All?gre Claude J. Isotope Geology
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234
U
¼
234
U
0
e
l
234
t
þ
238
U
1 e
l
234
t
230
Th
¼
230
Th
0
e
l
230
t
þ
234
U
e
l
234
t
e
l
230
t
:
This is the general equation for equilibration of a radioactive chain used for chronological
purposes.
From there, without resorting to long and tedions numerical simulation, let us try to answer
the question: at what speed does a greatly disturbed radioactive chain return to secular
equilibrium? Let us consider the preceding equation with
l
234
l
230
. The equation becomes:
l
230
230
Th ¼ l
230
Th
0
e
l
230
t
þ l
234
234
U1 e
l
230
t
:
For the chain to achieve equilibrium, it is necessary and sufficient that:
l
230
230
Th l
234
234
U:
For this e
l
230
t
must be virtually zero. So
t
must be less than to 6–10 periods of
230
Th. The
chains therefore achieve equilibrium after more than six half-lives of the daughter product
(with the smaller radioactive decay constant).
If
234
U/
238
U isotope fractionation occurs, which is the case in surface processes, it is
234
U
which is the ‘‘limiting factor’’ for the
238
U chain. The time required is therefore 1.5 million
years.
If there is no
234
U/
238
U isotope fractionation, the limiting factor is
230
Th and the equilibra-
tion time is 450 000 years.
For the
235
U chain the limiting factor is
231
Pa and therefore a time of 194 000 years. Both
chains of the two uraniums are equilibrated at about the same time in this case.
The isotopes of radioactive series used as geochronometers are those with decay constants of
more than one year.
Uranium-238 chain
234
U, half-life 248 ka, is used in sedimentar y or alteration processes because
234
U/
238
U
varies during alteration. The radioactive recoil of
234
U extracts this uranium from its
crystallographicsiteand so itis easilyaltered.
230
Th, half-life 75 ka.This element, named ionium, is certainly the most widely used for
surfaceandvolcanicprocesses.
226
Ra, half-life 1.622 ka. It is use d like
230
Th but for shorter-lived surface or volcanic
processes.
210
Pb, half-life 22 years. Used for studying glaciers, oceans or volcanics involving very
young phenomena.
Uranium-235 series
231
Pa, half-life 32.48 ka. This is the s ister of
230
Th but slightly more di⁄cult to master
analytically.
277
Ac, half-life 22 years. This element is not much used as yet because of di⁄culties in
mak ing precise analyses.
47 Radioactive chains
Th o rium-232 chain
228
Ra,half-life6.7 years.This is compl ementary to
226
Rato constrainthetimescaleofRa
fractionation.
228
Th, half-life1.9 years. Averygood complementfor
228
Ra and
230
Th.
These elements canbe m easured byalpha and gammaradioactive spectroscopyorbymass
spectrometry.The second technique is far more precise but less sensitive than counting. In
p ractice,
234
U,
230
Th,
226
Ra, and
231
Pa are measured by mass spectrometry and the others
bycounting.Pb-210 canbe measuredbymass spectrometrybutthis entailsgreatdi⁄culties
and requires specialprecautions. Forageneralreviewsee Ivanovich(1982).
A LITTLE HISTORY
The polemic that followed the discovery of radioactivity
Henri Becquerel discovered radioactivity almost by chance in 1898 while studying rays
from phosphorescent uranium salts excited by sunlight and trying to understand the
nature of x-rays discovered by Ro
¨
ntgen. But one day, although there was no sunlight, a
sample from the Joachimsthal mine in Bohemia spontaneously emitted radiation which
blackened a photographic plate, indicating as yet unknown properties of matter (see Barbo,
2003).
Some years later, when measuring the effect of these radioactive substances on an
electrometer (the particles ionized the air of the electrometer which then discharged)
Pierre and Marie Curie proposed calling the phenomenon radioactivity (activity created by
radiation). For them, it was the property certain substances, including uranium, had of
spontaneously emitting radiation.
They immediately came in for harsh criticism from British scientists relying on a crucial
observation: when the activity of 1 g of purified uranium was measured with an electro-
meter, the activity was less than that of 1 g of uranium contained in, say, 100 g of uranium
ore. In other words 1 g of uranium ‘‘diluted’’ in 100 g of inert rock was more ‘‘active’’ than 1 g
of pure uranium.
