lecture 5: ocean sediments - lamont-doherty earth ... · absolute vs. relative age ... • ocean...

EESC 2200The Solid Earth System

Geochronology29 Sep 08

Relative Age

Absolute Age

Homework 2:Due Wednesday

NY Times and Science, 26 September 2008, Jonathan O’Niel

Absolute vs. relative age

• Field and paleontological observations give us relative ages only (e.g., A is older than B)

• We want absolute ages (e.g., A is X million years old)

• Historical methods

• Biblical chronology (Ussher, 1650)

• Decline of the sea (De Maillet, 1748)

• Sediment accumulation (Walcott, 1893)

• Ocean salinity (Joly, 1899)

• Cooling of the earth (Kelvin, 1862-97)

Dating with Radioactive Decay

Half life…..

ES 371: T. Plank Lecture 1

Sodiumatom

23Na

nuclide

Z = 11

N = 12

A = 23

ANaZ 11


Oxygen

16O

Z =

N =

8 8 8

8 9 10

isotopes of oxygen

17O 18O


87Rb --> 87Sr

p

n

37

50

38

49

87Rb --> 87Sr + e

n --> p + e

87Rb --> 87Sr + β− + 0.273 Mev37 38

net nuclear reaction:


87Rb --> 87Sr + β− + 0.273 Mev37 38

n --> p + β− + ν + γ

beta particle

neutrino

gamma ray

net nuclear reaction:


Z

N

87Sr

87Rb

1. Beta Decay

β−

n --> p + β− + ν + γ


Z

N

2. Positron Decay (or electron capture)β+

40K

40Ar

p --> n + β+ + ν + γ


Z

N

2. Positron Decay (or electron capture)β+

40K

40Ar

p + e- --> n + ν + γ

e-fromKshell


Z

N

40K

40Ar

branching decay

40Ca β−


Z

N

40K

40Arisobar

40Ca β−

beta decay - no change in mass


Z

N

147Sm

3. Alpha Decay

143Nd

2p+2n

= 4He2

AP --> A-4D + α + γZ Z-2


4. Fission

235U

n 95Zr

137Cs

Nuclide chartand decay

Z

N

• Blue: β-

• Red: β+ or e.c.

• Either may undergo α-decay

(neutrons)

(protons)

N

ZLawrence Berkeley National Laboratory

Z=N

Stable nuclides represent lowest energy configuration for a given A = N + Z

Valley o

f stabi

lity

Why do some nuclei decay?

• A nucleus decays because it is unstable

• It may be energetically favorable for a nucleus to decay

• Why?

• Since energy is liberated, decay yields a lower energy state

• Forces that hold nuclei together are ~106 eV

• Forces required to remove an electron are ~10-100 eV

• Chemical forces that hold molecules together are ~1 eV

• Nuclear reactions liberate much more energy than chemical reactions

Can we calculate the mass of an atom by adding together the masses of the subatomic particles?

Mproton = 1.00727638 AMU (atomic mass units, 12C = 12 AMU)Mneutron = 1.00866491 AMUMelectron = 0.000548579867 AMU

Let’s take 56Fe, which has 26 protons and electrons and 30 neutrons

26 x 1.00727638 + 26 x 0.00054857 + 30 x 1.00866491 = 56.463396 AMU protons electrons neutrons

However, the actual mass of 56Fe is 55.934942

This is less than the mass obtained by adding protons and neutrons. There is a “mass defect” Δm.

Δm = 0.52845 AMU -- if you add up the constituent parts, 56Fe is “underweight” by about half of the mass of a proton or neutron

“Mass defects”: atoms are not the sum of their parts

Why is the “mass defect” important? Mass is equivalent to energy.

E = Mc2, where c is the speed of light (~3.00 x 108 m/s)

1 AMU = the mass of 12C/12 = 931.5 MeV

(1 MeV = 1.602 x 10-13 joule = 3.827 x 10-23 kcal)

The mass defect of 0.52845 AMU corresponds to a release in energy in the formation of 56Fe compared to the sum of the masses of the building blocks (i.e. protons, neutrons, and electrons).

This is known as the “binding energy” of a nuclide.

Lower mass means a lower energy state in the nucleus; a lower energy state is more stable.

