Ch__5

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GEOL 1376, Historical Geology

Chapter 5Chapter 5 The numerical dating

of the EarthThe

GeologicColumn

andTime Scale

Absolute Geochronology

• Add numbers to the stratigraphic columnbased on fossils

• Based on the regular radioactive decay ofsome chemical elements

Isotopes

atoms of elements (same number ofprotons) with varying numbers ofneutrons

examplesexamples:235235U, U, 238238UU 8787Sr, Sr, 8686SrSr 1414C, C, 1212CC

RadioactivityHenri Becquerel: 1895

discovered radioactivity, accidentlyexposed photographic plates touranium salts.

Marie Curie:discovered radium, 3 million timesas active as uranium, can detectheat with ordinary thermometer,coined term radioactivity

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RadioactivityErnst Rutherford: 3 types of raysα = He nucleus, 2 p + 2 nβ = high energy electronsγ = similar to X-rays.

Boltwood: 1907Realized lead (Pb) and helium

(He) were the stable decayproducts of uranium (U) and thatdecay rate is constant.

Radioactivity

Isotopic datingRadioactive elements (parents) decay to non-

radioactive (stable) elements (daughters)

The rate at which this decay occurs is constant andknowable

Therefore, if we know the rate of decay and theamount present of parent and daughter we cancalculate how long this reaction has beenproceeding.

Requirements for isotopic dating

1) Closed system2) decay rate constant3) initial daughter concentration

known (zero is best)

Half life

The half life of a radioactiveisotope is defined as the timerequired for half of it to decayaway.

Figure 9.15

The radioactivedecay curve

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Fig. 9.15Fig. 9.15

Proportion ofParent Atoms

Remaining as aFunction of

Time

Radioactive decay

decay of parent atoms

growth of daughter atoms

Radioactive decay

# of half lives # of half lives

Geologically useful decay schemes

parent daughter half life (years)235U 207Pb 4.47 x 109

238U 206Pb 0.704 x 109

40K 40Ar 1.25 x 109

87Rb 87Sr 47 x 109

14C 14N 5730

Important decay systems for geology

238U 206Pb t1/2= 4.47 x 109 a 235U 207Pb t1/2= 0.704 x 109 a 232Th 208Pb t1/2= 14.0 x 109 a 40K 40Ar t1/2= 1.25 x 109 a 87Rb 87Sr t1/2= 48.8 x 109 a147Sm 144Nd t1/2= 106 x 109 a

Decay series

• Some daughter products arethemselves radioactive.

• Ultimately, a series of radioactivedaughters will lead to a final stabledaughter product.

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The decay of 238U

atom

ic n

umbe

r

neutron number

92

Hg

TlTl

Pb

Pb

Pb

BiBi

Po

Po

Po

At

Rn

Rn

Ra

Th

Th

Pa

UU

91

9089

8887

8685

8483

8281

80124 126 128 130 132 134 136 138 140 142 144 146

!

92238U" 82

206Pb+82

4He+ 6# -

The decay of 235U

neutron number

Tl

Pb

Pb

BiBi

Po

Po

At

At

Rn

Fr

Ra

Ac

Th

Th

Pa

U

124 126 128 130 132 134 136 138 140 142 144 146

!

92235U" 82

207Pb+72

4He+ 4# -

atom

ic n

umbe

r

92

91

9089

8887

86

8483

8281

80

85

The decay of 232Th

neutron number

Tl

Pb

Pb

Bi

Po

Po

Rn

Ra

Ra

Ac

Th

Th

124 126 128 130 132 134 136 138 140 142 144 146

!

90232Th" 82

208Pb+62

4He+ 4# -

atom

ic n

umbe

r

92

91

9089

8887

86

8483

8281

80

85

UniformitarianismThe present is the key to the past

—— James HuttonJames Hutton

natural laws do not change —however, rates and intensity ofprocesses may

The big assumption

The half-lives of radioactive isotopes are thesame as they were billions of years ago.

What if the rates have varied?

time

rateof

decay

What we think happened:What we think happened:

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What if the rates have varied?

time

rateof

decay

What we know didnWhat we know didn’’t happen:t happen:

Best initial D = 0

Two ways around this problem:

1) Choose minerals with no initial daughter

2) Use method that tells you initialconcentration of D and P.

Minerals with no initial daughter

Zircon: ZrSiO4

ion radius (Å)

Zr4+ 0.92

U4+ 1.08

Pb2+ 1.37

Minerals with no initial daughter

40K decays to 40Ar (a gas)

Many methods have been used to determine the age of the Earth

1) Bible: In 1664, Archbishop Usher of Dublin usedchronology of the Book of Genesis to calculate that theworld began on Oct. 26, 4004 B.C.

2) Salt in the Ocean: (ca. 1899) Assuming the oceansbegan as fresh water, the rate at which rivers aretransporting salts to the oceans would lead to presentsalinity in ~100 m.y.

Many methods have been used to determine the age of the Earth

3) Sediment Thickness: Assuming the rate of deposition isthe same today as in the past, the thickest sedimentarysequences (e.g., Grand Canyon) would have beendeposited in ~ 100 m.y.