How could concentrated uranium be less active than diluted uranium? It smacked of
magic. It was Marie Curie who came up with the hypothesis of intermediate radioactive
products to explain this paradox. The discovery of radium must be set in this polemical
context, thus taking on its full significance. It was the second intermediate radioactive
product to be found after polonium.
The New Zealander Ernest Rutherford brought grist to the Curies’ mill and within a few
years the mechanisms of successive ‘‘cascade’’ decay was understood. Radioactive chains had
been discovered.
Shedding light on a paradox
Nowadays the paradox of diluted uranium being more active than pure uranium can be fully
explained. Suppose a radioactive chain is in equilibrium, say the
238
U chain:
l
1
N
1
¼ l
2
N
2
¼ l
3
N
3
¼¼l
n
N
n
noting
N
1
,
N
2
, ...,
N
n
the numbers of nuclides in the various isotopes of the chain. Thus in
secular equilibrium there is 14 times the
l
1
N
1
activity of
238
U in the chain. (The input from
the
235
U chain must be added to this although its contribution is small.)
48 The principles of radioactive dating
This is what happens in a rock several hundred million years old in which the chain has had
time to attain secular equilibrium.
Now, in purified uranium, the activity is merely
l
1
N
1
.
So, if the ‘‘activity’’ of 1 g of uranium is measured, it will be 14 times less than the activity
of 100 g of 1% uranium ore. Indeed, the ore would be slightly more active because there must
also be at least 0.5 g of thorium whose chain also produces 11 times more activity than pure
thorium. However, as the thorium constant is 3.5 times less, the outcome would be an
increase in the uranium activity of about 1.5 times.
In all, the rock is about 15.5 times more active than purified uranium. This is the paradox
behind the polemic!
2.4 Dating by extinct radioactivity
2.4.1 The historical discovery
Chemicalelements ^ thatis, thenucleithat makeup mostoftheir mass ^ havebeen manufac-
tured in stars ever since the Universe came into being.This is nucleosynthesis. Of the nuclei
form ed,somearestableandothersradioactive. Among the radioactivenucleisomehavevery
shorthalf-lives:theydecayquicklygivingr ise totheirstabledaughter isotopes. Allofthisgoes
on everywhere in interstellar space and iswhat provides the ordinary matterofthe Universe.
These isotopes areincorporatedintointerstellarmatterasgasesordust(seeChapter4).
Butsuppose that nucleosynthesis ofheavyelements (explosion ofa supernova) occurred
in the vicinity of the place where the Solar System formed giving rise to certain short-lived
radioactive isotopes. Suppose toothatthe solid bo dies ofthe Solar System form while these
radioactiveisotopes arenotyetextinct.These‘‘young’’radioactiveisotopes will be incorpo-
rated with the other interstellar material in these solid bodies (planets or meteorites) and
there they will decay and give rise to daughter isotopes.The solid objects having received
such inputs will therefore have abnor mal isotope abundances for the isotopes produced by
decayofthe radioactive isotope.Detectingsuchanomalies isthereforethe¢rststepin show-
ing the existenceofextinct radioactivity.
In1960 John Reynolds at Berkeleydiscovered a large excess ofthe isotope12 9 in the iso-
topic composition of xen on in the Richardton (H4) meteorite (see Reynolds, 196 0)
(Figure2.6).Now,this is notanyoldisotopebutthe de cayproductofio dine-129(radioactive
iodine we know how to make in nuclear reactors) whose half-life is 17 million years and
which, if it formed before thebirth ofthe Solar System, has disappeared today. And indeed
naturallyoccurring iodinehasonlya single isotope,
127
I.
To prove that the excess
129
Xe did come from the
129
I, Peter Je¡rey and John Reynolds
came up with a most ingenious experiment combining neutron activation analysis, mass
spe ctrometry, and stepwise outgassing by temperature increments.They irradiated a sam-
pleoftheRichardton meteoriteusinga£uxofneutrons.The
127
Iwastransformedbynuclear
reaction (n, ) into radioactive
128
I whichtransformed by
decay into
128
Xe.This reaction
iswritten
127
Iðn;Þ
128
I !
128
Xe:
49 Dating by extinct radioactivity
Theythen heatedtheirradiated sampleprogressively, after placing itin thevacuum andpuri-
¢cation line of a mass spectrometer. They analyzed the isotope composition of the xenon
extracted at each temperature increment and observed that the excess
129
Xe was extracted
atthes ametemperatureashalfofthe
128
Xe,whereas‘‘ordinary’’xenonwasextractedatadif-
ferenttemperature. Je¡reyand Reynolds (1961) conclud ed that
129
Xe is situated atthesame
(crystallographic) siteas naturaliodin e andtherefore is indeedthe daughterof
129
I.
