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Isotope Geochemistry
Geochemistry
PUCP 2015Isotope geochemistry
Dr. Jochen Smuda
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Isotope Geochemistry
Part IStable Isotopes
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Isotopes
• Isotopes have different ## of neutrons,and thus a different mass
• Affect on reactions in small, but real, andprovides another measurement ofreactions – affected by similarphysicochemical parameters!
• Also a critical tracer – the isotopes can beused to track molecules in a reaction!
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Measuring Isotopes• While different, isotopes of the same element
exist in certain fractions corresponding totheir natural abundance (adjusted byfractionation)
• We measure isotopes as a ratio of theisotope vs. a standard material (per mille ‰)
318 10×
=standard
standard sample
R
R ROδ
b
aab R
R=α
Where R a is the ratio of
heavy/light isotope and α isthe fractionation factor
‰
a
bba
a
b ∆=−≈ δ δ α ln10 3
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Fractionation
• A reaction or process which selects forone of the stable isotopes of a particularelement
• If the process selects for the heavierisotope, the reaction product is ‘heavy’, thereactant remaining is ‘light’
• Isotope fractionation occurs for isotopicexchange reactions and mass-dependentdifferences in the rates of chemicalreactions and physical processes
a
bba
a
b ∆=−≈ δ δ α
ln103
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Temperature effects onfractionation
• The fractionation factors, α , are affectedby T (recall that this affects E A) anddefined empirically:
• Then,
• As T increases, ∆ decreases – at high T ∆ goes to zero
BT
Aab
+×
=2
63 10ln10 α
Where A and B are constantsdetermined for particular reactionsand T is temp. in Kelvins
abba
ab ∆=−≈ δ δ α ln10 3
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Equilibrium vs. Kinetic fractionation
• Fractionation is a reaction,but one in which the freeenergy differences are onthe order of 1000x smallerthan other types of chemicalreactions
• Just like other chemicalreactions, we can describethe proportion of reactantsand products as anequilibrium or as a kineticfunction
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FRACTIONATION DURINGPHYSICAL PROCESSES
• Mass differences also give rise tofractionation during physical processes(diffusion, evaporation, freezing, etc.).
• Fractionation during physical process is aresult of differences in the velocities ofisotopic molecules of the same compound.
• Consider molecules in a gas. All moleculeshave the same average kinetic energy, whichis a function of temperature.
22
1 mv E kinetic =
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Because the kinetic energy for heavy and lightisotopes is the same, we can write:
In the case of 12 C16 O and 13 C16 O we have:
Regardless of the temperature, the velocity of12 C16 O is 1.0177 times that of 13 C16 O, so thelighter molecule will diffuse faster andevaporate faster.
L
H
H
L
mm
vv
=
0177.1994915.2799827.28 ==
H
L
vv
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Equilibrium Fractionation
• For an exchange reaction:½ C 16 O 2 + H 218 O ↔ ½ C 18 O2 + H 216 O
• Write the equilibrium:
• Where activity coefficients effectively cancelout
• For isotope reactions, K is always small,usually 1.0xx (this K is 1.047 for example)
)()()()(
2182
1
216
2
1621
2
18
O H OC O H OC K =
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WHY IS K DIFFERENT FROM1.0?
Because 18 O forms a stronger covalent bondwith C than does 16 O.
The vibrational energy of a molecule is given bythe equations:
HO
H
ν h E lvibrationa 21= mk
π ν
2
1= kxF −=
Thus, the frequency of vibration dependson the mass of the atoms, so the energyof a molecule depends on its mass.
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• The heavy isotope forms a lower energybond; it does not vibrate as violently.Therefore, it forms a stronger bond in
the compound.• The Rule of Bigeleisen (1965) - The
heavy isotope goes preferentially into
the compound with the strongest bonds.
