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

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 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 - ND = N0(1-e-t) + D0 = N (et-1) + D0

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), soN depends only on mass

With correct choice of sample, t depends only on D - the amount of He trapped in the mineral lattice

Rutherford’s chronometer

Pitchblende, or U ore, rich in UO2

U ~ 1.5x10-10

U 8

Time (yrs) moles He cc STP1000 5x10-9 1x10-4

1 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

Breakthrough: Aston’s positive ray device

Ions are passed through a magnetic field oriented orthogonalTo 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))

Intensity

Strength of B field

Finnigan TritonA modern thermal ionization mass spectrometer

Ion source

Collectors (faraday cupsand/or electron multipliers)

Momentum analyzer (electro magnet)

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

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-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

D/S

N/S

D0/S

m = et - 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

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: 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 Å ionic radius (like K; +1, 1.33 Å)

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

The ‘rare earth’ elements

Nor

mal

ized

abu

ndan

ce

Plagioclase

Pyroxene

Garnet

A fragment of the chondritic meteorite, Allende

A thin section of the chondritic meteorite, Allende

"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

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

The ‘bomb spike’

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

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 (?!?&*!)

Using 14C to reconstruct earthquakerecurrence intervals

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 isotope238U/235U is (nearly) constant in nature = 137.88

206Pb

204Pb

207Pb

204Pb

207Pb0

204Pb

206Pb0

204Pb

238U

204Pb

235U

204Pb

(et - 1)

(et - 1)

= +

= +

207Pb

204Pb

207Pb0

204Pb206Pb

204Pb

206Pb0

204Pb

-

-

=1

137.88

(et - 1)

(et - 1)

QuickTime™ and aTIFF (LZW) decompressor

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207Pb

204Pb

207Pb0

204Pb206Pb

204Pb

206Pb0

204Pb

-

-