Foundations of a modern approach to measuring

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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
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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
(e?t-1) D0
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Re-arrange decay equation to make time the
dependant variable
Pick mineral with no structural He D0 0

ln
(D-D0)
1
N
t
?
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
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Rutherfords chronometer
?U 1.5x10-10 U 8?
1 gram of UO2
Pitchblende, or U ore, rich in UO2

• 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

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)
Low momentum (low mass))
High momentum (high mass)
If energy is of all ions is equal, this acts as a
mass filter.
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Strength of B field
Intensity
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Finnigan Triton A modern thermal ionization mass
spectrometer
Momentum analyzer (electro magnet)
Collectors (faraday cups and/or electron
multipliers)
Ion source
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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 (Z1) (N-1) e- ? Q
e.g., 87Rb 87Sr e- ? 1.42x10-11 yr-1
e.g., 14C 14N e- ? 1.2x10-4 yr-1
?? decay Z N (Z-1) (N1) e ? Q
e.g., 18F 18O e ? 3.3x103 yr-1
Most geological chronometers depend on ? and ??
decay
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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 (e?t - 1) D0
D/S N/S (e?t - 1) D0/S
Y-axis value
Slope
Y-intercept
X-axis value
This is the equation for a line in the isochron
plot
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The anatomy of the isochron diagram
Measured composition of object
D/S
m e?t - 1
D0/S
N/S
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
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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 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)
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The Sm-Nd chronometer
Isotopes of Nd
Isotopes of Sm
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)
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)
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The rare earth elements
Plagioclase
Garnet
Normalized abundance
Pyroxene
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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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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
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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 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
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The bomb spike
Natural heterogeneity 14C ages of deep ocean
water
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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 (?!?!)
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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
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
206Pb0 204Pb
238U 204Pb
(e????t - 1)


207Pb 204Pb
207Pb0 204Pb
235U 204Pb
(e????t - 1)


207Pb 204Pb
207Pb0 204Pb
-
1 137.88
(e????t - 1)

206Pb 204Pb
206Pb0 204Pb
(e????t - 1)
-
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