This extraordinary discovery has two important consequences. First, it shows that,
before the Solar System formed (at a time in the past 5^10 times the half-life of
129
I, that is,
85^170 million years), there was a synthesis of heavy chemical elements. In addition, this
radioactive decay providedan exceptional andunexpected datingtoolfor studying the per-
iod wh en meteorites (and also, as we shall see, the Earth) were formed (see Figure 2.7).We
shall concentrate on this aspectnow.
2.4.2 Iodine–xenon dating
Let
129
I*(0)bethenumberofnuclidesformedbynucleosynthesisattimet ¼0,de¢nedasthe
endofthenucleosyntheticprocess.The radioactiveio dine dec aysbythelaw:
129
I
ðtÞ¼
129
I
ð0Þe
lt
:
Supposenowthat,attimet
1
,someoftheiodineisincorporatedin ameteorite(A)andattime
t
2
someother iodinein ameteorite(B).We canwrite:
129
I
A
ðt
1
Þ¼K
A
129
I
ð0Þe
lt
1
129
I
B
ðt
2
Þ¼K
B
129
I
ð0Þe
lt
2
:
x 10
136 134 132 131 130129 128 126 124
x 1
Xenon
Figure 2.6 Mass spectrum of xenon in the Richardton meteorite as measured by Reynolds. The bars
indicate the height of ordinary, say atmospheric, xenon.
50 The principles of radioactive dating
Here K
A
and K
B
arethefactorsofincorporation ofiodinebetweenthe interstellarcloudand
meteorites A and B, which is the ratio between iodine concentration in the interstellar
cloud and in the meteorite. For two meteor ites ofdi¡erent ch emical compositions, K
A
and
K
B
are di¡erent. In each meteorite, the
129
Idecays co mpletely into radiogenic
129
Xe,
129
Xe*
(withanasterisk):
129
Xe
A
¼
129
I
A
ðt
1
Þ
129
Xe
B
¼
129
I
B
ðt
2
Þ:
Howcanthisbeusedfordatingas we donotknow th e valuesofK
A
, K
B
,andI(0)?
Io dine has a stable isotope
127
I (the only one for that matter). We divide the express-
ions describing
129
Idecayby
127
I.We can assume that the incorporation of iodine by the
meteorites obeys chemical laws, and so the same rules apply for the 129 isotope as for the
127 isotope. This means the Kvalues are the sam e for both isotopes.The K coe⁄cients can
therefore be remove d from the equations describing the evolution ofthe isotopic ratios.This
gives:
129
I
127
I
ðt
1
Þ
A
¼
129
I
127
I
ð0Þ
e
lt
1
129
I
127
I
ðt
2
Þ
B
¼
129
I
127
I
ð0Þ
e
lt
2
:
There remains one unknown in these equations, namely the ratio
129
I
=
127
I0ðÞ,inother
wordsthe (
129
I/
127
I)isotoperatioattheendofnucleosynth esis.Itisareasonableassumption
that it was identical throughout the Solar System (and so for all meteorites).We can then
¢ndtheratiobetweenthetwoisotope ratiosofour two meteorites:
129
I
127
I
ðt
1
Þ
A
129
I
127
I
ðt
2
Þ
B
¼ e
lðt
2
t
1
Þ
:
ΔT
129
Xe
accumulation
Present
day
Condensation and
planetary accretion
(around 4.55 Ga)
Nucleosynthesis of
129
I
Time (arbitrary scale)
Figure 2.7 Evolution of
129
I in the Solar System and its trapping in planetary bodies;
T
is the time
between the end of nucleosynthesis and the accretion of planetary objects.
51 Dating by extinct radioactivity
By measuring the
129
I
=
127
IðtÞ
ratios inboth meteorites,we canin principle calculatethe
time interval between the formation of the two meteorites (t
2
t
1
).This method therefore
providesabsolute ^relative dating!
