Absolute Dating

Shmulik Marco and Neta Wechsler

Relative dating

Relative dating

Biochronology (relative dating, limited to fossil record)

Every parent atom of a particular type has the same probability of decaying to a specified daughter atom.Decay only depends on structure of atomic nucleus - NOT on external conditions.If N = number of parent atoms at time "t"andN0 is number of parent atoms present at start

                          where is the DECAY CONSTANT which is constant for a particular parent-daughter system.

The basic principle

1

, 2ln

21 t

Rb-> beta decay->Sr

Sr has several isotopes: 84, 85, 86, 87, 88

Only 87Sr has a radiogenic source – 87Rb

87Rb87Sr

How much 87Sr was at the beginning and how much came from 87Rb?

][ 870

870

8787tt RbRbSrSr

life half age, t; 870

87 t

t eRbRb

tt

t

t

tt

Rbt

SrSr

yyt

et

eRbSrSr

870

8787

99

870

8787

)10 t, 1070( 1

]1[

086

87

086

087

086

87

Sr

Rbt

Sr

Sr

Sr

Sr tt

For this method, t1/2 = 47 Byr

Rb-Sr MethodRb-Sr MethodAn example from some of the oldest rocks on Earth. A suite of different samples from a group of granites and gneisses were analyzed. These had different concentrations of parent rubidium 87 and so generated different amounts of the daughter (strontium 87). The resulting data plot on a straight line, called an isochron. This means that all samples have seen the same amount of time. If different samples had formed at different times (a random collection of rocks on earth) then the data would not fall on a straight line (no single isochron).

086

87

086

087

086

87

Sr

Rbt

Sr

Sr

Sr

Sr tt 0

86

87

086

087

086

87

Sr

Rbt

Sr

Sr

Sr

Sr tt

Dating meteorites with the 87Rb 87Sr method – the age of the Solar system

K-> beta decay->Ar40K – 89% -> 40Ca, 11% -> 40Ar

For this method, t1/2 = 1.93Byr

cek

ycey

.

10

. , 10 11 1058.01096.4

K-> beta decay->ArParent against daughter concentrations. In this hypothetical example there are no daughter atoms present in the original rock but a certain amount of parent atoms. Consequently a line passing through this point to the origin has zero slope. After time a number of parent atoms have decayed and the number of daughters increase. Eventually there will be no parents and only daughters - the composition will plot on the daughter axis. Note therefore the gradient of line connecting any composition withthe origin increases

with time. Or - the gradient of the line is a function of time and also a function of the decay constant.

Carbon datingCarbon dating

Carbon has 3 isotopes:Carbon has 3 isotopes:

1212CC – stable – stable1313CC – stable – stable

1212C:C:1313C = 98.89 : 1.11C = 98.89 : 1.11

1414CC – radioactive – radioactive

Abundance: Abundance: %10 8

RadiocarbonRadiocarbon

Forms:Forms: in the upper atmospherein the upper atmosphere

Decays:Decays:

tt ½ ½ = 5730 yr= 5730 yr..

pCnN 1414

NC 1414

tt eCC

01414

21

2ln

t

Half life Half life timetime

Half life Half life timetime

MeasuredMeasured

ConstantConstant

CalculatedCalculated

??????

DatingDating

Dating methods:Dating methods:

** Conventional wayConventional way

** Accelerator mass spectrometry (AMS) Accelerator mass spectrometry (AMS)

teAA 0

Bowman S., 1990

)ln(0A

At

AssumptionsAssumptions

** Constant production rateConstant production rate

** Constant and rapid mixingConstant and rapid mixing

** Constant exchange rateConstant exchange rate

** Constant reservoirs’ sizeConstant reservoirs’ size

** Same concentration in all parts of the biosphereSame concentration in all parts of the biosphere

** Decay determines the radiocarbon concentrationDecay determines the radiocarbon concentration

Problems concerning the Problems concerning the radiocarbon dating:radiocarbon dating:

-- Atmospheric Atmospheric 1414C variationsC variations

-- Alteration effectsAlteration effects

-- ContaminationContamination

-- Source or reservoir effectsSource or reservoir effects

Bowman S., 1990

Atmospheric 14C Atmospheric 14C variationsvariations

** Natural variationsNatural variations

- - Secular changesSecular changes

-- Sun spotsSun spots

** Men caused Men caused variations:variations:

-- Fossil fuel effectFossil fuel effect

-- Bomb effectBomb effect

Calibration curveCalibration curve

Hans Suess calibration curve – based on dendrochronologyHans Suess calibration curve – based on dendrochronology

Bowman S., 1990

Source or reservoir effectsSource or reservoir effects

Marine effectMarine effect

Hard water effectHard water effect

Volcanic effectVolcanic effect

Lake Kinneret reservoir time by Stiller M. et al., 2001