Homework 2: Due Wednesday Geochronology

Transcription

1 EESC 2200 The Solid Earth System Homework 2: Due Wednesday Geochronology 29 Sep 08 Relative Age Absolute Age

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

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4 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, )

5 Half life.. Dating with Radioactive Decay

6 Sodium atom nuclide Z = 11 N = 12 A = 23 A Na Z Na ES 371: T. Plank Lecture 1

7 Oxygen 16 O 17 O 18 O Z = N = isotopes of oxygen ES 371: T. Plank Lecture 1

8 87 Rb --> 87 Sr p n n --> p + e 87 Rb --> 87 Sr + e 87 Rb --> 87 Sr + β Mev net nuclear reaction: ES 371: T. Plank Lecture 1

9 87 Rb --> 87 Sr + β Mev net nuclear reaction: n --> p + β + ν + γ beta particle neutrino gamma ray ES 371: T. Plank Lecture 1

10 1. Beta Decay 87 Sr β Z 87 Rb N n --> p + β + ν + γ ES 371: T. Plank Lecture 1

11 2. Positron Decay (or electron capture) β+ Z 40 K 40 Ar N p --> n + β + + ν + γ ES 371: T. Plank Lecture 1

12 2. Positron Decay (or electron capture) β+ Z 40 K 40 Ar e- from K shell N p + e - --> n + ν + γ ES 371: T. Plank Lecture 1

13 branching decay 40 Ca β Z 40 K 40 Ar N ES 371: T. Plank Lecture 1

14 beta decay - no change in mass 40 Ca β Z 40 K 40 Ar isobar N ES 371: T. Plank Lecture 1

15 3. Alpha Decay 2p+ 2n = 4 He Sm Z 143 Nd N A P --> A-4 D + α + γ Z Z-2 ES 371: T. Plank Lecture 1

16 4. Fission n 95 Zr 235 U 137 Cs ES 371: T. Plank Lecture 1

17 Nuclide chart and decay (protons) Blue: β - Red: β + or e.c. Either may undergo α-decay Z N (neutrons)

18 Stable nuclides represent lowest energy configuration for a given A = N + Z Z=N Valley of stability Z Lawrence Berkeley National Laboratory N

19 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

20 Forces that hold nuclei together are ~10 6 ev Forces required to remove an electron are ~ ev Chemical forces that hold molecules together are ~1 ev Nuclear reactions liberate much more energy than chemical reactions

21 Mass defects : atoms are not the sum of their parts Can we calculate the mass of an atom by adding together the masses of the subatomic particles? M proton = AMU (atomic mass units, 12 C = 12 AMU) M neutron = AMU M electron = AMU Let s take 56 Fe, which has 26 protons and electrons and 30 neutrons 26 x x x = AMU protons electrons neutrons However, the actual mass of 56 Fe is This is less than the mass obtained by adding protons and neutrons. There is a mass defect Δm. Δm = AMU -- if you add up the constituent parts, 56 Fe is underweight by about half of the mass of a proton or neutron

22 Mass and energy Why is the mass defect important? Mass is equivalent to energy. E = Mc 2, where c is the speed of light (~3.00 x 10 8 m/s) 1 AMU = the mass of 12 C/12 = MeV (1 MeV = x joule = x kcal) The mass defect of AMU corresponds to a release in energy in the formation of 56 Fe 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.

