Martian Lafayette Asteroid
with patterns caused by the
passaged through the
atmosphere. Line on the
fusion crust were caused
by beads of molten rock.
Dating
AST111 Lecture 8a
❑Isotopic composition
❑Radioactive dating
Chemical separation
• Atoms become well mixed in a hot gas.
• Solid bodies, do not mix well, retaining the
molecular composition when they solidified.
• Melts tend to group with mineralogically
compatible counterparts.
• Condensing gas produces small grains, relatively
heterogeneous or homogenous, compared to
crystals.
Isotopic fractionation
• Isotopes are separated from each other by massdependent processes.
• Lighter molecules tend to escape.
• Molecular forces: Deuterium preferentially
combines with heavy elements, because of a
slightly lower energy from deuterium’s greater
mass.
• Nuclear processes can also lead to differences in
isotope ratios. For example cosmic rays produce
different isotopes (like 14C). Unstable nuclei also
decay changing the ratio of isotopes.
Radiometric Dating
• Formative age is the age since the meteorite was molten or
gaseous. Most meteorites have ages of 4.53 to 4.57×109
years.
• These dates are estimated from long lived radioactive
isotopes.
• Types of radioactive decay include β-decay (electron
emitted) and α decay (Helium nucleus emitted).
• For β-decay a neutron is converted to a proton so the
atomic number increases by 1. Example: 87
87
37
• For α-decay, the atomic weight is reduced
by 4 and the atomic number decreases by
2. Example:
Rb → 38 Sr
238
92
U→
234
90
Th
The decay rate
The abundance of a parent species as a function of time
Np (t) = Np (t0 )e
(t t0 )/⌧m
𝜏m decay time constant, depends on the parent nuclide
When is Np(t) = Np(t0)/2 ?
At a special time t1/2 from t0
t1/2 is the half-life
1/2 = e
half left
t1/2 /⌧m
t1/2 = ⌧m ln 2
Long Lived Radioactive nuclides
Parent
40K
87Rb
147Sm
187Re
232Th
235U
238U
Stable Daughters Half life t1/2
(Gyr)
40Ar, 40Ca
1.25
87Sr
48.8
143Nd, 4He
106
187Os
46
208Pb, 4He
14
207Pb, 4He
0.707
206Pb, 4He
4.47
Extinct radioactive nuclides
Parent
22Na
26Al
41Ca
53Mn
60Fe
107Pb
109I
Stable daughters
22Ne
26Mg
41K
53Cr
60Ni
107Ag
109Xe
Half life Myr
2.6
0.72
0.1
3.6
1.5
6.5
17
Isotopes of noble gases
• Some elements decay into noble gases which
are trapped in the rock, unless the rock is
heated. There is a build up of noble gases in
the rock.
• “Gas retention age” which can also tell you
about cooling history.
Radionuclides, daughters and references
❑ Nuclide is the name we use to refer to the nucleus of an
isotope of a given element.
❑ Radioactivity involves the decay of a radionuclide to a
daughter nuclide. Most useful if the daughter is rare.
❑ A stable isotope of the daughter species, one which is not
involved in radioactivity, serves as the reference nuclide.
❑ Suppose that within a given mineral sample, the numbers
of these three nuclides are n, d, and s, respectively. Define
the relative abundances of radionuclide and daughter:
N =n s , D=d s .
❑ These are independent of the amount of material
analyzed, since the amount is proportional to the stable
isotope s.
Radioactivity
Some nuclides are radioactive, and will transmute into other
nuclides over time. If one starts with a bunch of groups of a
given nuclide, each group having a total of n0 atoms at t = 0,
then after a time t the average number remaining in a group is
n = n0 e −λt
#####→ N = N 0 e −λt
divide by s
,
s=a stable isotope of daughter
where λ is the decay rate for the radionuclide, a quantity
that has usually been measured accurately in the
laboratory. λ is related to the commonly-quoted half-life:
N0
ln 2
− λ t1 2
= N0 e
⇒ − ln 2 = −λ t1 2 ⇒ t1 2 =
2
λ
.
Important example: the Rb-Sr system
❑ Rubidium is an alkali; it can replace the much-more-abundant
sodium and potassium in minerals (e.g. feldspars). It has one
stable isotope, 87Rb and one long-lived radioisotope 85Rb
❑ Strontium is an alkaline, and can replace magnesium and
calcium in feldspars. It has four stable isotopes: 84Sr, 86Sr, 87Sr,
88
Sr
❑
87
Rb beta decays into 87Sr
87
Rb →
87
Sr + e − + ν e + energy
❑ Commonly n 87 Rb
N= =
used:
86
s
Sr
d
, D= =
s
87
Sr
86
Sr
.
