Radioactive Decay Alpha Radiation – Emission of a helium nucleus Alternatively we write.
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Transcript of Radioactive Decay Alpha Radiation – Emission of a helium nucleus Alternatively we write.
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Radioactive Decay
• Alpha Radiation – Emission of a helium nucleus
• Alternatively we write
235 231 492 90 2U Th He
4 42 2He
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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
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Radioactive Decay
• Gamma Radiation – emission of photons by excited or metastable nuclei
60 60 027 27 0mCo Co
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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
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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
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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
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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
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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
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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
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Rubidium-strontium system
• Disadvantages– Rubidium and strontium are mobile– Rubidium does not occur in limestone or
ultramafic rocks
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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
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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
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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
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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.
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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
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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
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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
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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
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Argon-Argon
39 39
now nowAr c K
• The amount of 39Ar produce is given by
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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
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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
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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
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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
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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
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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
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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
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Spontaneous fission tracks Induced fission tracks
http://www.mnsu.edu/emuseum/archaeology/dating/dat_fission.html
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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
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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
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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
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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
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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
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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
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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