23 Mass defect and radioactive decay The product(s) of radioactive decay will show a smaller total mass than the parent. Mass of 40 K: AMU 40 Ca: AMU 40 Ar: AMU The energy release from the decay can be calculated by Einstein s equation: E = (Δm)c 2 For 40 K to 40 Ar: E = AMU x MeV/AMU =1.51 MeV per decay

24 Radioactive Decay Decay Rate N p dn p /dt = -λn p λ = "decay constant" N p Np i dn p = -λ dt N p 0 lnn p - lnn pi = -λt t ln(n p /N pi ) = -λt ES 371: T. Plank Lecture 5

25 ln(n p /N pi ) = -λt t 1/2 = half life, when N p /N pi = 1/2 t 1/2 = 0.693/λ 1.0 N p N pi t 1/2 2t1/2 3t 1/2 4t1/2 5t 1/2 87 Rb t 1/2 = 49 Ga 0.2 coin toss t (Ga) ES 371: T. Plank Lecture 5

26 Rule of Thumb: half-lives 1 50% 2 25% % % % 0.8 1t 1/2 2t1/2 N p 0.6 3t 1/2 4t1/2 N pi 0.4 5t 1/ t (Ga) not cats... ES 371: T. Plank Lecture 5

27 ln(n p /N pi ) = -λt N p = N pi e - λt N pi = N p + N d 87 Rbi = 87 Rb + 87 Sr Daughters! ES 371: T. Plank Lecture 5

28 ln(n p /N pi ) = -λt N p = N pi e - λt N pi = N p + N d 87 Rbi = 87 Rb + 87 Sr Daughters! ES 371: T. Plank Lecture 5

29 N pi = N p + N d ln(n p /N pi ) = -λt N p = N pi e - λt N d = N pi - N p N pi = N p e λ t N d = N p e λ t - Np N d = N p (e λ t -1) plus any initial daughters... ES 371: T. Plank Lecture 5

30 N pi = N p + N d ln(n p /N pi ) = -λt N p = N pi e - λt N d = N pi - N p N pi = N p e λ t N d = N p (e λ t -1) + N d i 87 Sr = 87 Sr i + 87 Rb(e λ t -1) ES 371: T. Plank Lecture 5

31 87Sr = 87 Sr i + 87 Rb (e λ t -1) measure ratios in mass spectrometer 86Sr is non-radiogenic, non-radioactive 87 Sr = 87 Sr i + 87 Rb (e λt -1) 86 Sr 86 Sr 86 Sr mass spectrometer... ES 371: T. Plank Lecture 5

32 heavy light TIMS Across Hall ES 371: T. Plank Lecture 5

33 87Sr = 87 Sr i + 87 Rb (e λ t -1) measure ratios in mass spectrometer 86Sr is non-radiogenic, non-radioactive 87 Sr = 87 Sr i + 87 Rb (e λt -1) 86 Sr 86 Sr 86 Sr initial?? ES 371: T. Plank Lecture 5

34 87Sr = 87 Sr i + 87 Rb (e λ t -1) measure ratios in mass spectrometer 86Sr is non-radiogenic, non-radioactive 87 Sr = 87 Sr i + 87 Rb (e λt -1) 86 Sr 86 Sr 86 Sr y = b + x m Isochron Equation ES 371: T. Plank Lecture 5

35 87Sr = 87 Sr i + 87 Rb (e λt -1) 86Sr 86Sr 86Sr 87Sr/ 86 Sr Slope = (e λt -1) rock 2 t = age rock 3 initial Sr ratio rock 1 87Rb/ 86 Sr ES 371: T. Plank Lecture 5

36 87Sr = 87 Sr i + 87 Rb (e λt -1) 86Sr 86Sr 86Sr 87Sr/ 86 Sr initial Sr t = 0 ratio rock 1 rock 2 rock 3 87Rb/ 86 Sr ES 371: T. Plank Lecture 5

37 87Sr = 87 Sr i + 87 Rb (e λt -1) 86Sr 86Sr 86Sr Slope = (e λt -1) 87Sr/ 86 Sr t = 100 Ma Isochron initial Sr ratio t = 0 rock 1 rock 2 rock 3 87Rb/ 86 Sr ES 371: T. Plank Lecture 5

38 87Sr = 87 Sr i + 87 Rb (e λt -1) 86Sr 86Sr 86Sr Slope = (e λt -1) t = age 87Sr/ 86 Sr Isochron initial Sr ratio t = 0 rock 1 rock 2 rock 3 87Rb/ 86 Sr ES 371: T. Plank Lecture 5

