Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology
Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.
-
Upload
crystal-revill -
Category
Documents
-
view
220 -
download
4
Transcript of Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.
![Page 1: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/1.jpg)
Ge 11a, 2014, Lecture 3Radioactivity and quantitative geochronology
![Page 2: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/2.jpg)
Radioactive decay
Marie Skłodowska-CurieExplored spontaneous radioactivityShockingly dangerous chemical separations to isolate and study heavy radioactive elementsMajor innovator of radiological medicine
First woman to Win a Nobel prize (physics) Win another Nobel prize (chemistry) (first human to win two…) Teach at the Sorbonne Be enshrined in the Paris Pantheon
Trained in Poland’s underground ‘Flying University’Transformative figure in women’s +minority’s rights
Antoine Henri BecquerelDiscovered spontaneous radioactivity
Ernest Rutherford, 1st Baron Rutherford of NelsonSynthesis of radioactive decaCreated experimental nuclear physicsFirst dates of geological materials
![Page 3: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/3.jpg)
• Rutherford recognized three types of radioactivity:
emits mass but no charge (4He nucleus)
emits charge but no (observable) mass (electron or positron)
emission has neither charge nor mass (high-frequency radiation)
• Realizes radiactivity has two key properties:- exothermic- some forms emit particles (a = 4He) that might accumulate as record
of the passage of time
• Postulates that rate of emission is independent of environment, history, etc. It is intrinsic & probabilistic.
The most well reasoned forms of creation science question this hypothesis. They are right to do so (though all experiments and nuclear theories to-date suggest it is a good approximation in geological environments)
![Page 4: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/4.jpg)
If rate of emission is invariant w/ time or setting, then radiation can serve as a clock:
- dN/dt = N
Constant of proportionality; now called ‘decay constant’
1/ = ‘mean life’ln2/ = ‘half life’
(a miracle of integration occurs)
N = N0e-t
For and radiation, nothing lasting is produced (at least, nothing detectable by 1900-era scientists). But particles accumulate in a measurable way:
Define ‘D’ as number of ‘daughter’ particles
D = D0 + D*D* = N0 - ND = N0(1-e-t) + D0 = N (et-1) + D0
![Page 5: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/5.jpg)
![Page 6: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/6.jpg)
Re-arrange decay equation to make time the dependant variable:
ln {[ (D-D0)N
] +1}
t =
Pick mineral with no structural He; D0 = 0
Radiation counting in lab
Pick mineral w/ stoichiometric Parent element (e.g., UO2), soN depends only on mass
With correct choice of sample, t depends only on D - the amount of He trapped in the mineral lattice
![Page 7: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/7.jpg)
Rutherford’s chronometer
Pitchblende, or U ore, rich in UO2
U ~ 1.5x10-10
U 8
Time (yrs) moles He cc STP1000 5x10-9 1x10-4
1 million 5x10-6 0.110 million 5x10-5 1.01 billion 5x10-3 100
1 gram of UO2
Found African pitchblende is ca. 500 million years old
Problems:• Sensitivity and precision of manometric measurements• Reaction is not fully described. U weighs ca. 238 g/mol; 8 He nuclei only 32 g/mol. Where is the rest of the mass!• He is not well retained by crystals
![Page 8: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/8.jpg)
Breakthrough: Aston’s positive ray device
![Page 9: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/9.jpg)
Ions are passed through a magnetic field oriented orthogonalTo their direction of motion. Ions are deflected with a radius of curvature set by the force balance between the magnetic field (qv x B) and the centripital force (mv2/r). That is, r = mv/(qB)
If energy is of all ions is equal, this acts as a mass filter.
High momentum(high mass)
Low momentum(low mass))
![Page 10: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/10.jpg)
Intensity
Strength of B field
![Page 11: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/11.jpg)
Finnigan TritonA modern thermal ionization mass spectrometer
Ion source
Collectors (faraday cupsand/or electron multipliers)
Momentum analyzer (electro magnet)
![Page 12: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/12.jpg)
Advances stemming from mass spectrometry• Precision improves from ca. ±1 % to ca. ±10-5
• Recognition of isotopes permits the definition of decay reactions
Zprotons + Nneutrons = Amass
decay: Z + N (Z-2) + (N-2) + 4He + + Qe.g., 238U 234Th + 4He; = 1.55x10-10
147Sm 143Nd + 4He; = 6.5x10-12 yr-1
decay: Z + N (Z+1) + (N-1) + e- + + Qe.g., 87Rb 87Sr + e-; = 1.42x10-11 yr-1
decay: Z + N (Z-1) + (N+1) + e+ + + Qe.g., 18F 18O + e+; = 3.3x103 yr-1
Most geological ‘chronometers’ depend on and decay
e.g., 14C 14N + e-; = 1.2x10-4 yr-1
![Page 13: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/13.jpg)
![Page 14: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/14.jpg)
Mass spectrometry is best at measuring relative abundances of isotopes. This motivates an additional change to age-dating equations:
D = Daughter (4He; 87Sr; 143Nd)N = Parent (238U; 87Rb; 147Sm)S = Stable (3He; 86Sr; 144Nd)
The ‘stable’ nuclide is always a non-radioactive, non-radiogeneicisotope of the same element as the ‘Daughter’ nuclide.
