1. RADIOGENIC ISOTOPES

2. AT THE HOME FOR OLD ATOMS…Al
Willy

3. HISTORY OF RADIOMETRIC DATING
1896 Henri Becquerel discovers that uranium is radioactive
1898 Marie Curie discovers that thorium is radioactive
1902 McGill University professor, Ernest Rutherford discovers law of radioactivity with PDF Frederick Soddy - dates uraninite from He content.
1907 Bertram Boltwood provide first U-Pb dates, 535 to 2,200 Ma

4. HISTORY OF RADIOMETRIC DATING
1911 Arthur Holmes publishes chemical U-Pb ages of rocks within 20% of modern values. Estimates age of Earth at 3.3 Ga
1919 Francis Aston invents the mass spectrometer
Alfred Nier lays foundations of modern U-Pb isotopic geochronometry.
1953 Clair Patterson measures
the primeval Pb in the Cañón Diablo meteorite and determines the modern age of the solar system 4.55 Ga.

5. STABLE AND RADIOGENIC ISOTOPES

6. BETA DECAY Radionuclides with excess neutrons undergo beta-minus decay
Proton + β- + v
Radionuclides with neutron deficiency undergo beta-plus decay
Proton
Neutron + β+ + v;
Proton + e-
Neutron + v

7. ALPHA DECAY
Spontaneous emission of a nuclear particle comprising 2 neutrons + 2 protons, i.e., a helium nucleus A P
D + He + Q
A - 4
Z - 2 4 2 Z
238
Th + He + Q
234 90 4 2 U 92

8. THE URANIUM-238 DECAY CHAIN

9. LAW OF RADIOACTIVITY dN - = λN dt20 40 60 80
100
120
140 2 4 6 8 10
Time, hours λN
λN0
λ =
Ernest Rutherford, McGill Professor of Physics,
Nobel, 1908
Frederick Soddy, McGill post-doctoral fellow
Nobel, 1921
Decay of 24Na; λ is the decay constant

10. LAW OF RADIOACTIVITY dN dt = λN - Ln N = - λt + C Ln N = - λt + Ln N0
Integrating we obtain or N0 N
Ln ( )
= - λt
N = N0e-λt or
Mass of daughter + parent equals initial parent isotope mass
D + P = N0 or D = N0 - P
P = N0e-λt and P/N0 = e-λt or N0/P = eλt and N0 = Peλt
D = Peλt – P
D = P(eλt – 1) and P = D/(e-λt – 1)

11. THE CONCEPT OF HALF-LIVES
= N0e-λt N0 2
1/2 N0 1
N = N0e-λt, ,
= e-λt ,
= e-λt
2N0
1/2 2
1/2
Ln1 – ln2 = -λt1/2 and ln2 – ln1 =λt1/2
t =
1/2
ln2 λ
and

12. DECAY CONSTANTS AND HALF-LIVES
Parent
Daughter
T1/2 (Years)
λ (Years-1)
40K
40Ar
1.19x1010
5.81x10-11
40k
40Ar + 40Ca
1.25x109
5.543x10-10
87Rb
87Sr
4.88x1010
1.42x10-11
147Sm
143Nd
1.06x1011
6.54x10-13
176Lu
176Hf
3.57x1010
1.94x10-11
187Re
187Os
4.56x1010
1.52x10-11
238U
206Pb
4.468x109
x10-10
235U
207Pb
7.038x108
9.8485x10-10
232Th
208Pb
1.4010x1010
4.9475x10-11

13. THE K-Ar METHOD
40K decays to 40Ar by electron capture: 40K + e-  40Ar
40K decays to 40Ca by β- decay: 40K  40Ca + β- + v
40Ar = (λe/λ)40K(eλt – 1)
λe is the decay constant for electron capture and λ is the total decay constant
K-Ar dates on biotite from gneisses in the Grenville province,
Canada