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Equilibrium Fractionation II
• For a mass-dependent reaction:• Ca 2+ + C 18 O32- CaC 18 O 3• Ca 2+ + C 16 O32- CaC 16 O 3• Measure δ18 O in calcite ( δ18 O cc ) and water
(δ18 O sw )• Assumes 18 O/ 16 O between H 2O and CO 32- at
some equilibrium
T ºC = 16.998 - 4.52 ( 18 O cc - 18 O sw ) + 0.028 ( 18 O cc- 18 O sw )2
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Empirical Relationship between Temp. &Oxygen Isotope Ratios in Carbonates
At lower temperatures, calcitecrystallization tends to incorporate arelatively larger proportion of 18O
because the energy level (vibration)of ions containing this heavier isotopedecreases by a greater amount than ionscontaining 16O.
As temperatures drop, the energy level
of 18O declines progressively by anamount that this disproportionatelygreater than that of the lighter 16O.
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Distillation• 2 varieties, Batch and Rayleigh distillation
dependent on if the products stay in contactand re-equilibrate with the reactants
• Batch Distillation:δ f = δ i – (1 – F) 10 3lnα CO2-Rock where the isotope of the rock ( δ i) depends on
it’s initial value ( δf ) and the fractionation factor
• Rayleigh Distillationδ f - δ i =10 3(F (α – 1) – 1)
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Effect of Rayleighdistillation on theδ18O value of watervapor remaining inthe air mass and ofmeteoric precipitationfalling from it at a
constant temperatureof 25°C.Complications:1) Re-evaporation2) Temperaturedependency of α
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Using isotopes to get information onphysical and chemical processes
• Fractionation is due to some reaction,different isotopes can have different
fractionation for the same reaction, anddifferent reactions have differentfractionations, as well as being different atdifferent temperatures and pressures
• Use this to understand physical-chemicalprocesses, mass transfer, temperaturechanges, and other things…
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Volatilization• calcite + quartz = wollastonite + carbon dioxide
CaCO 3 + SiO 2 = CaSiO 3 + CO 2 • As the CO 2 is produced, it is likely to be expelled
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• Other volatilization reaction examples…
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ISOTOPE FRACTIONATION IN THEHYDROSPHERE
Evaporation of surface water in equatorial regionscauses formation of air masses with H 2O vapordepleted in 18 O and D compared to seawater.
This moist air is forced into more northerly, cooler airin the northern hemisphere, where watercondenses, and this condensate is enriched in 18 Oand D compared to the remaining vapor.
The relationship between the isotopic composition ofliquid and vapor is:
331818 1010 −+=v
lvl OO δ α δ
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Assuming that δ18 Ov = -13.1‰ and α vl(O) =1.0092 at 25°C, then
and assuming δDv = -94.8‰ and α vl(H) = 1.074at 25°C, then
These equations give the isotopic compositionof the first bit of precipitation. As 18 O and Dare removed from the vapor, the remainingvapor becomes more and more depleted.
Thus, δ18 O and δD values become increasinglynegative with increasing geographic latititude(and altitude.
0003318
0.410101.130092.1 −=−+−=lOδ
( ) 00033 8.2710108.94074.1 −=−+−=
l Dδ
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Map of NorthAmerica showingcontours of the
approximateaverage δD valuesof meteoric surfacewaters.
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Because both H and O occur together in water, δ18O and δDare highly correlated, yielding the meteoric water line(MWL): δD ≈ 8δ18O + 10
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Deviation from MWL
• Any additional fractionation process whichaffects O and D differently, or one to theexclusion of the other will skew a wateraway from the MWL plot
• These effects include: – Elevation effects - ( δD -8‰/1000m, -4‰/ºC) – Temperature ( α different!) – Evapotranspiration and steam loss – Water/rock interaction (little H in most rocks)
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Kinetic Fractionation
• lighter isotopes form weaker bonds incompounds, so they are more easilybroken and hence react faster. Thus, in
reactions governed by kinetics, the lightisotopes are concentrated in the products.• Again, isotope reactions can be exchange
reactions or mass-dependent chemical orphysical reactions – kinetic factors may affectany of these!
