stages ofthe stratigra-

phers.The ¢rstsuccessfully tobuild a coherentwhole was Bar rell in191 7. As Holmes was to

do late r, Barrell use d radioactive datings and stratigraphic and geological observations to

correlate them. He judged some ages unrealistic, others acceptable, and by a series of

approximations and trials and errors h e came up with a genuine quantitative stratigraphic

scale in millions ofyears.Table 5.6 shows the ¢gures of his scale alongside the‘‘modern’’¢g-

ures.With hindsight, Barrell’s workwas outstanding ^ and yet no one believed it! When I

began studying geology in Par is i n1958^9 we were told there was an absolute stratigraphic

scale but that it was highly approximate and largely wrong and so should not be learned. If

truthwillout,itsometimestakes quiteawh ile to do so!

This absolute scale, and even more so the reason ing that underpinned it, that is, the age

attributions to geological phenomena in millions or billions ofyears, and the awareness of

189 The geological timescale

the extraordinary ge olo g ical myopia ofclassicalgeologybased on stratigraphic stages, did

notcometob e trulyaccepteduntilthe late1960s.

This scale must be subdivided into two separate periods because the conditions for age

determination arenotthe same (see Plate6).



The Precambrian period extends from the formation of the Earth to the appearance

of the ¢rst ‘‘unquestioned’’ fossils 550 million years ago. This period began with the

earliest rocks, the ¢rst terrestrial rocks of Greenland, which, as we have seen, are

aged 3.82 Ga.



The ‘‘classical’’ period is that of traditional geology whe re fossil-based geology

applies. Within this period a special place must be mad e for the interval ranging

from 0 to 200 Ma during which we have samples of a real oceanic crust ove rlain by

sediments that are well identi¢ed paleontologically thanks to microfossils. The under-

taking was to match the terrains identi¢ed on a worldwide scale and to classify

them, through their fossils, in time i ntervals measured in millions of years. The ¢rst

job, then, was to put numbers on the stratigraphic scale developed by stratigraphic

paleontology which divides the periods for which there is fossil evidence into eras

and stages. This scale was then exten ded to very ancient ages, and after that, its reso-

lution was improved for recent times.

5.5.2 The absolute scale of fossiliferous (Phanerozoic) times

The great di⁄culty in this undertaking is that the usual methods for dating long durations

such as

Rb^

Sr,

238

206

Pb,

147

Sm^

143

Ne,

187

Re ^

187

Os, or

Ar cann ot readilybe

Table 5.6 The absolute scale of geological times in millions of years

Barrell

(191 7)

Holmes

(1 947)

Holmes

(1 960)

Lambert

(1971)

Modern

ages

Quaternary

(Noozoic)

Pleistocene 1^1.5 1 1 4

Te r t i a r y

(Cenozoic)

Pliocene 7^9 12^15 11 7 12

Miocene 19^23 26^32 25 26 26

Oligocene 35^3 9 37^47 40 38 37

Paleocene

Eocene

5 5^65 58^68 70 65 65

Secondary

(Mesozoic)

Cretaceous 120^15 0 127^14 0 135 135 141

Juras s i c 155 ^195 152^ 167 18 0 2 0 0 195

Triassic 190^240 182^196 225 2 40 235

Primary

(Paleozoic)

Permian 215^280 203^220 270 280 280

Carboniferous 300^370 255^275 350 370 345

Devonian 350^42 0 313^318 4 00 415 395

Silurian 390^460 350 440 445 435

Ordovician 480^590 430 500 515 500

Cambrian 550^700 510 600 590 570

Single da tes indicatethebeginningofthe period.

Source:AfterHallam(1983), inwhichthereferences cited maybefound.

190 Uncertainties and results of radiometric dating

used for dating sedimentary rocks. Now, the stratigraphic scale is de¢ned by index sedi-

mentary st rata containing fossil associations chosen as the boundary beds.The reasons it

is di⁄culttodatesedimentarystrataarethateithersedimentary rocksaremadeup ofinher-

ited mater ial (sandstone and schists) ofvaried provenance and age and, in such cases, the

criteria for initial isotopichomogeneity are not satis¢ed, or theyare newly formed material

(limestone), in which cas e the rock is sensitive to secondary phenomena (particularly

water circulation) and are not closed systems. Despite p ainstak ing studies, whi ch have not

been entirely unsuccessful (which are always cited, of course) no general method has

emerged.

The absolute chronologyofsedimentarystrata isgenerallyestablished indirectlybydating

igneous rocks whose geometric and chronological relations with the strata are k nown.

