15 isotopes- measuring geological age

7/27/2019 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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15 isotopes- measuring geological age

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