14. AGE DATING AND ISOCHRONS
The isochron method depends on the idea that both radiogenic and non-radiogenic daughter isotopes (Di) are initially present.
D + P= Di + N0
P = N0e-λt
N0 = Peλt
P/N0 = e-λt
N0/P = eλt
D = Di+ N0 – P D = Di + P(eλt – 1)
Divide through by mass of stable daughter (SD) to avoid sample dependence by converting to ratios. The method requires multiple samples and assumes that the system is closed
(D/SD)t = (D/SD)0 + (P/SD)t (eλt – 1)
t = 1 λ ln
(D/SD)2 – (D/SD)1
(P/SD)2 – (P/SD)1

15. ( ) THE Rb-Sr ISOCHRON 87Sr/86Sr = (87Sr/86Sr)0 + 87Rb/86Sr(eλt - 1)a b c a1 b1 c1 t1 to
86Sr
87Sr
87Rb o ( )
87Rb
t = 1 λ ln
(87Rb/ 86Sr)t + (87Sr/ 86Sr)t – (87Sr/86Sr)0
(87Rb/ 86Sr)t

16. SECULAR VARIATION OF 87Sr/86Sr IN MARINE CARBONATES
Mountain Building
Seafloor Spreading

17. INITIAL 87Sr/86Sr RATIOS ACROSS THE ANDES
Initial 87Sr/86Sr ratios of andesites as a function of K-Ar determined age across the Andes
87Sr/86Sr increases from west to east, i.e. from trench to sub-continent, indicating increasing contribution of continental crust to magmas

18. URANIUM-LEAD GEOCHRONOLOGY
U and Th decay to stable isotopes of Pb (238U 206Pb, 235U  207Pb, and 232Th 2O8Pb). There is also a fourth stable isotope is 204Pb (common lead)
206Pb/204Pb = (206Pb/204Pb) U/204Pb(eλt-1)
207Pb/204Pb = (207Pb/204Pb) U/204Pb(eλt-1)
208Pb/204Pb = (208Pb/204Pb) Th/204Pb(eλt-1)
Problem: Most ages are discordant due to loss of Pb and gain or loss of U
Solution: Combine 238U and 235U decay equations and relate discordant ages to hypothetical concordant ages. 206Pb* and 207Pb* take into account the initial lead.
206Pb* = 238U (eλt -1) and 206Pb*/238U = eλt-1
207Pb* = 235U(eλt -1) and 207Pb*/235U = eλt-1

19. CONCORDIA DIAGRAM 206Pb*/238U = eλt-1 207Pb*/235U = eλt-1 Zircon
Crystallization age
Discordia
Concordia
U gain
Pb loss
Hudsonian Orogeny
U loss
Zircon

20. ELECTRON MICROPROBE DATING (U, Th, Pb) DATING OF MONAZITE
ThO2
UO2
PbO
Age
Y2O3

21. DATING USING COSMOGENIC RADIONUCLIDES
Isotopes created by interaction of cosmic rays with
Stable atoms of atmosphere 14N + n  12C + 3H
14N + n  12C + 3H
Formation
Decay
3H  3He + e- + v
n + 14N  14C + p
14C  14N + e- + v
10Be - Spallation of N, O and Si
26Al  26Mg + β+ v
10Be  10B + e- + v
26Al - Spallation of Ar and Si
Nuclide
T1/2 (Years)
λ (Years-1) 3H
12.26
5.653x10-2
10Be
1.5x106
4.62x10-5
14C
5,730
1.209x10-4
26Al
7.16x105
9.68x10-7

22. RADIOCARBON (14C) DATING
n + N C + p 7 6
C N + v + e β 14 6 7 _
14C/12C = (14C/12C)0e-λt
t = ln λ 1
14C0
14C

23. 10Be AS A PROXY FOR SOLAR ACTIVITY
Low solar activity correlates with higher10Be production and thermal minima. Data from arctic/antarctic ice cores
Sporer
Maunder
Dalton
Little Ice Age