Radioactive Decay

• Alpha Radiation – Emission of a helium nucleus

• Alternatively we write

235 231 492 90 2U Th He

4 42 2He

Radioactive Decay

• Beta Radiation – nuclear emission of an electron or β particle

1 1 0 00 1 1 0

39 39 0 018 19 1 0

*

*

n p

Ar K

Radioactive Decay

• Gamma Radiation – emission of photons by excited or metastable nuclei

60 60 027 27 0mCo Co

http://www.atral.com/U2381.html

Looking at the decay more carefully,We see that it undergoes a complex chainof reactions before reaching the stable isotope. This decay chain emits 8 α particles and 6 β particles.

If the half lives of the intermediate daughtersare orders of magnitude less than the Parent, then the rate of decay of the daughteris equal to the rate of decay of the parent.

238U

206Pb

Geochronometers

• Choice of radioactive dating method depends on several factors– Age of the sample• T1/2 should be same order of magnitude as rock age so

that there are an adequate number of parent and daughter products to accurately determine ratio

Geochronometers

• Other important factors– Amount of parent and daughter elements present

in the sample• Potassium is an abundant element so K – Ar dating can

be used on most rocks

– Was the system closed?• Was daughter or parent lost or gained by some other

mechanism, e.g.– Radiogenic lead may be deposited with Uranium– Argon can escape until the rock is below the closure

temperature

Rubidium-strontium system

• We cannot assume that all strontium in rocks is due to rubidium decay so we modify the above equation

87 87 ( 1)n

t

ow nowSr Rb e

87 87 87

0( 1)

ow n

t

n owSr Sr Rb e

Rubidium-strontium system

• Four naturally occurring isotopes of strontium– 84Sr: 0.6%, 86Sr: 10%, 87Sr: 7%, 88Sr: 83%

• 86Sr is not a product of radioactive decay so the amount present now should be equal to the amount present when the rock formed (t0)

86 86

0nowSr Sr

Rubidium-strontium system

• Normalize our equation by 86Sr to get

• This is a straight line with slope (eλt-1) and the intercept gives 87Sr/ 86Sr at the time the rock formed.

• Assumes that the initial Sr ratio was the same for all the minerals in rock or for all the rocks in a single location

• The straight line is called an isochron

87 87 87

86 86 86

0

( 1)t

now now

Sr Sr Rbe

Sr Sr Sr

Rubidium-strontium system

• Disadvantages– Rubidium and strontium are mobile– Rubidium does not occur in limestone or

ultramafic rocks

Rubidium-strontium system

• The [87Sr/ 86Sr]0 is an indicator of the rock origin– Rocks derived directly from the mantle will have

an initial ratio of less than .704– Rocks derived from remelting of crustal rocks will

have a initial ratio substantially greater than 0.704

Rubidium-strontium system

• Since t1/2 is much larger than the age of the earth, we can make the approximation for any rock

• Then plotting 87Sr/ 86Sr vs t defines the growth curve

87 87 87

86 86 86

0now now

Sr Sr Rb

Sr Sr Srt

Uranium-lead system

• Three naturally occurring isotopes of uranium– 238U: 99.3%, 235U: 0.7%, 234U: 0.006%– 238U and 235U are used for dating

235

238

238

235

206

238

207

235

207 235 235

206 238 238

1ln 1

1ln 1

1: 1/137.881

now

now

t

t

now now now

Pbt

U

Pbt

U

Pb U e U

Pb U e U

Concordia Diagrams• If a system has been closed to

uranium and lead and a correction is made for initial lead then the isotope ratios will plot on the concordia – an ideal plot of 206Pb/238U vs 207Pb/235U

• If lead or uranium are lost or gained then the ratios will lie along a straight line that intersects the concordia at the time the rock crystallized (t) and when it was disturbed (t’). This line is called the discordia.

U-Pb and Pb-Pb isochrons

238

235

206 206 238

204 204 204

0

207 207 235

204 204 204

0

( 1)

( 1)

t

now now

t

now now

Pb Pb Ue

Pb Pb Pb

Pb Pb Ue

Pb Pb Pb

U-Pb and Pb-Pb isochrons

235

238

235

238

207 204 207 204 2350

238206 204 206 204

0

/ / 1

1/ /

1 1

137.88 1

t

tnow

n wn

t

o

t

ow

Pb Pb Pb Pb U e

U ePb Pb Pb Pb

e

e

• U-Pb isochrons often fail because of extensive uranium loss

• Pb-Pb isochron is a straight line

Th-Pb

• The Th-Pb system can be more successful than U-Pb isochrons because thorium and lead tend to be less mobile than uranium

208 232

208 208 232

204 204 204

0

( 1)

( 1)

t

now now

t

now now

Pb Th e

Pb Pb The

Pb Pb Pb

Argon-Argon

• The argon-argon method depends on bombarding a sample with fast neutrons in a nuclear reactor converting some of the 39K into 39Ar

• Modern technique utilizes a laser to heat individual mineral grains or targeted spots within grains to release the argon after being irradiated.

