# isotopes

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### Slide 1:

Foundations of a modern approach to measuring geological age ~1900: Becquerel & Curie discover radioactivity in U, Pu, Ra and ‘ionium’ (Th) Rutherford proposes 3 types of radioactivity: emits mass but no charge (4He nucleus) emits charge but no (observable) mass (electron or positron) emission has neither charge nor mass (high-frequency radiation) Rutherford notes/postulates two key properties of radioactivity: • Reactions are exothermic • Emission is independent of properties or environment of elements

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If rate of emission is invariant w/ time or setting, then radiation can serve as a clock: - dN/dt = N Constant of proportionality; now called ‘decay constant’ 1/ = ‘mean life ln2/ = ‘half life’ (a miracle of integration occurs) N = N0e-t For  and  radiation, nothing lasting is produced (at least, nothing detectable by 1900-era scientists). But  particles accumulate in a measurable way: Define ‘D’ as number of ‘daughter’ particles D = D0 + D* D* = N0 - N D = N0(1-e-t) + D0 = N (et-1) + D0

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Re-arrange decay equation to make time the dependant variable: ln {[ (D-D0) N ] +1}  t = Pick mineral with no structural He; D0 = 0 Radiation counting in lab Pick mineral w/ stoichiometric Parent element (e.g., UO2), so N depends only on mass With correct choice of sample, t depends only on D - the amount of He trapped in the mineral lattice

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Rutherford’s chronometer Pitchblende, or U ore, rich in UO2 U ~ 1.5x10-10 U 8 Time (yrs) moles He cc STP 1000 5x10-9 1x10-4 1 million 5x10-6 0.1 10 million 5x10-5 1.0 1 billion 5x10-3 100 1 gram of UO2 Found African pitchblende is ca. 500 million years old Problems: • Sensitivity and precision of manometric measurements • Reaction is not fully described. U weighs ca. 238 g/mol; 8 He nuclei only 32 g/mol. Where is the rest of the mass! • He is not well retained by crystals

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Breakthrough: Aston’s positive ray device

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Ions are passed through a magnetic field oriented orthogonal To their direction of motion. Ions are deflected with a radius of curvature set by the force balance between the magnetic field (qv x B) and the centripital force (mv2/r). That is, r = mv/(qB) If energy is of all ions is equal, this acts as a mass filter. High momentum (high mass) Low momentum (low mass))

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Intensity Strength of B field

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Finnigan Triton A modern thermal ionization mass spectrometer Ion source Collectors (faraday cups and/or electron multipliers) Momentum analyzer (electro magnet)

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Advances stemming from mass spectrometry • Precision improves from ca. ±1 % to ca. ±10-5 • Recognition of isotopes permits the definition of decay reactions Zprotons + Nneutrons = Amass  decay: Z + N (Z-2) + (N-2) + 4He +  + Q e.g., 238U 234Th + 4He;  = 1.55x10-10 147Sm 143Nd + 4He;  = 6.5x10-12 yr-1  decay: Z + N (Z+1) + (N-1) + e- +  + Q e.g., 87Rb 87Sr + e-;  = 1.42x10-11 yr-1  decay: Z + N (Z-1) + (N+1) + e+ +  + Q e.g., 18F 18O + e+;  = 3.3x103 yr-1 Most geological ‘chronometers’ depend on  and  decay e.g., 14C 14N + e-;  = 1.2x10-4 yr-1

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Mass spectrometry is best at measuring relative abundances of isotopes. This motivates an additional change to age-dating equations: D = Daughter (4He; 87Sr; 143Nd) N = Parent (238U; 87Rb; 147Sm) S = Stable (3He; 86Sr; 144Nd) The ‘stable’ nuclide is always a non-radioactive, non-radiogeneic isotope of the same element as the ‘Daughter’ nuclide. D = N (et - 1) + D0 D/S = N/S (et - 1) + D0/S This is the equation for a line in the ‘isochron’ plot Y-axis value X-axis value Y-intercept Slope