Ki i f i i I
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Kinetic fractionation I –SO 42- reduction
• SO 42- + CH 4 + 2 H + H2S + CO 2 + 2 H 2O• This reaction is chemically slow at low T,
bacteria utilize this for E in anoxic settings• Isotope fractionation of S in sulfide generated
by microbes from this process generatessome of the biggest fractionations in theenvironment (-120‰ for S)
• THEN we need to think about exchangereactions with H 2S or FeS (aq) as it maycontinue to interact with other S species
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S isotopes and microbes• The fractionation of H 2S formed from
bacterial sulfate reduction (BSR) is affectedby several processes: – Recycling and physical differentiation yields
excessively depleted H 2S – Open systems – H 2S loss removes 34 S – Limited sulfate – governed by Rayleigh process,
enriching34
S – Different organisms and different organic
substrates yield very different experimental δ34 S
• Ends up as a poor indicator of BSR vs. TSR
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Iron IsotopesEarth’s Oceans 3 Ga had nooxygen and lots of Fe 2+ ,cyanobacteria evolved,produced O 2 which oxidizedthe iron to form BIFs – intime the Fe 2+ was moredepleted and the oceanswere stratified, then laterbecome oxic as they aretoday
This interpretation is largely based on ironisotopes in iron oxides and sulfide mineralsdeposited at those times (Rouxel et al., 2005)
No one has yet bothered tomeasure how iron isotopeschange when iron sulfideminerals precipitate …
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Mass-independent fractionation• Mass effects for 3 stable isotopes
(such as 18 O, 17 O, and 16 O) shouldhave a mass-dependent relationshipbetween each for any process
• Deviation from this is mass-independent and thought to be
indicative of a nuclear process(radiogenic, nucleosynthetic,spallation) as opposed to a physico-chemical process
• Found mainly associated withatmospheric chemistry, effect can bepreserved as many geochemicalreactions in water and rock are mass-dependent
http://www.sciencemag.org/content/vol283/issue5400/images/large/se0397162002.jpeg
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S-isotopic evidence of Archaenatmosphere
• Farquar et al., 2001; Mojzsis et al., 2003found MIF signal in S isotopes ( 32 S, 33 S,34
S) preserved in archaen pyritesprecipitated before 2.45 Ga• Interpreted to be signal from the photolysis
of SO 2 in that atmosphere – the reactionoccurs at 190-220nm light, indicating lowO 2 and O 3 (which very effficiently absorbthat wavelength)
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Part IIGEOCHRONOLOGY
Introduction to RadioactiveDecay and Dating of
Geological Materials
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The Debate about the Age ofthe Earth
• Prior to Geology becoming an accepted field ofscience, the age of the Earth was a matter forTheology.
• Bishop Usher proclaimed in 1650 that thecreation of the world took place in 4004 BC, aview that was unchallenged for over 100 years.
• The official position of the church was that all thesurface features of the Earth were related tocatastrophic events such as the Great Floodwhich occurred intermittently.
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Catastrophism versusUniformitarianism
• So what changed?• James Hutton arrived on the scene to shake up the establishment• Hutton argued that very slow but continuously acting processes
were what accounted for the surface features of the Earth• He cemented this idea, which became known as uniformitarianism,
in his book Theory of the Earth which was published in 1785.• Although initially greeted with horror by many, his ideas gradually
became accepted, including the conviction that very long periods oftime are required for the deposition of sedimentary rocks
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Early Estimates
• Early estimates were based on the principle ofsuperposition – In the late 1790’s early 1800’s, William Smith’s
nephew calculated using this principle that the Earthwas 96 million years old
• Estimates where also based on the rate of cooling of theEarth – In 1779 the French naturalist Comte du Buffon did an
experiment where he created a minature Earth andmeasured it’s rate of cooling. Doing this he estimatedthe Earth as being 75,000 years old.
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William Thompson• In 1862 the Scottish physicist William
Thompson calculated that the Earth wasbetween 24 and 400 million years old.
• He assumed that the Earth had started life asa ball of molten rock and calculated the time itwould take to cool to its current temperature.
• However, Charles Darwin, who had publishedhis theory of Evolution by Natural Selectiondid not feel that this was enough time toaccount for biological changes he hadobserved. Other biologists agreed
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William Thompson• However, Thompson’s ages were supported by independent
calculations by others – The German Physicist Herman von Helmholtz in 1856 calculated an age
of 22 million years – The Canadian astronomer Simon Newcomb in 1892 calculated an age
of 18 million years
– Charles Darwin’s son, the astronomer George Darwin calculated an ageof 56 million years based on the amount of time he thought was neededfor Earth to develop a 24 hour day from tidal friction
– In 1899-1900, John Joly, from the University of Dublin, calculated anage of 80 to 100 million years based on the amount of time needed toaccumulate all the salt in the oceans from erosion
– All these calculations tended to support William Thompson’s ideas andcalculations. So where did William Thompson go from here?