Mass and energy

Mass defect and radioactive decay

The product(s) of radioactive decay will show a smaller total mass than the parent.

Mass of 40K: 39.96400 AMU40Ca: 39.96260 AMU40Ar: 39.96238 AMU

The energy release from the decay can be calculated by Einstein’s equation:

E = (Δm)c2

For 40K to 40Ar: E = 0.00162 AMU x 931.5 MeV/AMU =1.51 MeV per decay


Radioactive Decay

Decay Rate ∝ Np dNp/dt = -λNp

λ = "decay constant"

dNp

Np

= -λ dt∫ ∫Npi

Np

0

t

lnNp - lnNpi = -λt

ln(Np/Npi) = -λt


t1/2 = half life, when Np/Npi = 1/2

t1/2 = 0.693/λ

30020010000.0

0.2

0.4

0.6

0.8

1.0

t (Ga)

NpNpi

87Rb

t1/2 = 49 Ga

1t1/22t1/2

3t1/24t1/2

5t1/2

ln(Np/Npi) = -λt

coin toss


30020010000.0

0.2

0.4

0.6

0.8

1.0

t (Ga)

NpNpi

1t1/22t1/2

3t1/24t1/2

5t1/2

Rule of Thumb: 5 half-lives

not cats...

1 50%2 25%3 12.5%4 6.25%5 3.125%


Np = Npi e-λt

ln(Np/Npi) = -λt

Npi = Np + Nd

87Rbi = 87Rb + 87Sr

Daughters!


Np = Npi e-λt

ln(Np/Npi) = -λt

Npi = Np + Nd

Nd = Np(eλt-1)

Npi = Np eλtNd = Npi - Np

Nd = Npeλt - Np

plus any initial daughters...


Np = Npi e-λt

ln(Np/Npi) = -λt

Npi = Np + Nd

87Sr = 87Sri + 87Rb(eλt-1)

Nd = Np(eλt-1) + Ndi

Npi = Np eλtNd = Npi - Np


86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb (eλt-1)

87Sr = 87Sri + 87Rb (eλt-1)

measure ratios in mass spectrometer

86Sr is non-radiogenic, non-radioactive

mass spectrometer...


TIMS Across Hall

light

heavy


86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb (eλt-1)

87Sr = 87Sri + 87Rb (eλt-1)



initial??


86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb (eλt-1)

y = b + x m

87Sr = 87Sri + 87Rb (eλt-1)

Isochron Equation




86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb(eλt-1)

87Rb/86Sr

87Sr/86Sr

Slope = (eλt-1)

initial Sr ratio

rock 2

rock 1

rock 3

t = age


86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb(eλt-1)

87Rb/86Sr

87Sr/86Sr

t = 0initial Sr ratio rock 1 rock 3rock 2


rock 1 rock 3rock 2

86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb(eλt-1)

87Rb/86Sr

87Sr/86Sr

Slope = (eλt-1)

Isochron

t = 0initial Sr ratio

t = 100 Ma


rock 1 rock 3rock 2

86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb(eλt-1)

87Rb/86Sr

87Sr/86Sr

Slope = (eλt-1)

Isochron

t = 0initial Sr ratio

t = 0

t = age

Rb-Sr dating of a meteorite


86Sr 86Sr 86Sr

87Sr = 87Sri + 87Rb(eλt-1)

87Rb/86Sr

87Sr/86Sr

t = 0initial Sr ratio min 1 min 3min 2


hiRb/SrKAlSi3O8

loRb/Sr

CaAl2Si2O8K-feldsparplag. feld.


U-Th-Pb

238U 206Pb + (α's +β's)

235U 207Pb + (α's +β's)

232Th 208Pb + (α's +β's)

t1/2

4.5 Ga

0.7 Ga

14 Ga

half lives relevant?


206Pb* = 238U(eλt -1)

207Pb* = 235U(eλt -1)

208Pb* = 232Th(eλt -1)

t1/2

4.5 Ga

0.7 Ga

14 Ga

* = radiogenic

Nd = Np(eλt-1)


206Pb* = 238U(eλt -1)

207Pb* = 235U(eλt -1)

* = radiogenic Pb only

Concordia

which materials best?


