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Isotopes

Isotopes. Reading: Winter, Chapter 9, pp. 167-180. 14. C. 6. Isotopes. Same Z, different A (variable # of neutrons) General notation for a nuclide:. 14. C. 6. Isotopes. Same Z, different A (variable # of neutrons) General notation for a nuclide:.

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Isotopes

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  1. Isotopes Reading: Winter, Chapter 9, pp. 167-180

  2. 14 C 6 Isotopes Same Z, different A (variable # of neutrons) General notation for a nuclide:

  3. 14 C 6 Isotopes Same Z, different A (variable # of neutrons) General notation for a nuclide: As n varies  different isotopes of an element 12C 13C 14C

  4. Stable Isotopes • Stable: last ~ forever • Chemical fractionation is impossible • Mass fractionation is the only discrimination possible

  5. Oxygen Isotopes 16O 99.756% of natural oxygen 17O 0.039% “ 18O 0.205% “ Concentrations expressed by reference to a standard International standard for O isotopes = standard mean ocean water (SMOW)

  6. - 18 16 18 16 ( O/ O) ( O/ O) sample SMOW x 1000 18 16 ( O/ O) SMOW 18O and 16O are the commonly used isotopes and their ratio is expressed as d: d (18O/16O) = eq 9-10 result expressed in per mille (‰) What is d of SMOW?? What is d for meteoric water?

  7. - 18 16 18 16 ( O/ O) ( O/ O) vapor SMOW x 1000 18 16 ( O/ O) SMOW 18 16 ( O/ O) 18 16 ( O/ O) SMOW Vapor What is d for meteoric water? Evaporation seawater  water vapor (clouds) • Light isotope enriched in vapor > liquid • Efficient, since D mass = 1/8 total mass d = therefore < thus dclouds is (-)

  8. Relationship between d(18O/16O) and mean annual temperature for meteoric precipitation, after Dansgaard (1964).Tellus, 16, 436-468.

  9. Stable isotopes are useful in assessing relative contribution of various reservoirs, each with a distinctive isotopic signature • O and H isotopes • Juvenile vs. meteoric vs. brine water • d18O for mantle rocks  surface-reworked sediments • Evaluate contamination of mantle-derived magmas by crustal sediments

  10. Radioactive Isotopes • Unstable isotopes decay to other nuclides • The rate of decay is constant, and not affected by P, T, X… • Parent nuclide = radioactive nuclide that decays • Daughter nuclide(s) are the radiogenic atomic products

  11. Isotopic variations between rocks, etc. due to: 1. Mass fractionation (as for stable isotopes) Only effective for light isotopes: H He C O S

  12. Isotopic variations between rocks, etc. due to: 1. Mass fractionation (as for stable isotopes) 2. Daughters produced in varying proportions resulting from previous event of chemical fractionation

  13. Isotopic variations between rocks, etc. due to: 1. Mass fractionation (as for stable isotopes) 2. Daughters produced in varying proportions resulting from previous event of chemical fractionation 40K 40Ar by radioactive decay Basalt  rhyolite by FX (a chemical fractionation process) Rhyolite has more K than basalt 40K  more 40Ar over time in rhyolite than in basalt 40Ar/39Ar ratio will be different in each

  14. Isotopic variations between rocks, etc. due to: 1. Mass fractionation (as for stable isotopes) 2. Daughters produced in varying proportions resulting from previous event of chemical fractionation 3. Time The longer 40K  40Ar decay takes place, the greater the difference between the basalt and rhyolite will be

  15. dN dN - µ - l N or = N dt dt Radioactive Decay The Law of Radioactive Decay eq. 9-11 1 ½ ¼ # parent atoms time 

  16. D = Nelt - N= N(elt -1) eq 9-14 age of a sample (t) if we know: D the amount of the daughter nuclide produced N the amount of the original parent nuclide remaining l the decay constant for the system in question

  17. The K-Ar System 40K  either 40Ca or 40Ar • 40Ca is common. Cannot distinguish radiogenic 40Ca from non-radiogenic 40Ca • 40Ar is an inert gas which can be trapped in many solid phases as it forms in them

  18. l æ ö e ç ÷ è ø l The appropriate decay equation is: eq 9-16 40Ar = 40Aro + 40K(e-lt -1) Where le = 0.581 x 10-10 a-1 (proton capture) and l = 5.543 x 10-10 a-1 (whole process)

  19. Blocking temperatures for various minerals differ • 40Ar-39Ar technique grew from this discovery

  20. Sr-Rb System • 87Rb 87Sr + a beta particle (l = 1.42 x 10-11 a-1) • Rb behaves like K  micas and alkali feldspar • Sr behaves like Ca  plagioclase and apatite (but not clinopyroxene) • 88Sr : 87Sr : 86Sr : 84Sr ave. sample = 10 : 0.7 : 1 : 0.07 • 86Sr is a stable isotope, and not created by breakdown of any other parent

  21. Isochron Technique Requires 3 or more cogenetic samples with a range of Rb/Sr • Could be: • 3 cogenetic rocks derived from a single source by partial melting, FX, etc. Figure 9-3. Change in the concentration of Rb and Sr in the melt derived by progressive batch melting of a basaltic rock consisting of plagioclase, augite, and olivine. From Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

  22. Isochron Technique Requires 3 or more cogenetic samples with a range of Rb/Sr • Could be: • 3 cogenetic rocks derived from a single source by partial melting, FX, etc. • 3 coexisting minerals with different K/Ca ratios in a single rock

  23. Recast age equation by dividing through by stable 86Sr 87Sr/86Sr = (87Sr/86Sr)o + (87Rb/86Sr)(elt -1) eq 9-17 l = 1.4 x 10-11 a-1 For values of lt less than 0.1: elt-1 lt Thus eq. 9-15 for t < 70 Ga (!!) reduces to: eq 9-18 87Sr/86Sr = (87Sr/86Sr)o + (87Rb/86Sr)lt y = b + x m = equation for a line in 87Sr/86Sr vs. 87Rb/86Sr plot

  24. ( ) 87Sr 86Sr o 87Sr 87Rb 86Sr 86Sr Begin with 3 rocks plotting at a b c at time to to a b c

  25. t1 c1 b1 a1 ( ) 87Sr to 86Sr a o b c 87Sr 87Rb 86Sr 86Sr After some time increment (t0t1) each sample loses some 87Rb and gains an equivalent amount of 87Sr

  26. t2 c2 t1 b2 c1 ( ) a2 b1 87Sr 86Sr a1 o to a b c 87Rb 87Sr 86Sr 86Sr At time t2 each rock system has evolved  new line Again still linear and steeper line

  27. Isochron technique produces 2 valuable things: • 1. The age of the rocks (from the slope = lt) • 2. (87Sr/86Sr)o= the initial value of 87Sr/86Sr Figure 9-9.Rb-Sr isochron for the Eagle Peak Pluton, central Sierra Nevada Batholith, California, USA. Filled circles are whole-rock analyses, open circles are hornblende separates. The regression equation for the data is also given.After Hill et al. (1988). Amer. J. Sci., 288-A, 213-241.

  28. Figure 9-13. Estimated Rb and Sr isotopic evolution of the Earth’s upper mantle, assuming a large-scale melting event producing granitic-type continental rocks at 3.0 Ga b.p After Wilson (1989). Igneous Petrogenesis. Unwin Hyman/Kluwer.

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