Geochronology, radiogenics

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Geochronology, radiogenics
Recall the four forces of contemporary physical
theory we have, so-far, explored the geophysics
of only two. Now lets look at the two remaining
Weak mediates ß-decay and ß-capture
processes Strong mediates nuclear fission and
a-decay
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Radioactivity

Radioactivity was discovered in 1896 by the
French scientist Henri Becquerel during his work
on the phosphorescence of uranium salts science
now had a method for quantifying the age-history
of the Earth, planets and Solar System. Within a
little more than a decade, radioactive decay
sequences were being used in geochronological
dating. Ernest Rutherford, then at McGill,
encouraged B. Boltwood to determine the age of
minerals by their lead accummulation in 1907...
work done partially is what is now the Shulich
Physical Sciences and Engineering Library, then
the MacDonald Physics Building.
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Decay modes
Radioactive decay is spontaneous generally, we
cannot stimulate a radionucleus to decay though
the condition of the atom is known or suspected
to bear on certain decay modes Electron (beta)
capture 26Al e- --gt 26Mg ?e 40K e-
--gt 40Ar ?e The decay rate of these processes
is slightly affected by the ionization state of
the mother nucleus (e.g. the 40K ) and by the
atom's chemical bond state which may be further
affected by extremely high pressures.
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Decay modes - II
Beta, beta (positron) decay 40K --gt 40Ca
e- ?e 40K --gt 40Ar e ?e Neutron
emission 13Be --gt 12Be n0 5He
--gt 4He n0 5He --gt a2 n0
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Decay modes - III
Alpha decay 238U --gt 234Th a2 235U
--gt 231Th a2 Spontaneous fission 235U,
238U --gt 90-100X 130-140Y
(x)n0 Neutron-forced fission
(x)n0 235U --gt 90-100X 130-140Y
(x)n0
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Decay modes - IV
Neutron-forced fission products
(x)n0 235U --gt 90-100X 130-140Y
(x)n0
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Decay modes - Exotic
Proton emission (in elements that have been
artificially created with major neutron
deficits) 151Lu --gt 150Yb p ...
(?) 147Tm --gt 146Er p ...
(?) Proton decay (The standard model of
particle physics predicts spontaneous proton
decay never observed) with a half-life of
1036 to 1040 years!
p --gt p0 e ...
p0 --gt 2?
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Decay transmutations
Proton number p
Neutron number n0
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Unstable atomic nuclei

½
½
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Interpreting ?

The decay constant, ?, might best be seen as a
measure of the probability of decay during some
time interval and ?N(t) as the number of decay
events per unit time. It is sometimes called the
activity of the radionucleide. The Bq
(becquerel) corresponds to one decay per second.
The activity of one litre of normal seawater is
about 12Bq, or a human body, about 5000-10000Bq.
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A generic decay system

½
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A generic decay clock

½
If we know N(t0), N(t) and the decay constant,
?, and if we know that the system holding our
radionuclei is closed, this simple equation
allows us to determine the passage of time. A
closed system is one in which the decay daughters
along with the current mothers are preserved,
typically within a crystal or rock mass in the
geological context.
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Decay daughters

The decay daughters may not be distinguishable
from any identical isotopes that had existed
within our crystal or rock mass at time t 0
i.e., D(t 0). Either we need to choose the
system under analysis carefully, with D(t 0)
known, or find some redundancy in the radiogenic
clock or some other reference in order to
establish quantities at time t 0.
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Referencing to stable isotopes
Except for promethium, Pm, uranium and thorium
all naturally occurring elements have stable
isotopes. We may use a stable isotope of the
same element as our mother and daughter
radiogenic isotopes for reference.

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14C-dating
Cosmic rays convert 14N to 14C in the upper
atmosphere 14N n0 --gt 14C p 14C is
radioactive with ? 1.21 x 10-4/yr or t½ 5730
yr 14C --gt 14N e- ?e 12C is the common
stable isotope of carbon.

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14C-dating - II

At the moment an animal stops metabolising food
or a plant stops photosynthesizing, it
establishes a 14C/12C ratio of about 10-12. Very
sophisticated systems are required for MS
analysis.
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14C-dating III (Calibration)
At the moment an animal stops metabolising food
or a plant stops photosynthesizing, it
establishes a 14C/12C ratio of about 10-12. We
know, however, that the cosmic ray excitation of
14N to 14C has varied with time. We use tight
archeological data correlations and tree-ring
data from long-lived Bristlecone Pines and their
correlatable now-dead ancestors to calibrate the
14C/12C ratio as a function of time. Future
14C-dating will have to contend with a special
calibration for the very large influx of 14C into
the atmosphere caused by the uncontained nuclear
weapons testing of the 1950s and 1960s.

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Rubidium-strontium system
For many geological or geophysical purposes,
14C-dating is not very useful because the short
5730-year half-life. Within a period of 10
half-lives, only 0.1 of the original 14C is left
for comparison. We are led to systems with much
slower decay rates 87Rb --gt 87Sr with a
half-life of 47.5 x 109 years! 86Sr is stable
and derives from no other radio-decay, so we
develop ratios of the original 87Rb mother and
87Sr daughter to 86Sr an equation of a
straight line, the isochron.
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Rubidium-strontium isochron
Slope
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Potassium-Argon dual decay system
40K decays by two modes into 40Ca and 40Ar
40K --gt 40Ca e- ?e 40K --gt 40Ar e
?e
40K --gt 40Ca
? 4.96 x 10-10/yr t½ 1.497 x 109 yr ?
5.81 x 10-11/yr t½ 11.93 x 109 yr
40K --gt 40Ar
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Potassium-Argon dual decay system - II
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Potassium-Argon dual decay system - III
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Uranium-lead dating dual mothers!
238U --gt 206Pb ...
Radium decay series ? 1.55 x 10-10/yr t½
4.471 x 109 yr Actinium decay series ?
9.85 x 10-10/yr t½ 7.037 x 108 yr We
have two internal clocks. One checks the other!
235U --gt 207Pb ...
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Uranium-lead decay sequence
Source website... check it out click here!
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Uranium-lead concordia diagram
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Jack Hills zircons suite

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Counting forward from the beginning 146Sm - 142Nd
146Sm --gt 142Nd a2 ? 6.73 x 10-9/yr
t½ 1.030 x 106 yr Essentially, all the
original 146Sm that accreted with the Earth has
already transmuted into 142Nd. We may, though,
compare rocks according to their 142Nd/144Nd
ratios. The short half-life leads us to conclude
that 146Sm became extinct very early in Earth's
history. To find rocks with a low 142Nd/144Nd
ratio suggests that 146Sm was already depleted in
the host and that the rock's host had not mixed
into the mantle. A low Sm/Nd (all isotopes)
ratio for the rock's reservoir argues for a very
old reservoir.
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4.280 (53,-81) x 109 yr Faux amphibolites