1. Geochronology, radiogenics
Recall the four forces of contemporary physical theory; we have, so-far, explored the geophysics of only two. Now lets look at the two remaining:
Weak: mediates β-decay and β-capture processes
Strong: mediates nuclear fission and α-decay

2. Radioactivity
Radioactivity was discovered in 1896 by the French scientist Henri Becquerel; during his work on the phosphorescence of uranium salts; science now had a method for quantifying the age-history of the Earth, planets and Solar System.
Within a little more than a decade, radioactive decay sequences were being used in geochronological dating. Ernest Rutherford, then at McGill, encouraged B. Boltwood to determine the age of minerals by their lead accummulation in work done partially is what is now the Shulich Physical Sciences and Engineering Library, then the MacDonald Physics Building.

3. Decay modes 40K + e- --> 40Ar + νe
Radioactive decay is spontaneous: generally, we cannot stimulate a radionucleus to decay though the condition of the atom is known or suspected to bear on certain decay modes:
Electron (beta) capture:
26Al + e- --> 26Mg + νe
40K + e- --> 40Ar + νe
The decay rate of these processes is slightly affected by the ionization state of the mother nucleus (e.g. the 40K ) and by the atom's chemical bond state which may be further affected by extremely high pressures.

4. Decay modes - II 40K --> 40Ca + e- + νe 40K --> 40Ar + e+ + νe
Beta, beta+ (positron) decay:
40K --> 40Ca + e- + νe
40K --> 40Ar + e+ + νe
Neutron emission:
13Be --> 12Be + n0
5He --> 4He + n0
5He --> α2+ + n0

5. Decay modes - III 238U --> 234Th + α2+ 235U --> 231Th + α2+
Alpha decay:
238U --> 234Th + α2+
235U --> 231Th + α2+
Spontaneous fission:
235U, 238U --> X Y + (x)n0
Neutron-forced fission:
(x)n U --> X Y + (x)n0

6. Decay modes - IV (x)n0 + 235U --> 90-100X + 130-140Y + (x)n0
Neutron-forced fission products:
(x)n U --> X Y + (x)n0

7. Decay modes - Exotic 151Lu --> 150Yb + p+ + ... (?)
Proton emission (in elements that have been artificially created with major neutron deficits):
151Lu --> 150Yb + p (?)
147Tm --> 146Er + p (?)
Proton decay (The “standard model” of particle physics predicts spontaneous proton decay – never observed):
with a half-life of 1036 to 1040 years!
p+ --> π e
π0 --> 2γ

8. Decay transmutations
Proton number: p+
Neutron number: n0

9. Unstable atomic nuclei

10. Interpreting λ
The decay constant, λ, might best be seen as a “measure” of the probability of decay during some time interval and λ N(t) as the number of decay events per unit time. It is sometimes called the “activity” of the radionucleide.
The Bq (becquerel) corresponds to one decay per second. The activity of one litre of normal seawater is about 12Bq, a human body, about Bq.

11. A generic decay system

12. A generic decay clock
If we know N(t=0), N(t) and the decay constant, λ, and if we know that the system holding our radionuclei is “closed”, this simple equation allows us to determine the passage of time.
A closed system is one in which the decay daughters along with the current mothers are preserved, typically within a crystal or rock mass in the geological context.

13. Decay daughters
The decay daughters may not be distinguishable from any identical isotopes that had existed within our crystal or rock mass at time t = 0 ; i.e., D(t = 0).
Either we need to choose the system under analysis carefully, with D(t = 0) known, or find some redundancy in the radiogenic clock or some other reference in order to establish quantities at time t = 0.

14. Referencing to stable isotopes
Except for promethium, Pm, technicium, Tc, uranium, U, and thorium, Th, all naturally occurring elements have stable isotopes. We may use a stable isotope of the same element as our mother and daughter radiogenic isotopes for reference.

15. 12C is the common stable isotope of carbon.
14C-dating
Cosmic rays convert 14N to 14C in the upper atmosphere:
14N + n0 --> 14C + p+
14C is radioactive with λ = 1.21 x 10-4/yr or t½ = 5730 yr :
14C --> 14N + e + ῡ
12C is the common stable isotope of carbon.

16. 14C-dating - II
At the moment an animal stops metabolising food or a plant stops photosynthesizing, it establishes a 14C/12C ratio of about Very sophisticated systems are required for MS analysis.

17. 14C-dating – III (Calibration)
At the moment an animal stops metabolising food or a plant stops photosynthesizing, it establishes a 14C/12C ratio of about
We know, however, that the cosmic ray excitation of 14N to 14C has varied with time and so the original 14C/12C ratio varied too.
We use tight archeological data correlations and tree-ring data from long-lived Bristlecone Pines and their correlatable now-dead ancestors to calibrate the 14C/12C ratio as a function of time.
Future 14C-dating will have to contend with a special calibration for the very large influx of 14C into the atmosphere caused by the uncontained nuclear weapons testing of the 1950s and 1960s.
Methodology for 14C dating: See this Science Learning Hub description

18. 87Rb --> 87Sr with a half-life of 47.5 x 109 years!
Rubidium-strontium system
For many geological or geophysical purposes, 14C-dating is not very useful because the short 5730-year half-life. Within a period of 10 half-lives, only 0.1% of the original 14C is left for comparison.
We are led to systems with much slower decay rates:
87Rb --> 87Sr with a half-life of 47.5 x 109 years!
86Sr is stable and derives from no other radio-decay, so we develop ratios of the original 87Rb mother and 87Sr daughter to 86Sr:
an equation of a straight line, the “isochron”.

19. Rubidium-strontium isochron
Slope

20. Potassium-Argon dual decay system
40K decays by two modes into 40Ca and 40Ar :
40K --> 40Ca + e- + νe
40K --> 40Ar + e+ + νe
40K --> 40Ca :
λ= 4.96 x 10-10/yr t½ = x 109 yr
λ = 5.81 x 10-11/yr t½ = x 109 yr
40K --> 40Ar :

21. Potassium-Argon dual decay system - II

22. Potassium-Argon dual decay system - III

23. Uranium-lead dating – dual mothers!
238U --> 206Pb + ...
Radium decay series:
λ= 1.55 x 10-10/yr t½ = x 109 yr
Actinium decay series:
λ = 9.85 x 10-10/yr t½ = x 108 yr
We have two internal clocks.
One checks the other!
235U --> 207Pb + ...

24. Uranium-lead decay sequence
Decay chains -- check it out: click here!

25. Uranium-lead concordia diagram

27. Jack Hills zircons suite

28. Counting forward from the beginning:
146Sm - 142Nd
146Sm --> 142Nd + α2+
λ= 6.73 x 10-9/yr τ½ = x 106 yr
Essentially, all the original 146Sm that accreted with the Earth has already transmuted into 142Nd. We may, though, compare rocks according to their 142Nd/144Nd ratios.
The short half-life leads us to conclude that 146Sm became extinct very early in Earth's history. To find rocks with a low 142Nd/144Nd ratio suggests that 146Sm was already depleted in the host and that the rock's host had not “mixed” into the mantle. A low Sm/Nd (all isotopes) ratio for the rock's reservoir argues for a very old reservoir.

29. 4.280 (+53,-81) x 109 yr
“Faux amphibolites”