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Lord Kelvin
• In 1869 William Thompson was involved in a veryfamous debate with a certain Thomas H Huxley…
• In 1892 he was rasied to the peerage and became LordKelvin in recognition for his many scientificachievements.
• In 1897 he delivered his famous lecture “The Age of theEarth as an Abode Fitted for Life” in which he reducedhis previous estimate to between 20 and 40 million
years.• But had he missed something…?
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Mantle Currents• Lord Kelvin has assumed that the cooling of the Earth was governed
only by thermal gradients and did not take into account convectivecurrents within the mantle which threw his age out
• In 1895, John Perry produced an estimate for the age of Earth of 2to 3 billions years old using a model of a convective mantle and thincrust
• Still a bit young but certainly better than 100 million years• Refinement of this model would only be possible some 60 years
later with the advent of plate tectonic theory
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The next big thing..• In 1896, the French chemist Henri Becquerel discovered
radioactivity.• In 1898, two other French researchers, Marie and Pierre Curie,
discovered the radioactive elements polonium and radium.• In 1903 Pierre Curie and his associate Albert Laborde announced
that radium produces enough heat to melt its own weight in ice inless than an hour.• What did this mean?
– The Earth produced it own internal heat – Calculations on the age of the Earth based on cooling underestimated
the age of the Earth – Lot’s of scientists died of cancer
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Radioactivity• In 1903 Marie and Pierre Curie and Henri Becquerel shared the Nobel Prize
for Physics for the discovery of radioactivity• By now scientists including JJ Thompson and Ernest Rutherford working at
the Cavendish Laboratory at Cambridge University had started to unravelthe internal structure of the atom.
• In 1898 Rutherford moved to MacGill University in Montreal as professor ofphysics where he reported that radiation consisted of three differentcomponents which he named alpha, beta and gamma.
• In 1900 Frederick Soddy came to MacGill as a demonstrator in Chemistry.Together, he and Rutherford formulated the theory of radioactive decay andgrowth which they expressed as –dN/dt = λN where λ is the decay constant,representing the probability that an atom will decay in unit time and N is the
number of radioactive atoms present.
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Radioactivity and Dating• The postulation that radioactive decay could be measured opened
the door to radioactive dating.• This possibility was recognised by Rutherford and Boltwood around
1905 and in a series of lectures at Yale University that yearRutherford proposed that the age of uranium minerals could bemeasured by the amount of helium that had accumulated in them,helium being the product of the radioactive decay. He carried outage determinations on several uranium minerals and obtained anage of 500 million years.
• The state of radioactive dating was reviewed by Arthur Holmes in1913 in his book “The Age of the Earth” which he wrote when hewas just 23.
R di i D i d
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Radioactive Dating andIsotopes
• Problems soon began to arise.• The development of radioactivity and the formula for the rate of
disintegration was based on assumed simple decay of one element toanother.
• As decay systems began to be worked out it seemed that there weredifferent types of radioactive elements and that the atomic weight ofelements was not whole numbers but fractions.
• Soddy suggested a solution in which he proposed that the place occupiedby an element in the periodic table could accommodate more than one kindof atom.
• A young scientist, F.W Aston, working at the Cavendish Laboratory at thetime, set out to examine this and eventually identified 212 of the 287naturally occurring isotopes.
• The presence of isotopes and their additional complication to the radioactivedecay schemes lead many scientists to abandon the idea of radioactivedating.
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Arthur Holmes• Arthur Holmes work was generally ignored until the 1920s, though in 1917 Joseph Barrell, aprofessor of geology at Yale, redrew geological history as it was understood at the time to conform
to Holmes's findings in radiometric dating.• Barrell's research determined that the layers of strata had not all been laid down at the same rate,
and so current rates of geological change could not be used to provide accurate timelines of thehistory of Earth.
