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

Slide 2:

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 (et-1) + D0

Slide 4:

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

Slide 5:

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

Slide 6:

Breakthrough: Aston’s positive ray device

Slide 7:

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))

Slide 8:

Intensity Strength of B field

Slide 9:

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

Slide 10:

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

Slide 12:

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 (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-intercept Slope

Slide 13:

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

Slide 14:

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)

The ‘rare earth’ elements Normalized abundance Plagioclase Pyroxene Garnet

Slide 17:

A fragment of the chondritic meteorite, Allende

Slide 18:

A thin section of the chondritic meteorite, Allende

Slide 21:

"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

Slide 23:

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

Slide 24:

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 (?!?&*!)

Slide 25:

Using 14C to reconstruct earthquake
recurrence intervals

Slide 26:

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 (et - 1) (et - 1) = + = + 207Pb
204Pb 207Pb0
204Pb 206Pb
204Pb 206Pb0
204Pb - - = 1
137.88 (et - 1) (et - 1)

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