Homework

1. Homework We made the point the geochronology is thermochronology because of the closure temperature. Give two general examples of rocks that, when dated with radiometric techniques truly record the age of formation and not just cooling.

2. Chronological Organization • 1. Radiogenic isotope chemistry • 2. Diffusion theory • 3. Individual chronometers (a) the standard story, and (b) new developments • 4. Unraveling the thermal history of crustal rocks; • Applications to tectonic/magmatic problems.

3. Nuclear stability • What is an isotope? • What isotopes are stable? • When are they “radioactive”? • How do we quantify decay? • Which systems are useful to geologists?

4. Atoms • Made of protons, neutrons, electrons • Sum of protons and neutrons = mass number • Only certain combinations of proton/neutron numbers are stable in nature;

5. Stability of nuclei as a function of proton (Z) vs. neutron (N) numbers A (mass #)= Z+N

7. Isotopes, isobars, isotones Isotones Isotopes (equal z’s) Isobars- same mass #, A (=N+Z)

8. Not all of these isotopes are stable as they depart from the idealized stability line. The isotopes that are not stable will tend to decay into more stable configurations. Let us look at the element Rb and its various isotopes.

9. Essentially there are only two isotopes that don’t decay away within short time scales, 87Rb and 85Rb. All others are not present in nature. Of these, one is stable (85Rb), and one is radiogenic (87Rb)

10. How do we quantify stable or not? If isotopes decay away within laboratory time scales, that’s a no brainer - they are not stable. Slower decaying species - need to know their: Decay constant or Half life

11. Measuring radioactive decay Half life (t1/2) = the time required for half of the parent atoms to decay, alternatively use: The decay constant () = ln2/t1/2

12. Decay systems of interest for geologists We will examine all of them.

13. Decay - basic mechanisms Alpha decay () - emission of a He (alpha) particle. Resulting isotope has a mass A1=A0-4; e.g. 147Sm decays into 144Nd; Beta decay (aka -) - transforming a neutron into a proton + an electron. Resulting isotope has a mass A1=A0, e.g. 87Rb decays into 87Sr. Electron capture (aka +) is essentially the reverse of 2. E.g. 40K decays to 40Ar; Gamma decay is the process of emitting a high energy photon - no examples in this class.

14. Decay equation Law of decay- the rate of decay of an unstable parent is proportional to the number of atoms remaining at any time t. The proportionality constant is lambda – decay constant - units reciprocal of time.

15. Integrate from 0 to time “t”

16. The # of radiogenic daughter atoms formed (D*) is equal to the # of parent atoms consumed

17. General geochronological equation

18. Example Recall

19. Plotting the decay equation daugther time

20. daugther time

21. Dividing by a stable isotope In practice it is impossible to accurately count isotopes but rather we collect isotopic ratios (see next week’s class). For that reason the decay equations are written as:

22. Example Choose a relatively abundant and easy to measure normalizing isotope

23. Branching decays In some cases, a radiogenic parent A decays to two daughters B and C: BB A C

24. Equations Or in general:

25. Example of branching decay 40K decays into: 40 Ar by electron capture and 40Ca by beta decay Both systems are in principle relevant to geochronology although only K-Ar is widely used

26. Successive decays … 206Pb

27. Equations

28. Homework for next Tuesday Assume you are dealing with a decay scheme in which the parent isotope decays into an intermediate daughter, which further decays to a stable daughter. Solve the equation for the intermediate decay system.

29. In a 2-decay scheme with one decay constant significantly different than the other: Transient equilibrium Secular equilibrium No equilibrium