39 Rb-Sr dating of a meteorite

40 87Sr = 87 Sr i + 87 Rb (e λt -1) 86Sr 86Sr 86Sr 87Sr/ 86 Sr initial Sr t = 0 ratio min 1 min 2 min 3 87Rb/ 86 Sr ES 371: T. Plank Lecture 5

41 hi Rb/Sr KAlSi 3 O 8 K-feldspar lo Rb/Sr CaAl 2 Si 2 O 8 plag. feld. ES 371: T. Plank Lecture 5

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43 U-Th-Pb 238 U 206 Pb + (α's +β's) 235 U 207 Pb + (α's +β's) 232 Th 208 Pb + (α's +β's) t 1/2 4.5 Ga 0.7 Ga 14 Ga half lives relevant? ES 371: T. Plank Lecture 6

44 N d = N p (e λ t -1) t 1/2 206 Pb* = 238 U(e λ t -1) 207 Pb* = 235 U(e λ t -1) 208 Pb* = 232 Th(e λ t -1) 4.5 Ga 0.7 Ga 14 Ga * = radiogenic ES 371: T. Plank Lecture 6

45 Concordia 206 Pb* = 238 U(e λ t -1) 207 Pb* = 235 U(e λ t -1) * = radiogenic Pb only which materials best? ES 371: T. Plank Lecture 6

46 Zircons ZrSiO 4 Zr(4+) = 0.08 nm U(4+) = nm Pb(2+) = nm 206 Pb* = 238 U(e λ t -1) virtually all Pb is radiogenic 207Pb* = 235 U(e λ t -1) ES 371: T. Plank Lecture 9

47 Concordia Curve Pb/ 238 U 2.0 Age (Ga) Pb/ 235 U curved shape? ES 371: T. Plank Lecture 6

48 Oldest Rocks on Earth Slave Craton Acasta Gneiss ES 371: T. Plank Lecture 9

49 Concordia Curve Age (Ga) Oldest Rock Pb/ 238 U 1.0 zircons in Acasta Gneiss 207 Pb/ 235 U ( Ga) Bowring & Williams, 1999 ES 371: T. Plank Lecture 9

50 oldest zircon! Ga Yilgarn craton, Australia (Jack Hills) ES 371: T. Plank Lecture 9