4) Kelvin’s Calculation: (1870): Lord Kelvin calculatedthat the present geothermal gradient of ~30°C/km wouldresult in an initially molten earth cooled for 30 – 100 m.y.

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Flawed assumptions• Bible is not a science text or history book (nor

entirely self-consistent)

• Salt is precipitated in sedimentary formations• Both erosion and non-deposition are major parts of

the sedimentary record

• Radioactivity provides another heat source

The heat inside the Earth

The discovery of radioactivity at the turn of thecentury by Bequerel, Curie, and Rutherford not onlyprovided the source of the heat to override Kelvin’scalculations but provided the basis for all laterquantitative estimates of the ages of rocks.

Oldest rocks on EarthSlave Province, northern Canada

Zircons in a metamorphosed granite dated at 4.02Ga by the U-Pb method

Yilgarn block, western Australia

detrital zircons in a sandstone dated at 4.10 Ga byU-Pb method.

Several other regions dated at 3.8 Ga by various methodsincluding Minnesota, Wyoming, Greenland, South Africa,and Antarctica

Age of the Earth

While the oldest rocks yet found on Earth are 4 Ga(or even 4.1) we believe that the age of the Earthis approximately 4.6 Ga. However, it seems allrocks of the age 4.6 to 4.2 Ga have beendestroyed (in the rock cycle) or are presentlycovered by younger rocks.

Age of the EarthThis is based on the age of rocks brought back from

the Moon (4.4 Ga), and meteorites (4.6 Ga) whichare thought to be good representatives of the earlysolar system as well as more complicatedgeochemical modeling which suggests the presentchemical composition of the crust must haveevolved for > 4.5 Ga.

Double it and add 1number of number of number of D/Phalf-lives parents daughters

0 64 0 0

1 32 32 1

2 16 48 3

3 8 56 7

4 4 60 15

5 2 62 31

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Calculating the age of a mineral

What is the age of a mineral that has a D/P = 3if the half-life of the parent is 3 years (initialconcentration of D = 0) ?

Calculating the age of a mineral

What is the age of a mineral that has a D/P = 7if the half-life of the parent is 100 years(initial concentration of D = 0) ?

Calculating the age of a mineral

What is the age of a mineral that has a D/P = 15if the half-life of the parent is 15 millionyears (initial concentration of D = 0) ?

Calculating the age of a mineral

What is the half life of an isotope if the D/P = 3in a mineral whose age is 100 million years(known from other sources)?

Calculating the age of a mineral

What is the D/P in a mineral which is 280million years old if the half life of the parentis 40 million years?

The geologic timescaleand absolute ages

Isotopic dating of inter-bedded volcanicrocks allows assignment of an absoluteage for fossil transitions

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The geologic timescale

66 Ma

245 Ma

540 Ma

Other attempts to numerically date

Tree ringsVarvesGlacial ice coresDeep sea cores

Pater NostraLake Summer silt vs

winter clay

Chronology for last 12,000-20,000 years:correlation of varves where lakes freeze.

Tree RingsA. From

living treeB. From a house

C. From an old house

1850

1870

1900

What do isotopic ages really mean?

• most isotopic systems are notclosed above a certain temperature

• At high temperatures the daughteris lost to the outside environment

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ThermochronologyCl

osur

e te

mpe

ratu

re 500

400

300

200

100

0

(U+Th)/Hehbl

musbio

Kf

zircon

ap

apatite

hydrocarbon hydrocarbon windowwindow

Quantifying the Temperature-time evolution ofrocks based on diffusion and radioactivity

sphene

calcite

FT40Ar/39Ar

monazite

calcite

What do isotopic ages really mean?

The temperature at which thedaughters begin to be retained iscalled the closure temperature.

What do isotopic ages really mean?So, most isotopic ages do not

reflect the age of formation butrather the last time the rocks wasat its closure temperature(different for different elementsand different minerals)

It is very important to keep this inmind when interpreting isotopicage data.

The geologic timescaleand absolute ages

Isotopic dating of inter-beddedvolcanic rocks allows assignmentof an absolute age for fossiltransitions

What are we measuring in ametamorphic rock?

What is the closure temperature?

What is a metamorphic date?

C12

6 P + 6 NC14

6 P + 8 N

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In all cases must remember whatyou are dating and the limitations

of the procedures.

Carbon 14: special caseFirst described - 1949 - by LibbyHigh energy neutrons (n) from outer

space enter the upper atmosphere,hit a nitrogen atom (N) and theneutron gets stuck in the nucleusbut knocks out a proton.

N = 7p + 7n,after collision = 6p + 8n.

6p + 8n = 14C (carbon)

Carbon 14: special case14C created from a non-radioactive

element (nitrogen).

Decays to the same element fromwhich it originated (nitrogen).

How do we measure the ageof a sedimentary rock?

How do we measure the ageof a sedimentary rock?

Radioactive age dating +Radioactive age dating +cross-cutting relationshipscross-cutting relationships& superposition.& superposition.

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How old is the shale?How old is the shale?

How old is this sandstone?

What if there is a mineral in this sandstone that is

dated at 525 Ma?