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Ch.5. Isotope Geochemistry

Ch.5. Isotope Geochemistry. A Few Definitions Isotopes: iso (same) + tope (position) Elements having the same number of protons, but different neutrons Same elements with different mass 40 Ca, 42 Ca, 12 C, 13 C, 14 C, etc. Isotones: Iso (same) + tone (pitch? pressure?)

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Ch.5. Isotope Geochemistry

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  1. Ch.5. Isotope Geochemistry • A Few Definitions • Isotopes: • iso (same) + tope (position) • Elements having the same number of protons, but different neutrons • Same elements with different mass • 40Ca, 42Ca, 12C, 13C, 14C, etc. • Isotones: • Iso (same) + tone (pitch? pressure?) • Elements having the same number of neutrons, but different protons • 36S, 37Cl, 38Ar • Isobars: • Iso (same) + bar (weight or pressure) • Elements having the same number of the sum of neutrons and protons • Elements having the same mass • 40Ar, 40K, 40Ca

  2. Types of Isotopes           • Stable isotopes: 12C, 13C • Unstable isotopes: 14C, 235U, 238U • Radioactive isotopes: 14C, 235U, 238U • Radiogenic isotopes: 206Pb, 207Pb, 208U • Light isotopes: H, D, T, 12C, 13C • Heavy isotopes: 235U, 238U

  3. Radioactive Decay          • Definition: tranformingnuclii from that of one to the other by decaying (transition) neutrons or protons in it. • Decay reaction is usually irreversible in nature  Is there any exception? • P (parent)  D (daughter)

  4. Mode of Radioactive Decay          • b (negatron): • n  p + e • Z Z+1, N  N-1, A=no change • 40K --> 40Ca + β- • Positron • p  n + p (positron) • Z  Z-1, N N+1, A=no change • 18F --> 18O + β+ • Electron capture • p + e  n • Z  Z-1, N N+1, A=no change • 40K --> 40Ar + E.C. • a • Loss of 2p + 2n (4He) • Z  Z-2, NN-2, A A-4 • 222Rn --> 218Po + α.

  5. GeologicalApplication of Istopes • Radiogenic isotopes • Age dating • ellucidation of Geological history • Identifying origin of materials • Evaluation of epoch and provenance • Stable isotopes • Tracing the sources • Indication of the environment • Geothermometry • Hydrological application • Evaluation of mixing processes

  6. Absolute Age Dating (Geochronology) • Decay equation • For P  D • -d[P]/dt = λ[P] • [P] = [P]oexp(-λt) • [D]* = [P]o-[P] • [D]* = [P]o(1-exp(-λt)) • Half life • Time required to be [P]=[P]o/2 • t1/2 = ln(1/2)/λ = 0.693/λ

  7. Decay constants and half lives of natural radioactive nuclides P Mode l t1/2 Abund(%) D

  8. Age Dating • When Do =0 • [D]* = ([D]*+[P])(1-exp(-λt)) • t = ln(1+[D]*/[P])/λ • 14C • n + 14N -> 14C + p + e- • 14C -> 14N + β + ν+ Q- • t = (1/λ) ln(Ao/A) • K-Ar • d[40Ar]/dt = λAr[40K], • d[40Ca]/dt = λCa[40K]  d[40Ca]/dt = (λCa/λAr) d[40Ar]/dt • d[40K]/dt = -(d[40Ar]/dt + d[40Ca]/dt)  d[40Ar] = -λArd[40K]/(λAr+λCa) • [40Ar]-[40Ar]o = -λAr/(λAr+λCa)([40K]-[40K]o) • [40Ar] = λAr[40K](exp(λt)-1)//(λAr+λCa)

  9. Age Dating • When Do ≠0 • [D]t/[D]n=[D]o/[D]n+([P]/[D]n)(exp(λt)-1) • Rb-Sr • Sm-Nd • Os-Re • U-Pb

  10. Reequilibium age

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