51 oldest bit of a zircon! ES 371: T. Plank Lecture 9

52 Oldest Zircon Fragment (4.404 Ga) Wilde, 2001, Nature ES 371: T. Plank Lecture 9

53 4.567 Ga Amelin, 2002 ES 371: T. Plank Lecture 6

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55 ICS INTERNATIONAL STRATIGRAPHIC CHART International Commission on Stratigraphy Eonothem Eon P h a n e r o z o i c Erathem Era System Period Quaternary * M e s o z o i c C e n o z o i c Cretaceous Paleogene Neogene * proposed by ICS Series Epoch Holocene Pleistocene Pliocene Miocene Oligocene Eocene Paleocene Upper Lower Stage Age Upper Middle Lower Gelasian Piacenzian Zanclean Messinian Tortonian Serravallian Langhian Burdigalian Aquitanian Chattian Rupelian Priabonian Bartonian Lutetian Ypresian Thanetian Selandian Danian Maastrichtian Campanian Santonian Coniacian Turonian Cenomanian Albian Aptian Barremian Hauterivian Valanginian Berriasian Age Ma ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±4.0 GSSP Eonothem Eon Erathem Era System P h a n e r o z o i c Period P a l e o z o i c M e s o z o i c Carboniferous Permian Triassic Jurassic Upper Middle Lower Upper Middle Lower Lopingian Guadalupian Cisuralian Series Epoch Upper Middle Lower Upper Middle Lower Stage Age Age Ma ±4.0 Tithonian ±4.0 Kimmeridgian ±4.0 Oxfordian ±4.0 Callovian ±4.0 Bathonian ±3.5 Bajocian ±3.0 Aalenian ±2.0 Toarcian ±1.5 Pliensbachian ±1.5 Sinemurian ±1.0 Hettangian ±0.6 Rhaetian ±1.5 Norian ±2.0 Carnian ±2.0 Ladinian ±2.0 Anisian ±1.5 Olenekian ±0.7 Induan ±0.4 Changhsingian ±0.7 Wuchiapingian ±0.7 Capitanian ±0.7 Wordian ±0.7 Roadian ±0.7 Kungurian ±0.7 Artinskian ±0.7 Sakmarian ±0.8 Asselian ±0.8 Gzhelian ±0.9 Kasimovian ±1.0 Moscovian ±1.1 Bashkirian ±1.3 Serpukhovian ±1.6 Visean ±2.1 Tournaisian ±2.5 GSSP Eonothem Eon Erathem Era ±2.5 Famennian Upper ±2.6 Frasnian ±2.6 Givetian Middle ±2.7 Eifelian ±2.7 Emsian ±2.8 Lower Pragian ±2.8 Lochkovian ±2.8 Pridoli ±2.7 Ludfordian Ludlow ±2.6 Gorstian ±2.5 Homerian Wenlock ±2.4 Sheinwoodian ±2.3 Telychian ±1.9 Llandovery Aeronian ±1.8 Rhuddanian ±1.5 Hirnantian ±1.5 Upper Stage ±1.6 Stage ±1.6 Darriwilian Middle ±1.6 Stage ±1.6 Stage 2 Lower ±1.7 Tremadocian ±1.7 Stage 10 ~ * Furongian Stage 9 ~ * Paibian ± 2.0 Stage 7 ~ * Series 3 Stage 6 ~ * Stage 5 ~ * Stage 4 Series 2 ~ * Stage 3 ~ * Stage 2 Series 1 ~ * Stage ±1.0 This chart was drafted by Gabi Ogg. Intra Cambrian unit ages with * are informal, and awaiting ratified definitions. Copyright 2006 International Commission on Stratigraphy P h a n e r o z o i c P a l e o z o i c System Period Devonian Silurian Cambrian Ordovician Series Epoch Stage Age Age Ma GSSP P r e c a m b r i a n Eonothem Eon Archean Proterozoic Erathem Era Pennsylvanian Mississippian Neoproterozoic Mesoproterozoic Paleoproterozoic Neoarchean Mesoarchean Paleoarchean Eoarchean System Period Ediacaran Cryogenian Tonian Stenian Ectasian Calymmian Statherian Orosirian Rhyacian Siderian Lower limit is not defined Age Ma 542 ~ GSSP GSSA Subdivisions of the global geologic record are formally defined by their lower boundary. Each unit of the Phanerozoic (~542 Ma to Present) and the base of Ediacaran are defined by a basal Global Standard Section and Point (GSSP ), whereas Precambrian units are formally subdivided by absolute age (Global Standard Stratigraphic Age, GSSA). Details of each GSSP are posted on the ICS website ( International chronostratigraphic units, rank, names and formal status are approved by the International Commission on Stratigraphy (ICS) and ratified by the International Union of Geological Sciences (IUGS). Numerical ages of the unit boundaries in the Phanerozoic are subject to revision. Some stages within the Ordovician and Cambrian will be formally named upon international agreement on their GSSP limits. Most sub-series boundaries (e.g., Middle and Upper Aptian) are not formally defined. Colors are according to the Commission for the Geological Map of the World ( The listed numerical ages are from 'A Geologic Time Scale 2004', by F.M. Gradstein, J.G. Ogg, A.G. Smith, et al. (2004; Cambridge University Press).

56 Tuff Anisian Tuff ~241 Ma Ladinian