• 39Ar is unstable with half life of 269 yr

39 39K n Ar p

Argon-Argon

39 39

now nowAr c K

• The amount of 39Ar produce is given by

Ar-Ar

• Now using the equation we derived previously for 40K decay to 40Ar we arrive at the following relations

40 40)

39 39

)

39

4

(

(

0

1( 1)

1

A C

A C

t

now now

t

now

A

A C

A C

A

Ar Ke

Ar c K

e

Jwhere

KJ c

K

Ar-Ar

• If we irradiate a standard sample (sample of known age, ts) at the same time then we can determine J

• And we can now find the age of our sample using

39)

4(

0( 1)A C s

s

t

now

ArJ e

Ar

)40 4(

(

0

)39 39

( 1)

( 1)

A C

A C s

st

t

now now

Ar e Ar

Ar e Ar

http://www.detectingdesign.com/radiometricdating.html

Fission Track Dating• 238U undergoes spontaneous

fission releasing two or three neutrons and a large amount of energy– λs =8.46x10-17 yr-1

– λ =1.55x10-10 yr-1

• Passage of charged particle results in a damage zone along its path or fission track

• Energy below a certain threshold leaves no track so the types of reactions recorded are limited

Fission Track Dating

• 238U can then be considered as undergoing a dual decay mechanism similar to the K-Ar-Ca system

( )238

238 ( )

( 1)

( 1)

s tss now

s

tss now

U e

D U e

D

Fission Track Dating

• Induced fission of 235U can be used to simplify dating problem– Requires bombarding sample with neutrons in a

nuclear reactor235

wI noU nD

Fission Track Dating

• Then taking the ratios we have

238 ( )

235

( 1)

1ln 1

137.88

ts s s

I Inow

s

I s

D NU e

U n D N

and

N nt

N

Fission Track Dating

• A major advantage of fission track dating is that the stability of the tracks is temperature dependent. – Healing of damaged zones is called annealing– Rate of annealing depends on the mineral and

temperature– The temperature history of rock can then be

determined by measuring dates of various minerals within the rock

Spontaneous fission tracks Induced fission tracks

http://www.mnsu.edu/emuseum/archaeology/dating/dat_fission.html

Samarium-neodymium

• T1/2 for 147Sm-143Nd is 106 Gy so this system is good for dating very old rocks– Meteorites and some basalts

• Abundance < 10 ppm• 147Sm/ 144Nd are ~0.1-0.2 in present rock samples• Advantage of this system is that geochemical processes

do not preferentially separate Sm-Nd

143 143 147

144 144 144

0

( 1)t

now now

Nd Nd Sme

Nd Nd Nd

Samarium-neodymium

• [143Nd/ 144Nd]0 gives and indication of the rocks origin similar to the Rb-Sr system– Concentration of 143Nd has increased through time

because of 147Sm decay– Model time dependence of 143Nd/ 144Nd by

assuming the that the ratio in the earth is the same as chondritic meteorites

CHUR model

• CHondritic Uniform Reservoir

143 143 147

144 144 144

0

( 1)

0.512638 0.1967( 1)

t

now now

t

Nd Nd Sme

Nd Nd Nd

e

143 144

0

143 144

0

/

/CHURNd

Nd Nd

Nd Nd

Age of the Earth

• Oldest rocks are found on the cratons – ancient continental cores– Acasta gneisses in Canada – 3962 Ma (U-Pb)– Isua supracrustal rocks in Greenland – 3772 Ma

(Sm-Nd) and 3769 (U-Pb)• So by 4000 Ma continents existed

Age of the Earth

• Meteorites are thought to have common origin with the planets– Chondrites are most common (90%) and contain

chondrules (small glassy spheres of silicate) indicating heating followed by rapid cooling

– Achondrites are crystalline silicates with no chondrules and low metal concentrations

– Iron

Lead Evolution of the Earth

• Holmes-Houtermans model– Assumes that earth quickly differentiated in to

mantle and core then U-Pb ratio changed only as a result of radioactive decay

– Further assumes that lead minerals completely separated from U and Th when formed

235 235

238 238

207 204 207 204

0206 204 206 204

0

/ / 1

137.88/ /

T tnow

T t

now

Pb Pb Pb Pb e e

e ePb Pb Pb Pb

Lead Evolution of the Earth

• Holmes-Houtermans model– Can be used with meteorites because they are

closed system with t=0

• Yields ages of between 4530 and 4570 Ma

235

238

207 204 207 204

0206 204 206 204

0

/ / 1 1

137.88 1/ /

Tnow

T

now

Pb Pb Pb Pb e

ePb Pb Pb Pb