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 ( 4 He 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: Constant of proportionality; now called ‘decay constant’ - dN/dt =  N 1/  ln 2/  = ‘mean life = ‘half life’

(a miracle of integration occurs)

N = N 0 e  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 = D 0 + D* D* = N 0 - N D = N 0 (1-e  t ) + D 0 = N (e  t -1) + D 0

Re-arrange decay equation to make time the dependant variable: Pick mineral with no structural He; D 0 = 0 t = ln {[ (D-D 0 ) N  ] +1 } Radiation counting in lab Pick mineral w/ stoichiometric Parent element (e.g., UO 2 ), 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

Rutherford’s chronometer  U ~ 1.5x10

-10 U 8  Pitchblende, or U ore, rich in UO 2 Time (yrs) 1000 1 million 10 million 1 billion 1 gram of UO 2 moles He 5x10 -9 5x10 -6 5x10 -5 5x10 -3 cc STP 1x10 -4 0.1

1.0

100 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 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 (mv 2 /r). That is, r = mv/(qB) Low momentum (low mass)) High momentum (high mass) If energy is of all ions is equal, this acts as a mass filter.

Intensity Strength of B field

Finnigan Triton

A modern thermal ionization mass spectrometer

Momentum analyzer (electro magnet) Collectors (faraday cups and/or electron multipliers) Ion source

Advances stemming from mass spectrometry • Precision improves from ca. ± 1 % to ca. ± 10 -5 • Recognition of isotopes permits the definition of decay reactions Z protons + N neutrons = A mass  decay: Z + N (Z-2) + (N-2) + 4 He +  + Q e.g., 238 U 234 Th + 4 He;  = 1.55x10

-10 147 Sm 143 Nd + 4 He;  = 6.5x10

-12 yr -1   decay: Z + N (Z+1) + (N-1) + e e.g., 87 Rb 87 Sr + e ;  +  + Q = 1.42x10

-11 yr -1 e.g., 14 C 14 N + e ;  = 1.2x10

-4 yr -1   decay: Z + N (Z-1) + (N+1) + e + e.g., 18 F 18 O + e + ;  +  + Q = 3.3x10

3 yr -1 Most geological ‘chronometers’ depend on  and   decay

Mass spectrometry is best at measuring

relative

abundances of isotopes. This motivates an additional change to age-dating equations: D = Daughter ( 4 He; 87 Sr; 143 Nd) N = Parent ( 238 U; 87 Rb; 147 Sm) S = Stable ( 3 He; 86 Sr; 144 Nd) The ‘stable’ nuclide is always a non-radioactive, non-radiogeneic isotope of the same element as the ‘Daughter’ nuclide.

D = N (e  t - 1) + D 0 D/S = N/S (e  t - 1) + D 0 /S Y-axis value Slope Y-intercept X-axis value This is the equation for a line in the ‘isochron’ plot

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

A common example: the Rb-Sr chronometer applied to granite Isotopes of Sr: 84 Sr: 0.56 % 86 Sr: 9.87 % 87 Sr: 7.04 % 88 Sr: 82.53 %

(all values approximate)

Sr: typically a +2 cation; 1.13 Å ionic radius (like Ca: +2, 0.99 Å) Isotopes of Rb: 85 Rb: Stable 87 Rb: Radioactive: l = 1.42x10

-11 yr -1 ;  - decay 85 Rb/ 87 Rb 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: 142 Nd: 27.1 % 143 Nd: 12.2 % 144 Nd: 23.9 % 145 Nd: 8.3 % 146 Nd: 17.2 % ( 147 Nd: 10.99 d half life) 148 Nd: 5.7 % 150 Nd 5.6 %

(all values approximate)

The Sm-Nd chronometer Isotopes of Sm: 144 Sm: 3.1 % (146 Sm: 10 8 yr half life) 147 Sm: 15.0 % (1.06x10

11 148 Sm: 11.2 % 149 Sm: 13.8 % 150 Sm: 7.4 % (151 Sm: 93 year half life) 152 Sm 26.7 % 154 Sm: 22.8 %

(all values approximate)

yr half life)

The ‘rare earth’ elements Garnet Plagioclase Pyroxene

A fragment of the chondritic meteorite, Allende

A thin section of the chondritic meteorite, Allende

Comparison with a modern ‘Kelvinistic’ argument:

Summary of typical stellar lifetimes, sizes and luminosities

"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

14 C decay: The basis of most ages for geologically young things 14 C is produced in the atmosphere: 14 N + n = 14 C + p

Cosmic-ray fast neutrons

Undergoes beta-decay with a half-life of 5730 yrs: 14 C = 14 N + e  = 1.209x10

-4 yr -1 Age (yrs) = 19,035 x log (C/C 0 ) [ or …’x log ( Activity / Activity0 )’] Key for application is assumption of a value of C 0 , which depends on 14 C/ 12 C 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: 14 C ‘ages’ of deep ocean water

∆ 14 C = (R i /R 0 -1)x1000 Where R i = 14 C/ 12 C at time of interest R 0 = 14 C/ 12 C of pre-1890 wood projected forward to 1950 (?!?&*!) Variation in atmospheric 14 C/ 12 C through time due to natural processes

Using 14 C to reconstruct earthquake recurrence intervals

The U-Pb system and the age of the Earth 238 U = 206 Pb + 8x 4 He   235 U = 207 Pb + 7x 4 He   = 1.55125x10

-10 = 9.8485x10

-10 (4.5 Ga half life) (0.7 Ga half life) 204 Pb is a stable isotope 238 U/ 235 U is (nearly) constant in nature = 137.88

206 Pb 204 Pb = 206 Pb 0 + 204 Pb 238 U 204 Pb (e  t - 1) 207 Pb 204 Pb = 207 Pb 0 + 204 Pb 235 U 204 Pb (e  t - 1) 207 Pb 204 Pb 206 Pb 204 Pb 207 Pb 0 204 Pb 206 Pb 0 204 Pb 1 = 137.88

(e  t - 1) (e  t - 1)

207 Pb 204 Pb 206 Pb 204 Pb 207 Pb 0 204 Pb 206 Pb 0 204 Pb QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.