GEOS 459/559 - Thermochronometry

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Homework
We made the point the geochronology is
thermochronology because of the closure
temperature. Give two general examples of rocks
that, when dated with radiometric techniques
truly record the age of formation and not just
cooling.
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Chronological Organization

• 1. Radiogenic isotope chemistry
• 2. Diffusion theory
• 3. Individual chronometers (a) the standard
  story, and (b) new developments
• 4. Unraveling the thermal history of crustal
  rocks
• Applications to tectonic/magmatic problems.

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Nuclear stability

• What is an isotope?
• What isotopes are stable?
• When are they radioactive?
• How do we quantify decay?
• Which systems are useful to geologists?

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Atoms

• Made of protons, neutrons, electrons
• Sum of protons and neutrons mass number
• Only certain combinations of proton/neutron
  numbers are stable in nature

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Stability of nuclei as a function of proton (Z)
vs. neutron (N) numbers
A (mass ) ZN
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(No Transcript)
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Isotopes, isobars, isotones
Isotones
Isotopes (equal zs)
Isobars- same mass , A (NZ)
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Not all of these isotopes are stable as they
depart from the idealized stability line. The
isotopes that are not stable will tend to decay
into more stable configurations.
Let us look at the element Rb and its various
isotopes.
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Essentially there are only two isotopes that
dont decay away within short time scales, 87Rb
and 85Rb. All others are not present in nature.
Of these, one is stable (85Rb), and one is
radiogenic (87Rb)
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How do we quantify stable or not?

• If isotopes decay away within laboratory time
  scales, thats a no brainer - they are not
  stable.
• Slower decaying species - need to know their
• Decay constant or
• Half life

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Measuring radioactive decay
Half life (t1/2) the time required for half of
the parent atoms to decay, alternatively
use The decay constant (?) ln2/t1/2
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Decay systems of interest for geologists
We will examine all of them.
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Decay - basic mechanisms

• Alpha decay (?) - emission of a He (alpha)
  particle. Resulting isotope has a mass A1A0-4
  e.g. 147Sm decays into 144Nd
• Beta decay (aka ?-) - transforming a neutron into
  a proton an electron. Resulting isotope has a
  mass A1A0, e.g. 87Rb decays into 87Sr.
• Electron capture (aka ?) is essentially the
  reverse of 2. E.g. 40K decays to 40Ar
• Gamma decay is the process of emitting a high
  energy photon - no examples in this class.

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Decay equation
Law of decay- the rate of decay of an unstable
parent is proportional to the number of atoms
remaining at any time t. The proportionality
constant is lambda decay constant - units
reciprocal of time.
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Integrate from 0 to time t
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The of radiogenic daughter atoms formed (D) is
equal to the of parent atoms consumed
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General geochronological equation
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Example
Recall
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Plotting the decay equation
daugther
time
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daugther
time
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Dividing by a stable isotope
In practice it is impossible to accurately count
isotopes but rather we collect isotopic ratios
(see next weeks class). For that reason the
decay equations are written as
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Example
Choose a relatively abundant and easy to measure
normalizing isotope
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Branching decays
In some cases, a radiogenic parent A decays to
two daughters B and C
BB
A
C
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Equations
Or in general
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Example of branching decay

• 40K decays into
• 40 Ar by electron capture and
• 40Ca by beta decay
• Both systems are in principle relevant to
  geochronology although only K-Ar is widely used

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Successive decays
206Pb
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Equations
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Homework for next Tuesday
Assume you are dealing with a decay scheme in
which the parent isotope decays into an
intermediate daughter, which further decays to a
stable daughter. Solve the equation for the
intermediate decay system.
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In a 2-decay scheme with one decay constant
significantly different than the other

1. Transient equilibrium
2. Secular equilibrium
3. No equilibrium