The problem comes down to measuring the (
129
I*/
127
I) isotope ratio at the time the
meteorite formed.Total
129
Xe is the sum of initial
129
Xe þ
129
I*(t). Today
129
I*(t) ¼
129
Xe*,
sinc e
129
I has decayed entirely.Therefore:
129
Xe
¼
129
Xe
total
129
Xe
initial
:
Theinteresting ratiois:
129
I
127
I
ðtÞ¼
129
Xe
127
I
¼
129
Xe
Xe
total
Xe
total
I
total
¼ A e
lt
withA ¼
129
I=
127
I0ðÞatthe endofnucleosynthesis.
The problem comes down to measuring the fraction of radiogenic
129
Xe* in total xenon,
and then measuringthe chemical(Xe/I) ratio, sincethe iodineis all
127
I.
We can calculate the age to the nearest coe⁄cient and therefore, by taking the ratio
between the values for the two meteorites, determine the relative age ofthe two meteorites.
Thebeautyofthis method lies in its capacity to measureverybrief intervals oftimebetween
the formationofplanetaryobjectsbillions ofyears ago.
Exercise
The
129
I/
127
I isotope composition measured on the Karoonda and Saint-Se
´
verin meteorites is
1.3 10
4
and 0.8 10
4
, respectively. Given that the half-life of iodine is 17 Ma, what is the
age difference between the two meteorites?
Answer
If
T
1
2
¼17 Ma
l ¼
ln 2
T
¼ 4 10
8
yr
1
:
The dating formula is applied:
129
I
127
I
A
129
I
127
I
B
¼
1:3 10
4
0:8 10
4
¼ e
l D
t
;
hence D
t
¼
1
l
ln 1:3=0:8ðÞ¼12:1 million years. This age is actually the maximum interval
measured.
Exercise
Given that the half-life of
129
I is 17 Ma, what is the shortest interval of time that can be
estimated, given the uncertainty in measuring the
129
Xe*/
127
I ratio is 2%?
Answer
Suppose we always take the same reference, say, Karoonda. There will no longer be any error
relative to Karoonda but everything will be expressed in terms of this reference. Let us take
52 The principles of radioactive dating
the previous measurement and look at the limits of uncertainty. The value 0.8 has two limits,
at 0.816 and 0.784. Let us calculate the age
t
. We obtain 11.64 and 12.64, or 1 million years.
The age of Saint-Se
´
verin (relative to Karoonda) is written 12.1 0.5 Ma.
2.4.3 Discoveries of other forms of extinct radioactivity
Since then many forms ofextinct radioactivity have been discovered, whichwe shall use as
required.Each discoveryhas requiredthe identi¢cationbyexperimentofparent^daughter
relations in meteorites.We reviewth emwithafewbriefcomments.
Iodin e^Xenon
129
I^
129
Xe, ¼25 Ma,discovered byReynolds (196 0).
Plutoniu m^Xenon
244
Pu^Xe
¢ssion
, ¼84 Ma.Thisradioactivity, discoveredbyKuroda
(196 0), produces ¢ssion tracks and the ¢ssion isotopes of xenon
131
Xe,
132
Xe,
134
Xe, and
136
Xe. It is an important supplement to the iodine^xenon method and was discovered
veryshortlyafter it.
Sam a ri um ^Neodymi um
146
Sm^
142
Nd, ¼146 Ma. This form of radioactivity, discov-
ered at San Diego by Lugmair et al.(1975), is interesting because it is has a long half-li fe
and allowsus to connect long-duration phenomenathatoccurred around the time of 4.5
billionyearsago.
Aluminum^Magnesium
26
Al^
29
Mg, ¼1Ma. This form of radioactivity was ¢rst
detected in certai n minerals from very ancient meteorites by the team of Gerald
Wa s se rb u rg at the California Institute of Technology (Caltech) (Lee et al.,1977). It was
of historical importance but it is probably more importantstill that aluminum is a deci-
sive constituent of meteorites (2^3%). It is probable that
26
Al was instrumental in the
veryearly thermalhistoryofplanetesimalsanditsin£uence shouldbeaddedtothe calcu-
lations alreadydone onthistopic inChapter1.
Palladium ^Silver
107
Pd ^
107
Ag, ¼9.4 Ma. This form of radioactivity was detected in
iron meteorites by the Caltech team (Kelly and Wa s s er b u r g , 1978). It has shown how
old these meteorites are. This means that metallic iron di¡erentiation is a very ancient
phenomenon inthe pro cesses offormationofthe Solar System.