Interstrati¢ed volcanism is a particularly favorable case, of course. Another case directly

der ived from the process of oceanic expansion is that of the ancient ocean ridges, that is,

sea-£oorspreading whereastill-fresh layerofbasalt(thatcanbe radiometricallyandmagnet-

icallydated) is overlainbya layeroflimestone that isvery rich in microfossils. Ocean drilling

has allowed such dating (although the basalt must not be overly a¡ected by hydrothermal

circulation or by exchange with sea water at low temperature). The most commonly used

method fordatingbasaltis the

Ar^

Ar method. Butsuch dating is increasinglydi⁄cultas

we go back in time because ofweathering, since the older theyare, the more the basalts have

b eenalteredbyreactionwithseawater, withwhichthesedimentisimpreg nated.

In addition, direct methods yield dates for a few reference strata only. Other results must

be interpolated from them. The principle behind the method is simple enough. Suppose

that inwhat is considered a continuous sedimentaryseries we know fro m one ofthe earlier

methods the ages t

and t

of two points in the series, separated by a thickness

D(X) ¼X

X

. As a ¢rst approximation, all of the strata in the interval may be dated by

interpolation.

Thesedimentationrate oftheseries is

V ¼

 X

 t



;

sothe aget

ofapointlocated atX

¼ t



 X



To apply th e method, ¢rst the series must be continuous, in other words, there must be no

se d i me ntary gap or h iatu s, which stratigraphers are exper ienced at detecting. Next, sedi-

mentation mustbeofthe sa metypeifweareto assumethesedimentationratehasremained

con stant. All of this is done by comparing, correlating, obtaini ng n ew dates, by modifying

olddata, or con¢rmingotherdata, littlebylittle and casebycase. As canbe seen, itis a long,

hard slog and there is scope for constant improvement. It is understandable, then, that the

age boundaries between stages or eras are a¡ected by uncertainty which varies with the

dateofpublication.

The st ratig rap hic scale is shown in Plate 6. A few brief remarks are cal led for.The eras,

which our forebears thought were about equal in length, are in fact highly unequal:

191 The geological timescale

Paleozoic (P rimary) 340 Ma, Mesozoic (Secondary) 145 Ma, Cenozoic (Tertiary) 65 Ma,

and Quaternary 5 Ma. Ifwe plot the geological eras and the traditional subdivisions, it can

beseen thattheloss of information is aboutexponentialwithtime (Figure5.22).

Remark

With scientiﬁc advances, the names of the reference terrains do not change, but the ages of these

terrains are constantly changing. Uncertainties on the limits are not symmetrical because geolo-

gical constraints are not symmetrical either.

ThecaseoftheQuaternary

In recent periods, ranging from 1 to 5 Ma, which is the time in which humankind has

appeared and developed, the situation is ve ry di¡erent for two reasons. The ¢rst is that

manyd ati ng methods can be appli ed directly to sediments.This is the case with

Be,

and methods based o n radioactive disequilibrium. Direct dating can therefore be prac-

ticed.The second is thatthere are many indirect metho ds: £uctuations in

Oisotope

ratios (to which we shall return in Chapter 8), ¢ssion tracks, paleomagnetism, micropa-

leontolog y, etc. All of these methods can be used for intercalibration and re¢ned

interpolation.

In short, we can now draw up avery precise chronological scale for the Quaternary but

onethatisbasedon climaticphenomena.We shallspeakofthis in Chapter 6.

5.5.3 The Precambrian timescale

The Cambrian is theageat whichthe¢rstcommon fossil faunas appeared.The twotypesof

characteristic fossils are trilobite s and Archeocyatha. Its lower boundary is dated

540

þ40

10

Ma.

As Precambrian terrains cannot be subdivided on the basis of fossils, we work the other

way around: we set numerical limits and then map the corresponding terrains at de¢n ed

time intervals.The essential boundary has been set at 2.5 Ga. It divides the period before,

known as the Archean, and the period ranging from 2.6 Ga to 0.4 Ga, known as the

Time (log)

Age (log)

Quaternary

Cenozoic

Mesozoic

Paleozoic

Precambrian

468

Figure 5.22 Relationship between duration and ages of geological eras. ‘‘Classical geologists’’ thought

these durations were about equal. We are indeed dealing with a case of geological myopia.

192 Uncertainties and results of radiometric dating

Prote rozoic becausewesupposethatitwasduringthispe riodthatlifedeveloped.Theques-

tion, ofcourse,ishowto determinethelowerlimitto this scale.

We assume that the continental crust as it is today has not exis ted since the ¢rst age of

the Earth but that it appeared after a time T

or that it appeared at an early date but

was d estroyed by multiple phen omena (meteorite bombardment?) and subsi sted from

only.This ageT

is therefore the upper limit of the Arch ean. Between the formation of

the Earth and T

wehave de¢ned aperiod for whichthereis littleandoften only‘‘indirect’’

evidence (meaning there are no whole rocks) and that is known as the Hadean (see

Chapter 7).