Zircons ZrSiO4

206Pb* = 238U(eλt -1)

207Pb* = 235U(eλt -1)

Zr(4+) = 0.08 nmU(4+) = 0.093 nmPb(2+) = 0.132 nm

• virtually all Pb is radiogenic


1.0

2.0

3.0

3.5

Age (Ga)

Concordia Curve

207Pb/235U

206Pb/238U

curved shape?


Oldest Rocks on EarthSlave Craton

Acasta Gneiss


1.0

2.0

3.0

4.0Age (Ga)

Concordia Curve

207Pb/235U

206Pb/238U

4.5

zircons inAcasta Gneiss

(4.00 - 4.03 Ga)Bowring & Williams, 1999

Oldest Rock


oldest zircon!

Yilgarn craton, Australia (Jack Hills)

4.34 - 4.44 Ga


oldest bit of a zircon!


Oldest Zircon Fragment

(4.404 Ga)

Wilde, 2001, Nature

ES 371: T. Plank Lecture 6Amelin, 2002

4.567 Ga

Famennian

Givetian

Eifelian

Lochkovian

Pragian

Frasnian

Emsian

Ludfordian

Gorstian

Homerian

Sheinwoodian

Telychian

Aeronian

Rhuddanian

P h

a n

e r

o z

o i c

P a

l e

o z o

i c

Pridoli

Ludlow

Wenlock

Llandovery

Upper

Middle

Lower

Devonia

n

411.2 ±2.8

416.0 ±2.8

422.9 ±2.5

428.2 ±2.3

Lopingian

Guadalupian

Cisuralian

Upper

Upper

Middle

Middle

Lower

Lower

Upper

Upper

Middle

Middle

Lower

Lower

P h

a n

e r

o z

o i c

P a

l e

o z o

i c

M e

s o

z o

i c

Carb

onifero

us

Perm

ian

Jura

ssic

Triassic

150.8 ±4.0

155.7 ±4.0

161.2 ±4.0

164.7 ±4.0

167.7 ±3.5

171.6 ±3.0

175.6 ±2.0

183.0 ±1.5

189.6 ±1.5

196.5 ±1.0

199.6 ±0.6

203.6 ±1.5

216.5 ±2.0

228.0 ±2.0

237.0 ±2.0

245.0 ±1.5

249.7 ±0.7

251.0 ±0.4

318.1 ±1.3

260.4 ±0.7

253.8 ±0.7

265.8 ±0.7

268.0 ±0.7

270.6 ±0.7

275.6 ±0.7

284.4 ±0.7

294.6 ±0.8

299.0 ±0.8

303.9 ±0.9

306.5 ±1.0

311.7 ±1.1

Tithonian

Kimmeridgian

Oxfordian

Callovian

Bajocian

Bathonian

Aalenian

Toarcian

Pliensbachian

Sinemurian

Hettangian

Rhaetian

Norian

Carnian

Ladinian

Anisian

Olenekian

Induan

Changhsingian

Wuchiapingian

Capitanian

Wordian

Roadian

Kungurian

Artinskian

Sakmarian

Asselian

Gzhelian

Kasimovian

Moscovian

Bashkirian

Serpukhovian

Visean

Tournaisian

Pe

nn

-sylv

an

ian

Mis

sis

-sip

pia

n

359.2 ±2.5

345.3 ±2.1

326.4 ±1.6

374.5 ±2.6

385.3 ±2.6

391.8 ±2.7

397.5 ±2.7

407.0 ±2.8

443.7 ±1.5

436.0 ±1.9

439.0 ±1.8

418.7 ±2.7

Ediacaran

Cryogenian

Tonian

Stenian

Ectasian

Calymmian

Statherian

Orosirian

Rhyacian

Siderian

Neo-

proterozoic

Neoarchean

Mesoarchean

Paleoarchean

Eoarchean

Meso-

proterozoic

Paleo-

proterozoic

Arc

hean

Pro

tero

zoic

P r

e c

a m

b r

i a

n

~630

850

1000

1200

1400

1600

1800

2050

2300

2500

2800

3200

3600

Upper

Middle

Lower

Selandian

Tortonian

Serravallian

Langhian

Burdigalian

Aquitanian

Ypresian

Chattian

Rupelian

Priabonian

Danian

Thanetian

Bartonian

Lutetian

Campanian

Santonian

Turonian

Coniacian

Albian

Aptian

Berriasian

Barremian

Valanginian

Hauterivian

Maastrichtian

Cenomanian

Piacenzian

Messinian

Zanclean

Gelasian

P h

a n

e r

o z

o i c C

e n

o z

o i c

M e

s o

z o

i c

1.806

0.126

0.781

2.588