The use of radionuclides to find out how long
ago an igneous rock was last melted
❑ There are many radioisotopes, with halflives spread from
thousands to billions of years, all accurately and precisely
measured in the laboratory.
❑ We can measure the abundances of stable and radioactive
nuclides “simply” by taking rocks apart into the minerals
of which they are made, and in turn taking the minerals
apart into atoms, counting the number for each element
and isotope in a mass spectrometer.
❑ This gives values of N and D, a pair for each mineral. Plot
the Ds against the Ns: the slope of the resulting line
depends upon how many halflives have passed since it
froze, and the intercept depends upon the initial relative
abundance of the daughter nuclide.
12
The use of radionuclides to find out how long ago an igneous
rock was last melted (continued)
Minerals after aging
by a fixed number of
half lives
Measure slope and intercept to
find age and initial relative
abundance of the daughter
nuclide.
D (e.g.
87
Sr !
""
86
Sr #
Molten rock
W
Y
X
Minerals after freezing
Z
!All the same
"D, since daughter
"
# and stable ref.
"are chemically
"identical.
$
N (e.g. 87 Rb 86 Sr)
13
A two-mineral system
The initial relative abundances N0 and D0 The relative
abundance of daughter nuclides as a function of time is:
amount decayed
D = D0 + (N 0 − N ) = D0 + N eλt − 1
(
)
.
Suppose we have a rock consisting of two minerals, A and B,
with equal initial relative abundances of the daughter nuclide.
We can measure the present abundances of A and B:
(
DA = D0 + N A e
λt
−1
)
(
, DB = D0 + N B e
λt
−1
)
Two equations,
two
. unknowns:
D0 and t.
This can be solved for t, in terms of measurable quantities:
#
1 " DA − DB
t = ln %
+ 1& .
λ ' N A − NB
(
14
Example two-mineral system
The rate at which 87Rb decays into 87Sr is
λ = 1.39 × 10 −11 yr -1
Samples of two different minerals from the same plutonic
rock from northern Ontario are analyzed in a mass
spectrometer, with these results:
Sample
87
Rb
86
Sr
87
Sr
86
Sr
A
NA=0.0755
DA=0.7037
B
NB=0.3280
DB=0.7133
How old is the rock?
15
Example two-mineral system (continued)
Solution:
0.712
# 0.7133 − 0.7037
$
× ln %
+ 1&
' 0.328 − 0.0755
(
9
= 2.7 × 10 yr.
A
D =87Sr/86Sr
$
1 # DA − DB
t = ln %
+ 1&
λ ' N A − NB
(
1
=
1.39 × 10 −11 yr -1
r
68S
0.708
/
r
78S
=
D0.704
B
0.700
0
0.1
0.2
0.3
0.4
N = 87Rb/86Sr
The y intercept gives the value of D that the rock had at the
time it froze: D0 = d s = 87 Sr 86 Sr = 0.7008.
16
Results for Earth and Moon
❑ The Moon began
to solidify about
4.5 billion years
ago.
❑ The highlands are
clearly older than
the maria, as the
cratering record
also shows.
❑ The Moon
solidified long
before the Earth
did.
Figure from Jay Frogel.
Dating rocks containing radioactive
isotopes
Consider both the abundance of the parent and
daughter species
N p (t ) = e −(t −t0 ) / τ m N p (t0 )
N d (t ) = N d (t0 ) + (1 − e −(t −t0 ) / τ m ) N p (t0 )
We have two unknowns:
t − t0 , the age and
N d (t0 ), the initial amount of daughter species
Different ratios of parent daughter
nuclides
• To break the uncertainty caused by the two
unknowns, different samples of rock from the same
meteor are used.
• Each crystal has a different ratio of elements.
Compare the ratio of parent and daughter elements
to another nuclide which is stable and not
changing.
• Use another isotope of the same element as the
daughter nuclide. The initial isotope ratios should
be the same in the different rock samples.
Ns is a stable
isotope of Nd
Slope which only depends
on the decay time.
N d (t ) / N s = N d (t0 ) / N s + (1 − e
Original daughter isotope
ratio. Should be the same in all
crystals.
Original parent ratio which
depends on the crystal.
Observed daughter ratio,
depends on decay.
− ( t −t0 ) / τ m
) N p (t0 ) / N s
Since intercepts and
slopes should be the same,
points from different crystals
should all fall on a line. The
slope of the line determines
the age of the rock.
