15 Isotopes- Measuring Geological Age
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Transcript of 15 Isotopes- Measuring Geological Age
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Foundations of a modern approach to measuringgeological 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, thenradiation can serve as a clock:
- dN/dt = N
Constant of proportionality;now called decay constant
1/= mean lifeln2/= 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 (et-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/ stoichiometricParent element (e.g., UO2), soN 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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Rutherfords chronometer
Pitchblende, or U ore, rich in UO2
U ~ 1.5x10-10
U 8
Time (yrs) moles He cc STP1000 5x10-9 1x10-41 million 5x10-6 0.110 million 5x10-5 1.01 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: Astons 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 TritonA 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- + + Qe.g., 87Rb 87Sr + e-; = 1.42x10-11 yr-1
decay: Z + N (Z-1) + (N+1) + e+ + + Qe.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 ofisotopes. This motivates an additional change to age-dating equations:
D = Daughter (4He; 87Sr; 143Nd)
N = Parent (238
U;87
Rb;147
Sm)S = Stable (3He; 86Sr; 144Nd)
The stable nuclide is always a non-radioactive, non-radiogeneicisotope of the same element as the Daughter nuclide.
D = N (et - 1) + D0
D/S = N/S (et - 1) + D0/S
This is the equation for a line in the isochron plot
Y-axis value
X-axis value
Y-interceptSlope
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D/S
N/S
D0/S
m = et - 1
Measured compositionof 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, yieldingboth age (t) and D0/S as dependent variables. These objectsmust be of same age, have started life with identical D
0/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 %88
Sr: 82.53 %(all values approximate)
Sr: typically a +2 cation; 1.13 ionic radius (like Ca: +2, 0.99 )
Isotopes of Rb:85Rb: Stable87Rb: 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 ionic radius (like K; +1, 1.33 )
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Isotopes of Nd:
142Nd: 27.1 %143Nd: 12.2 %144Nd: 23.9 %145Nd: 8.3 %146Nd: 17.2 %
(147
Nd: 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 %150
Sm: 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
Normaliz
edabundance
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 assumptionsabout its composition, indicates that it has taken the sun about five billion years to attain its present observedradius and luminosity.
W. Fowler
Comparison with a modern Kelvinistic argument:
Summary of typical stellar lifetimes, sizes and luminosities
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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 on14C/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/12Cthrough 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
238
U =206
Pb + 8x4
He = 1.55125x10-10
(4.5 Ga half life)235U = 207Pb + 7x4He = 9.8485x10-10 (0.7 Ga half life)
204Pb is a stable isotope238U/235U is (nearly) constant in nature = 137.88
206Pb204Pb
207Pb
204Pb
207Pb0
204Pb
206Pb0204Pb
238U204Pb
235U
204Pb
(et - 1)
(et - 1)
= +
= +
207Pb
204Pb
207Pb0
204Pb206Pb
204
Pb
206Pb0
204
Pb
-
-
=1
137.88
(et - 1)
(et - 1)
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QuickTime and aTIFF (LZW) decompressor
are needed to see this picture.
207Pb
204Pb
207Pb0
204Pb206Pb
204Pb
206Pb0
204Pb
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