Manganes e ^Chromium
53
Mn^
53
Cr, ¼5.3 Ma.This form of radioactivity, discovered
in Par is by Bi rck and Alle
'
gre in 1985, is interesting because the manganese and chro-
mium fractionatebecause oftheirdi¡erent volatilities.
Iron^ Nickel
60
Fe ^
60
Ni, ¼2.1Ma. This form of radioactivity has been fou nd in just a
fewbasaltic meteoritesby Shukoly ukov andLugmai r(1993)atSanDiego.Itisimportant
because iron is averyabundantelement.
Calciu m^Potassiu m
41
Ca^
41
K, ¼0.143 Ma. This form of exti nct radioactivity is
importantbecause of its shorthalf-life.It was discoveredbySrin ivasan etal.(1994).
Haf nium ^Tu n gsten
182
Hf^
182
W, ¼13 Ma. This form of extinct radioactivity, discov-
ered by Harp e r and Jacobsen (1994)atHarvardandthenbyLee and Hall i d ay (1995)at
the University of Michigan, is very important bec ause Hf and W fractionate during
metal^s ilicate separation, allowing this separation tobe dated, including in planets(dif-
ferentiationofthe core).Weshallusethis schemelateron.
Niob ium^Zirconium
92
Nb^
92
Zr, ¼36 Ma. This newcomer to the ‘‘club’’ of forms of
extinctradioactivity,discoveredinZurichbySchonbachleretal.(20 02), is yet tobe exploited.
53 Dating by extinct radioactivity
Chlorine ^ Sulfur
36
Cl^98%
36
Ar / 2%
36
S, ¼0.43 Ma was discovered recently by a
Chinesetea m, Lin etal.(2005). Noanomalyon
36
Ar wasfound,onlyon
36
S.
Beryllium ^Boron
10
Be^
10
B, T ¼15 Ma was discovered by McKeegan, Chau ssi don,
and Robert (200 0).
Lead ^Thall i u m
205
Pb^
205
Tl, T ¼15.1 Ma was recently discovered by Neilsen,
Rehka
«
mpe r,andHalliday (20 06).
Othershavenotbeen con¢rme d andarenotlisted here.
2.5 Determining geo logically useful radioactive
decay constants
Asjustseen,whatallowsu s to calculate ageandistheveryessence oftheradioactive clock is
the radioactive constant l, namely the probability that anucleus will decay. How canthisbe
determined? This is di⁄cult a priori, given that the constants are generally very small
because activity is low (see Figure 2.8). To si mplify there are three m ethods more or less
derivedfrom the dating method:
(1) direct measurementofradioactivitybylNactivity: i fwe knowN,wecandeducel;
(2) measu rement of accumulation of the daughter isotope (both these series of measure-
ments are doneinthe laboratory);
(3) geological‘‘comparison’’ofagesobtaine d by various methods.
Weshall examinethese threetechniquesin the case of
87
Rb.
2.5.1 Measurement of activity
Westart withthefundamental equationdescribingdecay
d
87
Rb
dt
¼ l
87
Rb;
thatis,the numberof particles emitted by unittime is equalto l
87
Rb.
Let us take 1kg of
87
Rb, which corresponds to 10
3
=87 6:023 10
23
g (6.23 10
23
is
Avogadro’s number), or 6.92 10
24
atoms of
87
Rb. If l ¼1.42 10
11
yr
1
, the number of
particles emitted in 1 year is 6.92 10
24
1.41 10
11
,or9.826410
13
parti cles.
2.0
1.6
1.2
0.8
1930 1940 1950 1960 1970
147
Sm half-life by year of publication
T
=
1.06 ± 0.01
x
10
11
yr
T (10
11
yr)
Figure 2.8 Improvement in determination of decay constants over time: the example of
147
Sm.
54 The principles of radioactive dating
Remembering that 1 year 3 10
7
seconds, that corresponds to 3.275 10
6
disintegrations
per second, which isa measurablevalue:even10 gofpurerubidiumwill su⁄ce.
The di⁄cultylies in measuring
particles. Some of these particles are absorbed by the
rubidium deposititself. It is fundamentalthen to make layers ofr ubidium ofvariable thick-
nesses andto correctwhatisknownas auto-absorption.Thesearetricky methodstomaster.
2.5.2 The radiogenic isotope produced
For
87
Rb we try to measure the
87
Sr accumulated.Take 1kg of pure
87
Rb. How much
87
Sr
does itp roduce in1year?