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D/S N/S D0/S m = et - 1 Measured composition of object Three strategies for use: • Measured objects known to have D0/S ~ 0 • Assume or infer D0/S from independent constraint • Define slope from two or more related objects, yielding both age (t) and D0/S as dependent variables. These objects must be of same age, have started life with identical D0/S, but differ significantly in N/S The anatomy of the isochron diagram

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A common example: the Rb-Sr chronometer applied to granite Isotopes of Sr: 84Sr: 0.56 % 86Sr: 9.87 % 87Sr: 7.04 % 88Sr: 82.53 % (all values approximate) Sr: typically a +2 cation; 1.13 Å ionic radius (like Ca: +2, 0.99 Å) Isotopes of Rb: 85Rb: Stable 87Rb: Radioactive: l = 1.42x10-11 yr-1;- decay 85Rb/87Rb in all substances from earth and moon assumed = 2.59265 Rb: typically a +1 cation; 1.48 Å ionic radius (like K; +1, 1.33 Å)

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Isotopes of Nd: 142Nd: 27.1 % 143Nd: 12.2 % 144Nd: 23.9 % 145Nd: 8.3 % 146Nd: 17.2 % (147Nd: 10.99 d half life) 148Nd: 5.7 % 150Nd 5.6 % (all values approximate) Isotopes of Sm: 144Sm: 3.1 % (146Sm: 108 yr half life) 147Sm: 15.0 % (1.06x1011 yr half life) 148Sm: 11.2 % 149Sm: 13.8 % 150Sm: 7.4 % (151Sm: 93 year half life) 152Sm 26.7 % 154Sm: 22.8 % (all values approximate) The Sm-Nd chronometer

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The ‘rare earth’ elements Normalized abundance Plagioclase Pyroxene Garnet

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A fragment of the chondritic meteorite, Allende

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A thin section of the chondritic meteorite, Allende

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"There is one independent check on the age of the solar system determined by radioactivity in meteorites. Detailed theoretical studies of the structure of the sun, using its known mass and reasonable assumptions about its composition, indicates that it has taken the sun about five billion years to attain its present observed radius and luminosity.” W. Fowler Comparison with a modern ‘Kelvinistic’ argument: Summary of typical stellar lifetimes, sizes and luminosities

### Slide 22:

14C decay: The basis of most ages for geologically young things 14C is produced in the atmosphere: 14N + n = 14C + p Cosmic-ray fast neutrons Undergoes beta-decay with a half-life of 5730 yrs: 14C = 14N + e-  = 1.209x10-4 yr-1 Age (yrs) = 19,035 x log (C/C0) [ or …’x log (Activity/Activity0)’] Key for application is assumption of a value of C0, which depends on 14C/12C ratio in atmosphere Real applications require correction for natural isotopic fractionation (e.g., during photosynthesis) and must consider variations in production rate with time and isotopic heterogeneity of surface carbon pools

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The ‘bomb spike’ Natural heterogeneity: 14C ‘ages’ of deep ocean water

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Variation in atmospheric 14C/12C through time due to natural processes ∆14C = (Ri/R0 -1)x1000 Where Ri = 14C/12C at time of interest R0 = 14C/12C of pre-1890 wood projected forward to 1950 (?!?&*!)

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Using 14C to reconstruct earthquake recurrence intervals

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The U-Pb system and the age of the Earth 238U = 206Pb + 8x4He  = 1.55125x10-10 (4.5 Ga half life) 235U = 207Pb + 7x4He  = 9.8485x10-10 (0.7 Ga half life) 204Pb is a stable isotope 238U/235U is (nearly) constant in nature = 137.88 206Pb 204Pb 207Pb 204Pb 207Pb0 204Pb 206Pb0 204Pb 238U 204Pb 235U 204Pb (et - 1) (et - 1) = + = + 207Pb 204Pb 207Pb0 204Pb 206Pb 204Pb 206Pb0 204Pb - - = 1 137.88 (et - 1) (et - 1)