### Lecture 33 - Earth and Atmospheric Sciences

```U & Th Decay
Series Isotope
Geochemistry
Lecture 33
U and Th Decay Series
Decay Series and Radioactive
Equilibrium
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238U, 235U,
and 232Th decay to Pb through a series of α decays (8, 7, and 6,
respectively). Since the daughters tend to be neutron-rich, some also βdecay. Most of these are too short-lived to be useful, but the longer-lived
ones have uses in geology, geochronology, and oceanography.
Consider a daughter (e.g., 234U) that is both radiogenic and radioactive.
The rate of change of its abundance is its rate of production less its rate
of decay:
dN D
= lP N p - l D N D
dt
The steady-state condition is:
0 = lP N p - l D N D
•
•
•
and
lP N p = l D N D
N D lP
=
N p lD
This is the condition that a system to which a system will eventually return
if perturbed; i.e., the (radioactive) equilibrium condition.
The rate at which a system returns to equilibrium occurs at a predictable
rate. Therefore, the extent of disequilibrium is a function of time and can
be used for geochronology.
So that:
‘Activities’
• Traditionally, decay series nuclides were measured by
measuring their decay (using alpha or gamma detectors). As
a consequence, the abundances were traditionally reported
as their (radio)activity: the number of decays per unit time
(usually dpm, although the SI unit is the bacquerel, dps).
• Activity is related to atomic abundance through the basic
equation:
dN
-
o
dt
= lN
the quantity on the left is the activity.
• The activity is written as the isotope in parentheses, e.g., (234U).
We’ll now mainly use activity and this notation.
• The longer-lived nuclides are now measured by mass
spectrometry, but use of activity has stuck, partly because it is
useful.
• Radioactive equilibrium is the condition where activities of
parent and daughter are equal.
234U-238U
Dating
is the great-granddaughter of 238U, and the first long-lived
daughter in the chain. We’ll ignoring the two short-lived
intermediates (assuming they quickly come to equilibrium).
• The half-live of 234U is 246,000 yrs, that of 238U is 4.47 billion years.
On times scales of interest in this system, the abundance (and
activity) of 238U does not change.
• The activity of 234U then can be expressed as:
•
234U
æ
çè
éæ
Uö
=
1+
êç
238
U ÷ø
êëè
234
0
ù -l t
Uö
-1
ú e 234
238
÷
Uø
úû
234
• After long times, the activity ratio will be 1. Before that, it will
be a function of time. If we know the initial ratio, we can use it
as a geologic clock.
• Coral carbonates incorporate U from seawater, which has
(234U/238U) ≈ 1.15 (why?). After many half-lives, the ratio will
decline to 1. Hence we can use this to date corals.
Unfortunately, (234U/238U) hasn’t been exactly constant through
time.
230Th-234U
•
•
234U
α-decays to 230Th (half-life: 75,000 yrs). Disequilibrium between U and
Th is greater than among U isotopes, and in this sense this is a better
geochronological tool.
We can consider two possibilities:
o
o
•
234U
and 238U were also in disequilibrium (e.g., corals), in which case we much take account of the (234U/238U)
ratio.
234U and 238U were also in equilibrium (volcanic rocks), in which case we can ignore 234U and treat 230Th as if
it were the direct daughter of 238U.
For the former case:
æ
çè
•
•
•
Dating
Th ö
1- e- l230t
l230
=
+
234
234
238
÷
U ø ( U / U) l230 - l234
230
1
é
ù
-( l230 - l234 )t
)
ê1- ( 234U / 238U) ú (1- e
ë
û
This technique has been extensively used for dating corals (which
exclude Th, so the ratio on the left starts at close to 0). Because corals
also incorporate C, it has been used to calibrate 14C dates beyond the
point where they can be calibrated by dendrochronology.
Because reef-building corals live at sealevel, dating of fossil corals has
provided a record of sealevel change as the last glacial period ended.
This tells us how ice volume changed.
It is also used to date carbonates in caves, and by dating ‘spelothem’
coatings on cave painting, constrain the age of the cave paintings.
230Th-238U
•
•
In volcanic rocks, we can assume 234U
and 238U are in equilibrium. Here we
divide by the activity of the long-lived
Th isotope, 232Th (half-life 14 billion
years). It does not decay appreciably
on the time scales of interest.
The relevant equation is:
æ
çè
•
•
Th ö æ
=
232
Th ÷ø çè
230
0
Th ö - l230t æ
e
+ç
232
Th ÷ø
è
230
Uö
1- e- l230t )
(
÷
Th ø
238
232
If we plot a series of cogenetic
samples on a (230Th/232Th) vs (238U/232Th)
plot, the slope will be a function of
time. Unlike the conventional isochron
equation, the intercept is also a
function of time.