5.332

7.246

11.608

13.65

15.97

20.43

70.6 ±0.6

65.5 ±0.3

83.5 ±0.7

85.8 ±0.7

89.3 ±1.0

93.5 ±0.8

40.4 ±0.2

37.2 ±0.1

33.9 ±0.1

28.4 ±0.1

23.03

48.6 ±0.2

55.8 ±0.2

58.7 ±0.2

61.7 ±0.2

99.6 ±0.9

112.0 ±1.0

125.0 ±1.0

130.0 ±1.5

136.4 ±2.0

140.2 ±3.0

145.5 ±4.0

Cre

taceous

Pale

ogene

Neogene

Syste

mP

eriod

Eonoth

em

Eon

Era

them

Era

Sta

ge

Age

Age

Ma

GS

SP

Epoch

Series

Eonoth

em

Eon

Era

them

Era

Syste

m

Sta

ge

Age

Age

Ma

GS

SP

Epoch

Series

Period

Eonoth

em

Eon

Era

them

Era

Age

Ma

GS

SP

GS

SA

Syste

mP

eriod

Eonoth

em

Eon

Era

Sta

ge

Age

Age

Ma

GS

SP

Epoch

Series

Period

3.600

Oligocene

Eocene

Paleocene

Pliocene

Miocene

Pleistocene

Upper

Lower

Holocene0.0118

INTERNATIONAL STRATIGRAPHIC CHARTInternational Commission on Stratigraphy

421.3 ±2.6

426.2 ±2.4

Tremadocian

Darriwilian

Hirnantian

Paibian

Upper

Middle

Lower

Series 3

Stage 3

Stage 2

Stage 1

Stage 5

Stage 6

Stage 7

Stage 9

Stage 10

Stage 2

Stage 3

Stage 5

Stage 6

Stage 4Series 2

Series 1

Furongian

Cam

brian

Ord

ovic

ian

~ 503.0 *

~ 506.5 *

~ 510.0 *

~ 517.0 *

~ 521.0 *

~ 534.6 *

460.9 ±1.6

471.8 ±1.6

488.3 ±1.7

~ 492.0 *

~ 496.0 *

501.0 ± 2.0

542.0 ±1.0

455.8 ±1.6

445.6 ±1.5

468.1 ±1.6

478.6 ±1.7

Lower limit is

not defined

Silu

rian

* proposed by ICS

Era

them

Syste

m

542359.2 ±2.5145.5 ±4.0

Qu

ate

rna

ry *

ICS

Copyright © 2006 International Commission on Stratigraphy

Subdivisions of the global geologic record are formally defined by their lower boundary. Each unitof the Phanerozoic (~542 Ma to Present) and thebase of Ediacaran are defined by a basal GlobalStandard Section and Point (GSSP ), whereasPrecambrian units are formally subdivided byabsolute age (Global Standard Stratigraphic Age,GSSA). Details of each GSSP are posted on theICS website (www.stratigraphy.org). International chronostratigraphic units, rank,names and formal status are approved by theInternational Commission on Stratigraphy (ICS)and ratified by the International Union of GeologicalSciences (IUGS). Numerical ages of the unit boundaries in thePhanerozoic are subject to revision. Some stageswithin the Ordovician and Cambrian will be formallynamed upon international agreement on their GSSPlimits. Most sub-Series boundaries (e.g., Middleand Upper Aptian) are not formally defined. Colors are according to the Commission for theGeological Map of the World (www.cgmw.org). The listed numerical ages are from 'A GeologicTime Scale 2004', by F.M. Gradstein, J.G. Ogg,A.G. Smith, et al. (2004; Cambridge University Press).

This chart was drafted by Gabi Ogg. Intra Cambrian unit ageswith * are informal, and awaiting ratified definitions.

Ladinian

Anisian

Tuff

Tuff

~241 Ma

lecture 5: ocean sediments - lamont-doherty earth ... · absolute vs. relative age ... • ocean...

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