But what is the value of T

? Howold are th e oldest terrains, in the sense ofun interrupted

geological formations that can be mapped? The Isua and Amitsoq formations of

Greenland already mentioned and dated 3.77 G a and 3.65 Ga, respectively, are the oldest

terrestrial rocks k nown as yet. But sedimentary rocks in Australia have been found to con-

tain zi rcon whose U^Pbages concord at 4.3 Ga (anda feweven at 4.37 Ga).These areindis-

putably th e oldest terrestrial m inerals. But what is the meaning of that? Zircon is a typical

mineral ofgranitic rocks, and so the remains seem to testify that there were pieces of conti-

nent at that ti me. Were those continents preserved, buried somewhere, or were they

destroyed by erosion, meteorite bombardment, and Hadean tecton ism? This is a question

geochronology raises.We therefore provisionally ¢x the Hadean^Archean boundary at

3.8 Ga (see Plate 6 for the azoic (Precambrian) timescale). Here wehave an uncertaintydue

to lackof information.We mustthereforebe prepared to change these ¢gures as newdiscov-

eries are made.

5.6 The age of the Earth

The age of the Earthwas touched upon in Chapter 2 and could in itself be the subje ct of an

entire book, such is its historical and philosophical signi¢cance. We shall give a brief sum-

mar y of it, emphasizing the approaches taken by those who attempted to answer the

question.

5.6.1 History

TheBibleindicatesthatthe Earth is 4000yearsold.Around1650ArchbishopUssherestab-

lished by bibliographical studies that the Earth had been created on 26 October in the year

4004 BCat9.00 i n the morning!

By contrast with this, in the late seventeenth century, the founde r of geology, Scotsman

James Hutton, had dismissedthe very idea ofthe Earth having an age we can estimate.The

Earth hadalwaysbeen hereandwastheseatofthesamephenomenadescribedbygeological

cycles and would be until the end of time.‘‘No vestige of a beginning ^ no prospect of an

end,’’ashe putit.

Inth e mid nineteenth century,while classicalgeology wasthriving, theBritishphysicist

William Thomson,latertobecomeLord Kelvin, began to critici ze the idea of an eternal

Earth and repetitive geology. His ideawas simple. Geological processes consume energy,

if only to make reliefs, power volcanoes, or generate earthquakes. Now, the ene rgy the

Earth contains is not i nexhaustible. He identi¢ed the source of terrestrial en ergyas being

193 The age of the Earth

of thermal origin.The inside of the E arth is hot and the Earth is cooling because it loses

heat from its surface by radiation. He thus c ame up with the ¢ gure of 100 Ma, con¢rmed

in two ways. First, he had used the same theory to calculate an age for cooling of the Sun

(this time by calculating the energy dissipated by radiation) of 100 Ma. Second, the

Ir ish man Joly had also calculated the age of the ocean and found 100 Ma. T he age of

100 Mawas a must!

However, geologists, and foremost among them Charles Lyell and C harles Darwi n,

rejected this age which they thought too young.

In 1910 Rutherford and then Boltwood

d etermined the ¢rst radiometric ages exceeding 1 bi llion years. Pierre Curie and

Labo rde showed that radioactivity gave o¡ heat, and so there was an energy source inside

the Earth, which implied Lord Kelvin’s cal culationwas false. Andyet it was onlyafte r the

Second World War that Kelvin’s ¢gure was seriously revised (see Burch¢eld, 1975;

Dalrymple,1991).

EXAMPLE

Kelvin’s problem

Kelvin considered the cooling of the Earth, ignoring its roundness. He assumed the surface

was plane and supposed it was maintained at constant temperature as it lost its heat by

radiation into space.

For a semi-inﬁnite solid separated by a plane surface, Fourier’s theory states that if we take

depth (

) with depth at the surface

¼0 and assume the solid is at a temperature

at the

initial time and we allow it to cool by conduction, the temperature

(

) is a function of

and

/2(

)

1/2

,where

is time and

is thermal conductivity. The thermal gradient (or geothermal

gradient as we say for the Earth) is written:

1=2

exp





Near the surface

¼0 and the exponential equals 1. The geothermal gradient

is:

G ¼

ðp

1=2

If we take

¼7000 8F, then

¼1/1480. With

¼0.0118 we get

¼0.93 Ma.

EXAMPLE

The age of the oceans

The Irishman Joly (who was one of the ﬁrst to use radioactivity in geology) decided to calculate

the age of the ocean (but attributed to it the same age as the Earth).