The line pivots around the ‘equipoint’
and after many half-lives will have a
slope of 1: the equiline.
Dating
Decay Series Summary
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have also been used for
dating, including 226Ra (t1/2 =
1600 yr), 231Pa (t1/2 33,000 yrs),
and 210Pb (t1/2 = 22 yrs).
also used to place constraints
on rates and extent of
melting in the mantle, on
mantle Th/U ratios, and on
sedimentation rates and
processes within the ocean
phenomena (of Th in
particular).
(You’ll have to take EAS6560
to learn about these!)
Noble Isotope Geochemistry
• Isotopes of all 6 noble gases are produced to some
degree by nuclear processes:
o 4He by alpha decay
o 40Ar by 40K decay
o heavy Xe isotopes (and Kr) by U fission
o Rn by U decay
o Extinct radionuclides: 129Xe/130Xe varies in the Earth (and solar system) due to
decay of the ‘fossil’ radionuclide 129I (t1/2 = 16 Ma). Other Xe isotopes also show
effects of 244Pu fission (t1/2 = 82 Ma), but hard to separate from 238U fission.
o Ne by nuclear reactions initiated by interactions with neutrons and α-particles
(these can also produce 3He).
o All to some degree by cosmic-ray interactions (in the atmosphere or at the
surface of planetary bodies).
• The last two processes affect other elements, but are
more significant on the noble gases because they are so
rare.
Helium
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He is the only element for which the Earth is
not a closed system - it is light enough to
‘bleed’ to space from the atmosphere. He
continually leaks from the Earth to replace it;
residence time in the atmosphere is a
couple of million years.
The usual (but not universal) convention in
the case of 3He is to put the radiogenic
isotope in the denominator, i.e., 3He/4He.
Ratios are commonly reported relative to the
atmospheric value (1.4 x 10-6) as R/RA.
These ratios are very low in the crust because
it is outgassed and 4He is produced by αdecay (a wee-tad of 3He is produced by
interactions on Li such as 6Li(n,α)3He - limiting
the ratio to ~0.01 R/RA.
Higher ratios are found in mantle-derived
volcanic rocks - telling us that the mantle has
not been completely outgassed. OIB have
higher 3He/4He (in most, but not all, cases),
indicating they come from a less degassed
reservoir. This supports the notion that OIB are
produced by mantle plumes that rise from
the deepest part of the mantle.
He in seawater
• High 3He/4He values were
first discovered in deep
ocean water over midocean ridges - pumped
into the ocean by
hydrothermal systems (this
led to the discovery of
‘black smokers’).
• 3He/4He is still used to
‘prospect’ for
hydrothermal vents and
as a tracer of ocean
circulation.
Ne Isotopes
•
Ne isotopes vary in the solar system due to
o
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Atmospheric Ne is depleted in light Ne isotopes in
proportion to mass - indicating mass dependent
fractionation, due to preferential escape of
lighter Ne isotopes.
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mass dependent fractionation
cosmogenic production (not relevant to planetary interiors)
‘nucleogenic’ production, particularly of 21Ne through reactions
such as 18O(α,n) 21Ne.
The degree to which this happened in the early Earth or in the
precursor materials that formed the Earth is not entirely clear.
Ne in mantle-derived rocks is less light isotopedepleted and some ratios approach those in the
Sun.
‘Mantle’ and crustal Ne (including Ne dissolved in
old groundwater and petroleum) is also enriched
in 21Ne - a consequence of nucleogenic
production.
MORB tend to have higher 21Ne/22Ne than OIB.
Nucleogenic production rate depends on U/Ne
ratio - so these data also suggest the OIB reservoir
is less degassed than the MORB ones.
Most or all volcanic rocks suffer some
atmospheric contamination, so the data lie on
line point to atmospheric Ne.
K-Ar
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40Ca
is the principal product of 40K decay, but is so abundant the 40Ca/44Ca ratio
doesn’t change much.
Since Ar is a rare gas, radiogenic 40Ar is readily detected.
Because volcanic rocks almost completely degas upon eruption, Ar/K ratios are
near 0, and any initial Ar can, to a first approximation, be neglected (or assumed
to have the atmospheric ratio). Because of the short half-life of 40K, 40Ar builds up
rapidly, so this is an excellent system for dating relatively young materials (as young
as 10’s of thousands of years).
Since Ar is a rare gas, it is quite mobile and the K-Ar system is readily reset (but it
can be an advantage if you are dating low-T events or processes, like catagenesis
(genesis of oil and gas).
In a commonly used version of this technique, the sample is irradiated with neutrons
in a reactor, producing 39Ar from 39K (the principal K isotope). The K/Ar ratio can be
determined from the 39Ar/36Ar ratio simultaneously with the 40Ar/36Ar ratio - this is
known as ‘40-39’ dating.