87
Sr¼10
3
g1:42 10
11
¼1:42 10
8
g;
thatis14.2 ng. As strange as it mayseem, suchaquantity can easilybe m easuredwitha mass
spe ctrometerby isotope dilution.
Naturally, inpracticewetrytouseboth methods andtocomparethe results.Thequestion
is,ofcourse,howdoweobtain1kgofpureoralmostpure
87
Rb? Isotopeseparation is expen-
sive sowetryrathertousenaturalrubidium,inwhichthereisonlyafraction of
87
Rb.Thedif-
¢culty is that there must be very little
87
Sr in the rubidium being measured.The rubidium
must therefore be very carefully puri¢ed by chemical methods, which is di⁄cult for such a
largeamountofrubidium.The measurementuncertaintystemsfrom this.
2.5.3 The method of geological comparison
If we know the age of certain rocks from methods with decay constants that are easier to
determine (such as uranium) we can then calculate the constant l
Rb
by measuring the
87
Sr/
87
Rb ratioson aseries ofrocksor mineralswhose (U/Pb) age is known.
This method toois di⁄culttoimplementas we mustbe surethatthevarious systems have
remained closed, as we shall see in the next chapter. Even so, the method is essential for
ensuring the geological reliability of the di¡erent methods.To avoid geological di⁄culties,
much use is made of cross-calibrations with meteorites and moon rocks.Why so? Because
meteoritesare rocks dating from the origin ofthe Solar System (and thereforeold) and have
not been subjected to major ‘‘disruptive’’events.We proceed by trial and error combining
the di¡erentapproaches.An international commission makes regular reviewsandupdates
the constantsas needbe.
Let us give th ree important geological comparisons that use the constants given in the
table.
Moon rocks
We c hooseRoc k10072 ,w hic hhascomeinf orpa rticular lyclosescrutin y.AstheU/ Pbratioislo w
thisdating methodisnotgoodbutitisagoodwayofcomparingRb^Sr,K^Ar, andSm^Nd.
Dating method
Rock10072 K ^A r Rb^Sr Sm^Nd
Time (Ga) 3 .520.4 3 .570.05 3.570.03
55 Useful radioactive decay constants
E ucrites (basaltic achondrites)
These are basalt meteorites, in other words an cient extraterrestrial lava £ows. Dating by
U^Pb is extremely precise because the U/Pb ratios are high. As said, the uranium decay
constants are the references. However, Rb^Sr is not ver y p recise as Rb/Sr ratios are really
low. (We are anticipating a little on the nextchapter.)TheK^Ar,Lu^Hf,andSm^Nddat-
ings are alsorelatively precise.
Dating method
Eucrite
meteorites
U^Pb Rb^Sr K^Ar Sm^Nd Lu^Hf
Time (Ga) 4.5 50.05 4.500. 1 4 4.500. 1 4.530.04 4.570.1 9
Ordinarychondrites
These are the most common meteorites characterized by the presence of chondrules.
Comparison of Pb^Pb and Rb^Sr datingsis very precise. Similarly, K^Arand Re^Os are
in suitable agre ement.
Dating method
Ordinary chondrites U^Pb Rb^Sr K^Ar Re^Os
Time (Ga) 4.550.05 4.550.08 4.520.05 4.540.02
Table 2.3 Comparison of methods for determining radioactive decay constants
Isotope Laboratorycounting Accumulation Geological comparison
238
U,
235
U,
232
Th,
and radioactive
chains
This isthe reference
method andis (relatively)
precise
Notused This is the reference for
other methods
87
Rb Di⁄cultbecause ofauto -
absorptionof
raysby
the powderbeing
counted
Di⁄culttoshow up
because oftracesof initial
87
Sr, which ishardto
remove
Comparisonbetween
methods and in
particularbetween
meteor ites is essential
187
Re Impossible:insu⁄cient
energy (highauto-
absorption)
This is thebest method;
wemeasureaccumulated
187
Os
Comparisonwithother
methods and particularly
meteor itesremains
essential
176
Lu Poordetermination Di⁄cultbecause ofthe
importance ofinitialHf
Comparisonsbetween
methods areuseful
147
Sm Poordeterm ination Di⁄cultbecause of
initial Nd, which ishard
to remove
Comparisonsbetween
methods areuseful
40
K Very precise counting Shouldbepossiblein a
well-sealed£ask
Comparison is di⁄cult
because
40
Ardi¡uses
readily
56 The principles of radioactive dating