• Holmes's persistence finally began to pay off in 1921, when the speakers at the yearly meeting ofthe British Association for the Advancement of Science came to a rough consensus that Earthwas a few billion years old, and that radiometric dating was credible.
• Holmes published The Age of the Earth, an Introduction to Geological Ideas in 1927 in which hepresented a range of 1.6 to 3.0 billion years, although this was still largely ignored by thegeological community.
• The growing weight of evidence finally tilted the balance in 1931, when the National ResearchCouncil of the US National Academy of Sciences finally decided to resolve the question of the ageof Earth by appointing a committee to investigate.
• Holmes, being one of the few people on Earth who was trained in radiometric dating techniques,was a committee member, and in fact wrote most of the final report.
• The age of the Earth as it is accepted today was determined by CC Patterson in 1956 (more aboutthat later…)
St bl U t bl
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Stable versus UnstableNuclides
• Not all combinations of N and Z result in stable nuclides.• Some combinations result in stable configurations
– Relatively few combinations
– Generally N ≈ Z – However, as A becomes larger, N > Z• For some combinations of N+Z a nucleus forms but is
unstable with half lives of > 10 5 yrs to < 10 -12 sec
• These unstable nuclides transform to stable nuclidesthrough radioactive decay
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Radioactive Decay
• Nuclear decay takes place at a rate that follows the lawof radioactive decay
• Radioactive decay has three important features1. The decay rate is dependent only on the energy state
of the nuclide2. The decay rate is independent of the history of the
nucleus3. The decay rate is independent of pressure,
temperature and chemical composition• The timing of radioactive decay is impossible to predict
but we can predict the probability of its decay in a giventime interval
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Radioactive Decay
• The probability of decay in someinfinitesimally small time interval, dt, is λdt,where λ is the decay constant for theparticular isotope
• The rate of decay among some number, N, ofnuclides is thereforedN / dt = - λN [eq. 1]
• The minus sign indicates that N decreasesover time.• Essentially all significant equations of
radiogenic isotope geochronology can be
derived from this expression.
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Types of Radioactive Decay
• Beta Decay• Positron Decay• Electron Capture Decay• Branched Decay• Alpha Decay
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Beta Decay• Beta decay is essentially the transformationof a neutron into a proton and an electron and
the subsequent expulsion of the electron fromthe nucleus as a negative beta particle.
• Beta decay can be written as an equation ofthe form 19 K40 -> 20 Ca 40 + β - + ν + Q
Where β- is the beta particle, ν is theantineutrino and Q stands for the maximumdecay energy.
_
_
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Positron Decay• Similar to Beta decay except that now a proton in thenucleus is transformed into a neutron, positron and
neutrino.• Only possible when the mass of the parent is greater
than that of the daughter by at least two electronmasses.
• Positron decay can be written as an equation of theform
9F18 ->
8O18 + β+ + ν + Q
Where β+ is the positron, ν is the neutrino and Q stands for the maximum decay energy.
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Positron VS Beta DecayThe atomic number of thedaughter isotope is decreased by1 while the neutron number isincreased by 1.
The atomic number of thedaughter isotope is increased by1 while the neutron number isdecreased by 1.
Therefore in both cases the parent and daughter isotopes have thesame mass number and therefore sit on an isobar.
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Electron Capture Decay
• Electron capture decay occurs when anucleus captures one of its extranuclearelectrons and in the process decreasesits proton number by one and increasesits neutron number by one.
• This results in the same relationshipbetween the parent and the daughterisotope as in positron decay wherebythey both occupy the same isobar.
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Alpha Emission
• Represents the spontaneous emission ofalpha particles from the nuclei ofradionuclides.
• Only available to nuclides of atomic number
of 58 (Cerium) or greater as well as a few oflow atomic number including He, Li and Be.• Alpha emission can be written as:
92 U238 -> 90 Th 234 + 2He 4 + Q
Where 2He 4 is the alpha particle and Q is the total alpha decayenergy
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Alpha Emission
A daughter isotope produced byalpha emission will notnecessarily be stable and canitself decay by either alphaemission, or beta emission orboth.
