Dating AST111 Lecture 8aMartian Lafayette Asteroid

with patterns caused by the passaged through the

atmosphere. Line on the fusion crust were caused by beads of molten rock.

❑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 mass-dependent 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:

238 23492 90U Th→

87 8737 38Rb Sr→

• For α-decay, the atomic weight is reduced by 4 and the atomic number decreases by 2. Example:

The decay rate

Np(t) = Np(t0)e�(t�t0)/⌧m

The abundance of a parent species as a function of time

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�t1/2/⌧m

t1/2 = ⌧m ln 2

half left

Long Lived Radioactive nuclidesParent Stable Daughters Half life t1/2

(Gyr)40K 40Ar, 40Ca 1.2587Rb 87Sr 48.8147Sm 143Nd, 4He 106187Re 187Os 46232Th 208Pb, 4He 14235U 207Pb, 4He 0.707238U 206Pb, 4He 4.47

Extinct radioactive nuclidesParent Stable daughters Half life Myr22Na 22Ne 2.626Al 26Mg 0.7241Ca 41K 0.153Mn 53Cr 3.660Fe 60Ni 1.5107Pb 107Ag 6.5109I 109Xe 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

0 0divide by ,t t

sn n e N N eλ λ− −= #####→ =

1 200 1 2 1 2

ln 2ln 2 .2

tN N e t tλλ

λ−

= ⇒ − = − ⇒ =

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:

s=a stable isotope of daughter

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, 88Sr

❑ 87Rb beta decays into 87Sr

87 87Rb Sr energyee ν−→ + + +

87 87

86 86Rb Sr, .Sr Sr

n dN Ds s

= = = =❑ Commonly

used:

12

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.

13

The use of radionuclides to find out how long ago an igneous rock was last melted (continued)

Molten rock

Minerals after freezing

Minerals after aging by a fixed number of half lives

ZYXW

Measure slope and intercept to find age and initial relative abundance of the daughter nuclide.

All the same , since daughter

and stable ref. are chemically identical.

D!""#""$

87 86 (e.g. Rb Sr)N

87

86

(e.g.

SrSr

D

!""#

14

A two-mineral system

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:

( ) ( )0 0 0 1 .tD D N N D N eλ= + − = + −

( ) ( )0 01 , 1 .t tA A B BD D N e D D N eλ λ= + − = + −

1 ln 1 .A B

A B

D DtN Nλ

" #−= +% &

−' (

Two equations, two unknowns: D0 and t.

The initial relative abundances N0 and D0 The relative abundance of daughter nuclides as a function of time is:

This can be solved for t, in terms of measurable quantities:

amount decayed

15

Example two-mineral system

A NA=0.0755 DA=0.7037

B NB=0.3280 DB=0.7133

87 86Sr Sr87 86Rb Sr

11 -11.39 10 yrλ −= ×

The rate at which 87Rb decays into 87Sr is

Samples of two different minerals from the same plutonic rock from northern Ontario are analyzed in a mass spectrometer, with these results:

How old is the rock?

Sample

16

Example two-mineral system (continued)

11 -1

9

1 ln 1

11.39 10 yr

0.7133 0.7037ln 10.328 0.0755

2.7 10 yr.

A B

A B

D DtN Nλ

−

# $−= +% &

−' (

=×

−# $× +% &−' (

= ×

The y intercept gives the value of D that the rock had at the time it froze: 87 86

0 Sr Sr 0.7008.D d s= = =

0.700

0.704

0.708

0.712

0 0.1 0.2 0.3 0.4

D=

87Sr/86Sr

N= 87Rb/86SrD

=87

Sr/86

Sr

Solution:A

B

Results for Earth and Moon

Figure from Jay Frogel.

❑ 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.

Dating rocks containing radioactive isotopes

0

0

( ) /0

( ) /0 0

0

0

Consider both the abundance of the parent and daughter species

( ) ( )( ) ( ) (1 ) ( )

We have two unknowns: , the age and ( ), the initial amount of da

m

m

t tp p

t td d p

d

N t e N tN t N t e N t

t tN t

τ

τ

− −

− −

=

= + −

−ughter 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.

0( ) /0 0( ) / ( ) / (1 ) ( ) /mt t

d s d s p sN t N N t N e N t Nτ− −= + −

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.

Slope which only depends on the decay time.Ns is a stable

isotope of Nd

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.