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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
2
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
3
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.
4
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:
5
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.
6
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
7
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
8
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
9
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
10
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.
11
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?