D = N (et - 1) + D0
D/S = N/S (et - 1) + D0/S
This is the equation for a line in the ‘isochron’ plot
Y-axis value
X-axis value
Y-interceptSlope
![Page 15: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/15.jpg)
D/S
N/S
D0/S
m = et - 1
Measured composition of object
Three strategies for use:• Measured objects known to have D0/S ~ 0• Assume or infer D0/S from independent constraint• Define slope from two or more related objects, yielding both age (t) and D0/S as dependent variables. These objects must be of same age, have started life with identical D0/S, but differ significantly in N/S
The anatomy of the isochron diagram
![Page 16: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/16.jpg)
A common example:the Rb-Sr chronometer applied
to granite
Isotopes of Sr:84Sr: 0.56 %86Sr: 9.87 %87Sr: 7.04 %88Sr: 82.53 %(all values approximate)
Sr: typically a +2 cation; 1.13 Å ionic radius (like Ca: +2, 0.99 Å)
Isotopes of Rb:85Rb: Stable87Rb: Radioactive: l = 1.42x10-11 yr-1;- decay
85Rb/87Rb in all substances from earth and moon assumed = 2.59265
Rb: typically a +1 cation; 1.48 Å ionic radius (like K; +1, 1.33 Å)
![Page 17: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/17.jpg)
Isotopes of Nd:142Nd: 27.1 %143Nd: 12.2 %144Nd: 23.9 %145Nd: 8.3 %146Nd: 17.2 %(147Nd: 10.99 d half life)148Nd: 5.7 %150Nd 5.6 %(all values approximate)
Isotopes of Sm:144Sm: 3.1 %(146Sm: 108 yr half life)147Sm: 15.0 % (1.06x1011 yr half life)148Sm: 11.2 %149Sm: 13.8 %150Sm: 7.4 %(151Sm: 93 year half life)152Sm 26.7 %154Sm: 22.8 %(all values approximate)
The Sm-Nd chronometer
![Page 18: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/18.jpg)
The ‘rare earth’ elements
Nor
mal
ized
abun
danc
e Plagioclase
Pyroxene
Garnet
![Page 19: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/19.jpg)
A fragment of the chondritic meteorite, Allende
![Page 20: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/20.jpg)
A thin section of the chondritic meteorite, Allende
![Page 21: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/21.jpg)
![Page 22: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/22.jpg)
![Page 23: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/23.jpg)
"There is one independent check on the age of the solar system determined by radioactivity in meteorites. Detailed theoretical studies of the structure of the sun, using its known mass and reasonable assumptions about its composition, indicates that it has taken the sun about five billion years to attain its present observed radius and luminosity.”
W. Fowler
Comparison with a modern ‘Kelvinistic’ argument:
Summary of typical stellar lifetimes, sizes and luminosities
![Page 24: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/24.jpg)
14C decay: The basis of most ages for geologically young things
14C is produced in the atmosphere: 14N + n = 14C + p
Cosmic-ray fast neutrons
Undergoes beta-decay with a half-life of 5730 yrs: 14C = 14N + e-
= 1.209x10-4 yr-1
Age (yrs) = 19,035 x log (C/C0) [ or …’x log (Activity/Activity0)’]
Key for application is assumption of a value of C0, which depends on14C/12C ratio in atmosphere
Real applications require correction for natural isotopic fractionation (e.g., during photosynthesis) and must consider variations in production rate with time and isotopic heterogeneity of surface carbon pools
![Page 25: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/25.jpg)
The ‘bomb spike’
Natural heterogeneity: 14C ‘ages’ of deep ocean water
![Page 26: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/26.jpg)
Variation in atmospheric 14C/12Cthrough time due to natural processes
∆14C = (Ri/R0 -1)x1000
Where Ri = 14C/12C at time of interest
R0 = 14C/12C of pre-1890 wood projected forward to 1950 (?!?&*!)
![Page 27: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/27.jpg)
Using 14C to reconstruct earthquakerecurrence intervals
![Page 28: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/28.jpg)
The U-Pb system and the age of the Earth
238U = 206Pb + 8x4He = 1.55125x10-10 (4.5 Ga half life)235U = 207Pb + 7x4He = 9.8485x10-10 (0.7 Ga half life)
204Pb is a stable isotope238U/235U is (nearly) constant in nature = 137.88
206Pb204Pb
207Pb204Pb
207Pb0
204Pb
206Pb0
204Pb
238U204Pb
235U204Pb
(et - 1)
(et - 1)
= +
= +
207Pb204Pb
207Pb0
204Pb206Pb204Pb
206Pb0
204Pb
-
-=
1
137.88
(et - 1)(et - 1)
![Page 29: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/29.jpg)
![Page 30: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/30.jpg)
![Page 31: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/31.jpg)
K-Ar dating
40K
40Ca 40Ar88.8 % 11.2 %
e- capture; e = 0.581x10-10 yr-11e- emission; = 4.982x10-10 yr-1
40Ar = e/40K(et-1) + 40Ar0
= e + = 5.543x10-10 yr-1
0.01167 % of natural K
![Page 32: Ge 11a, 2014, Lecture 3 Radioactivity and quantitative geochronology.](https://reader035.fdocuments.net/reader035/viewer/2022062516/56649d835503460f94a689f7/html5/thumbnails/32.jpg)
Some ‘closure temperatures’ w/r to K/Ar dating:
Amphibole: 500 to 700 ˚C
Biotite: 300 to 400 ˚C
K-feldspar: 200-250 ˚C