Isochron diagrams
Animation by
Jon Fleming
Isochron
diagram
Radiometric dating assumption
Ratio of original daughter isotope to stable isotope
of daughter , D0 is independent of solidification,
crystallization and cooling.
No ``fractionation"
Extinct nuclide dating
• Search for rare daughter products of short
lived nuclides.
• For example, Xenon is fairly rare, much
rarer than Iodine. 129I beta decays to 129Xe
with a half life of 17 million years.
• The total amount of Xenon in the meteor is
related to the initial amount of radioactive
129I.
The interval between nucleosynthesis
and condensation
• In a supernovae r-process elements are produced when
there is a high flux of energetic neutrons. The unstable
nuclei do not necessarily have time to β-decay before they
gain another neutron.
• The r-process produces a particular nuclide distribution.
• Unstable r-process elements including 129I decay after
formation. The amount of 129I inferred in the rock (by
looking at the amount of present Xenon) gives a timescale
between the supernova and the condensation of the solar
nebula.
• --- The protosolar nebula was probably condensed only 80
million years after a supernova enriched the gas which was
incorporated into the solar nebula.
Light elements with short half lives
• There is a correlation in chondrites between Al abundance
and 26Mg/24Mg ratio.
• This cannot be a result of mass dependent fractionation
because 25Mg/24Mg is normal.
• So probably 26Al beta decays into 26Mg, 26Al half life is
720,000 years.
• Since Al is abundant, this could have provided a substantial
amount of energy for melting planetesimals.
• Supernova, nearby enriching protosolar nebula.
• The decay also produces a gamma ray which is detected
from the Galaxy.
Cosmic ray exposure ages
• Galactic cosmic rays (energy above 1Gev, mostly protons)
penetrate to 1m or so in asteroids.
• The amount of cosmic rays a meteor has been exposed to
indicates how long it was in space.
• Rare isotopes only produced by this process must be
identified. Such as 21Ne and 38Ar, or 10Be. Abundance
varies with depth so this must be estimated independently.
• Typical “cosmic ray exposure ages” range from 106 years
for carbonaceous chondrites to 107 for stones, to 108 for
stony irons and 109 for irons.
• To explain this dependence: There could be a tendency for
weaker materials to erode. Also the Yarkovski force has a
weaker effect on denser materials.
Chondrites
• Abundances of chondrites are very regular, being
almost exactly solar in composition with the
exception of the loss of some volatile elements,
and those resulting from radioactive decay.
• Are there any anomalies due to other processes?
• Chondrites have not been melted for 4.56 billion
years but they are not uniform.
• Chondrites also contain Chondrules and CAI
inclusions (calcium and aluminum rich).
• Chondrites include 0-80% of mass in chondrules.
Solar System Abundances
Ir=77
Chondrules
• Chondrules 0.1-2mm, must have cooled on
order of 10 minutes to a few hours to explain
their crystalline properties.
• Correlations between size and composition
are difficult to explain, but must have been
formed before becoming part of larger
bodies.
The matrix
• The matrix consists of smaller grains, a lot
of olivine and pyroxine (also seen in IR
spectra of extra-solar debris disks and
comets)
• Can also have grains from other stars mixed
in (including diamonds).
Clues to formation of the solar system
• The Allende CV3 meteorite is 4.563±0.004×109
years old.
• This pretty much dates the solar system.
• Moon rocks are younger (3--4.45×109), so have
melted since then. Terrestrial rocks are less than
4×109 years old.
• Differences in composition tell you about where
they formed (mass fractionation), nuclear decay,
processing by melting and water and cosmic rays.
Meteorites from differentiated bodies
• Excess 60Ni which is a stable decay product of 60Fe
suggest that some rocks differentiated within 107
years after nuclear synthesis.
• Retention of noble gases can also be related to a
cooling history. A cooling history depends on the
size of the body.
• There is a consensus that some smaller bodies
<100km melted.
Origin of Chondrules and CAIs
Possible scenarios:
• Drag during passage through an accretion
shock.
• X-wind acceleration followed by cooling in
a shaded region.
• Lightning
• Nebular shock waves
D/H ratio
• Some organic material in carbonaceous chondrites
contain high D/H ratios more than 1000 times
solar.
• Some fractionation could occur in the solar nebula
due to temperature differences as a function of
radius, and high D/H at large radii (factor of 10).
• Cold interstellar clouds, however are needed to
produce such a large variation (factor of 1000).
• Interstellar grains probably were processed into the
proto-solar nebula.
Summary
❑Isotopic fractionation.
❑Long lived and short lived nuclides.
❑Radioactive dating and how to do it.
❑ Cosmic ray exposure times.
❑ Time between nucleo-synthesis and
condensation.