The 40Ar/36Ar ratio of the atmosphere is constant at 396. The initial ratio of the solar
system was <<1: Thus virtually all the Ar in the atmosphere is radiogenic - derived
from degassing of the Earth’s interior. This helps us understand this process.
To account for the Ar in the atmosphere requires a K concentration in the silicate Earth of ~120 ppm. Estimates of K in
the Earth range from about 160 to 240 ppm. This implies that 50% to 75% of the Earth’s Ar is now in the atmosphere.
Conversely, as much as 50% may still be in the mantle (crust has very little).
40Ar/36Ar ratios in MORB are higher (up to 40,000) than they are in OIB (up to
o
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~10,000). Since this depends on the K/Ar ratio, it also indicates that the MORB
source reservoir is more degassed than the OIB source reservoir.
Cosmogenic Nuclides
• Cosmic rays are high energy nuclei (mainly of H and He) from
space. When they collide with nuclei in the atmosphere or the
surface of the Earth, they induce nuclear reactions. The
resulting particles also have high energies and can induce
further reactions. The one of greatest interest is 14N(n,p)14C
where the neutron is a secondary particle.
• A number of other nuclides are produced in this way that are
useful in geochemistry and geochronology: 3He, 10Be, 21Ne,
26Al, and 36Cl. Production restricted to the atmosphere or
uppermost meter of the solid Earth.
• Some of these are used to ‘date’ exposure of surfaces (lava
flows, glacial moraines). 10Be (t1/2 15 Ma) is used to trace
subduction of sediments into the mantle and also in dating
sediments.36Cl (t1/2 300 ka) is used to date water in hydrology.
• Cosmogenic nuclides are also used to date meteorites exposure ages are much less than ‘formation’ ages, telling us
meteorites come from larger bodies in which they were
shielded from cosmic rays.
Carbon-14 Dating
•
14C
in a sample of carbon withdrawn from the atmosphere
(by, for example, photosynthesis) will decay according to
N = N 0 e- lt14
• Assuming constant production of C in the atmosphere, and
therefore a constant specific activity (dpm/g C), we can
determine t simply by measuring the activity of 14C in the
sample (traditionally by β-counting, but increasingly by
accelerator mass spectrometry).
• The catch is that specific activity has not been constant due
to:
o
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Variable production rates partly linked to solar activity (enhanced solar wind tends
to deflect cosmic rays from the inner solar system).
Dilution by non-radiogenic carbon (anthropogenicly by fossil fuel burning, naturally
as CO2 exsolved from the ocean at the end of the last ice age.
Addition of ‘bomb’ carbon from atmospheric nuclear tests.
• This variability requires calibration of 14C ages by U-Th dating
and ‘dendrochronology’.
• The young Solar System was ‘hot’ in many senses,
including radioactive, as we’ll see in Chapter 10. We
know this from the presence of their decay products.
• The short-lived nuclides decay away and are now gone,
but some (146Sm, 129I, 244Pu) were still around when the
Earth formed and even when some of the oldest rocks
formed.
• Mantle Xe has higher 129Xe/130Xe than the atmosphere.
This indicates much of the atmosphere has formed
before 129I had decayed away (16Ma × 5 = 80 Ma),
producing high 129Xe/130Xe in a relatively Xe-poor
mantle.
•
o Degassing of the Earth’s interior must have been a two step process: extensive
early degassing, to account for atmosphere’s 129Xe deficit and much slower
subsequent degassing to account for 40Ar.
There is also evidence of the presence of 244Pu - but it
complicated.
142Nd/144Nd
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Modern terrestrial rocks have higher
142Nd/144Nd than chondrites (chondrites
themselves vary).
This indicates the Earth, or the ‘observable’
part of it - the crust and the mantle giving
rise to magmas, have 146Sm/144Nd higher
than chondritic. This suggests the Earth has
higher than chondritic Sm/Nd.
o
o
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and extinct
Two common explanations: an earlier-formed low Sm/Nd
crust either sunk to the bottom of the mantle or was lost
through ‘collisional erosion’.
Also possible 146Sm or 142Nd were not uniformly distributed in
solar nebula.
Early Archean (~3.8 Ma) rocks from Isua,
Greenland and Nuvvuagittug, Labrador
(and now a few other places) have
142Nd/144Nd different than the modern
terrestrial value.
o
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146Sm
would have been effectively extinct by then.
The precursors/sources of these rocks must have formed very
early with higher and lower Sm/Nd ratios than the bulk Earth.
Among other things, it tells us that the Earth began to
differentiate into incompatible element-enriched and
depleted reservoirs (such as crust and residual mantle) very
early.
146Sm
```