His reasoning ran like this: in the beginning the sea was fresh water. It became salty

through the input of rivers and evaporation of water. So if we divide the mass of sodium in

the ocean by the mass added annually by rivers, we will get the age of the ocean. To do this,

Kelvin changed his calculation somewhat and at different times his age for the Earth varied between

25 Ma and 400 Ma, but that did not change the order of magnitude at stake!

194 Uncertainties and results of radiometric dating

he used the values of his day. That of sodium in rivers was 2  10

4

moles kg

1

while the

sodium content of sea water was 0.5 moles kg

1

. And he asked: how long has it taken to make

the sea salty? Given that the mass of the ocean is 1.5  10

g and the mass of inﬂow from

rivers is 4  10

g, he found an age of

0:50

2  10

4



mass of ocean

mass of rivers

¼ 0:93  10

years:

5.6.2 The isotopic approach

In1938 Alfred Nier, then doing postdoctoralworkatHarvardUniversity, measuredtheiso-

topic composition ofleadin galena (PbS) fromvariousgeologicalsettings andtowhichvar-

ious ‘‘geological’’ages had been attributed. Nier undertook to calculate the

207

Pb^

206

ages of the galena and found ages of 2.5 billion years. Now, at that time the astronomer

Edwin Hubble, working at the California In stitute of Technology, had used the gradual

recession ofgalaxies to determin e the age of th e Un iverse and had come up w ith a ¢gure of

2 billionyears!

Rocks that were older than the Universe! Wasn’t that impossible? Three scientists set

about using Nier’s results to re calculate the age of the Earth: Gerl ing (1942), Holmes

(1946), and Houtermans (1946).Their common starting point was Nier’s isotope analyses

ongalenain1938atHarvard.Someofthesampleswerefromgeologicalformationsof

known age. Asgalenadoes notcontain uranium its isotopic c omposition is frozen from the

time it becomes isolated. If we wr ite the isotopi c compositions  ¼

206

Pb/

204

Pb and

 ¼

207

Pb/

204

Pb and assume that th e isotopic composition of the galenawas‘‘constitute d’’

in a closed system (mantle or crust) which has been isolated since the origins of the Earth,

we canwrite:

 ¼ 

238

204

ðe

 e

 ¼ 

235

204

ðe

 e

whereT

isthe ageofthe Earth,T

the ageofthegalena, 

and 

the initialisotopic compo-

sitions of the Earth, and where l corresponds to

238

Uandl

235

U. As we have al ready

done, we canrewritethese equationsas:

  

  

¼ 137:8

 e



Unfortunately, to calculatetheageof theEarthT

in this equation,twounknowns are miss-

ing, theinitial isotopic compositions ofterrestriall ead (

and 

Gerling,attheInstituteofPrec ambrianGeologyatLeningrad(nowSt.Petersburg),sim-

pli¢ed the problem and adop ted a new assumption (Gerling,1942) (Figure 5.23). He chose

This age is now referred to as the residence time of sodium in the oceans. See Chapter 8.

195 The age of the Earth

thegalena fromIvigtutinGreenlandfrom amongthoseNierhadmeasured, whoseisotopic

ratios were th e lowest, and assumed those ratios corresponded almost to 

and 

.To

remove the complication of the geological age of the galena, he con sidered recent galena

whoseageheassumed tobe0.The equationbeca me:

  

Ivig

  

Ivig

¼ 137:8

 1



Hethusfoundanageforthe Earthof3.1Ga.

Exercise

We take two samples of galena of recent ages, one from Joplin (United States) and the other

from Clausthal (Austria).

For the ﬁrst,

206

Pb/

204

Pb ¼22.28 and

207

Pb/

204

Pb ¼16.10. For the second,

206

Pb/

204

Pb ¼18.46 and

207

Pb/

204

Pb ¼15.6. (For the Ivigtut galena

206

Pb/

204

Pb ¼14.54 and

207

Pb/

204

Pb ¼14.6.)

(1) Determine the age of the Earth by Gerling’s method.

(2) What would the ages be if we assumed 

¼0 and 

¼0?

Answer

(1)

Joplin

¼2.83 Ga and

Clausthal

¼3.2 Ga.

(2)

Joplin

¼4.73 Ga and

Clausthal

¼5 Ga.

Holm es used a more sophisticated method (Figure 5.24) butstill bas e d on th e sa m e p rin -

ciple of a closed system for isotopic evolution a s provided by the galena measu red by

Nier.We take two galena specimen s of ‘‘known’’ages T

and T

.We have two equations.

Forgalena1:



 



 

137:8

 e



15 16 17

Mean of 7 galenas

(

3.1 Ga)

Ivigtut

galenas

= 0

(130 Ma)

207

Pb/

204

206

Pb/

204

Figure 5.23 Principle of Gerling’s method of calculating the age of the Earth.

196 Uncertainties and results of radiometric dating