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Branched Decay• The difference in the atomic number of two stable
isobars is greater than one, ie two adjacent isobarscannot both be stable.
• Implication is that two stable isobars must be
separated by a radioactive isobar that can decay bydifferent mechanisms to produce either stable isobar.• Example
71 Lu176 decays to 72 Hf 176 via negative beta decay
72 Hf 176 decays to 70 Yb176 by positron decay orelectron capture.
Branched decay scheme for
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Branched decay scheme for A=38 isobar
Branched decay scheme for
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Branched decay scheme for A=132 isobar
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Radiogenic Isotope
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Radiogenic IsotopeGeochemistry
• Can be used in two important ways1. Tracer Studies
Makes use of the differences in the ratio ofthe radiogenic daughter isotope to otherisotopes of the elementCan make use of the differences in
radiogenic isotopes to look at EarthEvolution and the interaction anddifferentiation of different reservoirs
Radiogenic Isotope
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Radiogenic IsotopeGeochemistry
2. GeochronologyMakes use of the constancy of the rate ofradioactive decay
Since a radioactive nuclide decays to itsdaughter at a rate independent of everything,it is possible to determine time simply bydetermining how much of the nuclide hasdecayed.
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Radiogenic Isotope Systems
• The radiogenic isotope systems that are ofinterest in geology include the following• K-Ar• Ar-Ar• Fission Track• Cosmogenic Isotopes• Rb-Sr• Sm-Nd• Re-Os• U-Th-Pb• Lu-Hf
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Table of the elements
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Geochronology and Tracer
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Geochronology and TracerStudies
Isotopic variations between rocks and minerals due to1. Daughters produced in varying proportions resulting from
previous event of chemical fractionation
• 40 K → 40 Ar by radioactive decay
• Basalt → rhyolite by FX (a chemical fractionationprocess)
• Rhyolite has more K than basalt
• 40 K → more 40 Ar over time in rhyolite than in basalt
• 40 Ar/39 Ar ratio will be different in each2. Time: the longer 40 K → 40 Ar decay takes place, the greater
the difference between the basalt and rhyolite will be
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The Decay Constant• Over time the amount of the daughter (radiogenic) isotope in a
system increases and the amount of the parent (radioactive)isotope decreases as it decays away. If the rate of radioactivedecay is known we can use the increase in the amount ofradiogenic isotopes to measure time.
• The rate of decay of a radioactive (parent) isotope is directlyproportional to the number of atoms of that isotope that arepresent in a system, ie Equation 1 that we have seen previously. – dN/dt = - λN, [eq. 1] – where N = the number of parent atoms and λ is the decay
constant – The -ve sign means that the rate decreases over time
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Geologically Important Isotopes and their Decay Constants
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Using the Decay ConstantThe number of radiogenic daughter atoms (D*)
produced from the decay of the parent since date offormation of the sample is given by
D* = N o - N [eq. 2]Where D* is the number of daughter atoms
produced by decay of the parent atom and N o isthe number of original parent atoms
Therefore the total number of daughter atoms, D, in asample is given by
D = D o + D* [eq. 3]
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Using the Decay Constant
The two equations can be combined to give
D = D o + N o – N [eq. 4]
Generally, when rocks or minerals first form they contain agreater or lesser amount of the daughter atoms of a
particular isotope system, i.e., not all the daughter atomsthat we measure in a sample today were formed by
decay of the parent isotope since the rock first formed.
Dating of Rocks from
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Dating of Rocks fromRadioactive Decay
Recalling that-dN/dt = λN [eq. 1]
Integration of the above yields
N=N oe-λ t
[eq. 5]
We can substitute this into equation 4 to getD=D o + Ne λ t – N [eq. 6]
which simplifies toD=D o + N(e λ t – 1) [eq. 7]
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Plotting Geochron Data• There are two methods for graphically illustrating
geochron data• 1. The Isochron Technique
– Used when the decay scheme has one parentisotope decaying to a daughter isotope.
– Results in a straight line plot
• 2. The Concordia Diagram
– Used when more than one decay scheme results
in the formation of the daughter isotopes – Results in a curved diagram
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Preguntas?