1. Figure 9.14: Geologists determine the ages of rocks using the principles of radioactivity. Certain elements like uranium, radium and other elements are unstable and have the tendency to spontaneously disintegrate, forming an atom of a different element and emitting radiation in the process.

2. Figure 9.14: It was discovered around the turn of the century that unstable nuclei called parent isotopes decayed to daughter isotopes through the process of radioactive decay. The decay is accompanied by emissions of radiation that occur in one of three forms: alpha particles (helium), beta particles (free electrons) and/or gamma rays (similar to x-rays).

3. There are three types of radioactive decay:

(a) alpha emission: loss of two protons and two neutrons. The atomic number of the isotope is decreased by two and the atomic weight is decreased by four.

(b) beta emission: neutron is converted into a proton through emission of a beta particle(electron). The atomic number increases by one, but there is no change in the atomic weight.

(c) electron capture: proton is converted into a neutron through the capture of an electron. The atomic number decreases by one, but there is no change in the atomic weight.

4. Radioactive decay is a statistical event based on the probability of decay. Observations of many emission events from many atoms of a particular nuclear species over an extended period provide a statistical average rate at which certain elements decay.

5. The rate of radioactive decay is measured in terms of half-life, or the time required for one-half of a given amount of any particular nuclear species to decay.

6. Figure 9.15: The rate of decay of parent isotopes is not constant but is greatest early in the decay history when the system contains the largest number of parent isotopes. Afterwards, the decay rate gradually decreases with time as fewer and fewer parent isotopes remain.

7. A newly-crystallized mineral starts out with a certain number of parent isotopes in its crystal matrix. Soon afterwards, parent isotopes within the mineral start to decay. For each parent isotope that decays, a daughter isotope takes its place. Over time, the number of parent isotopes decreases while the number of daughter isotopes increase. If none of the isotopes escape the mineral, the age of the mineral, and rock within which it is contained, can be determined by comparing the number of daughter isotopes to the number of initial parent isotopes. The greater the number of daughter isotopes relative to the number of initial parent isotopes, the older the mineral.

8. Table 9.1: The rate (half life) at which a radioactive element decays depends on the element.

9. Table 9.1: The half-lives of different parent isotopes vary greatly. The longer the half-life, the older the minerals must be in order to be effectively dated. U-Pb and Rb-Sr have long half lives and therefore are only applicable to the dating of rocks and minerals older than 10 m.y. (younger minerals did not have time to acquire sufficient numbers of daughter isotopes to be detected using these elements).

10. Carbon 14, on the other hand, has a relatively short half-life and is therefore useful for dating materials younger than 80,000 years.

1. Minerals in a rock can be separated from one another and analyzed individually (e.g. plagioclase can be analyzed separately from biotite). The age obtained from analyzing individual minerals in a rock may indicate the time when the minerals first crystallized from magma. This method of isotopic dating of minerals can therefore determine the crystallization age of an igneous rock.

2. When a parent isotope decays to its daughter, the daughter remains in the same lattice site within the crystal structure of the mineral. Often, the daughter doesn’t fit as well into the lattice site formerly occupied by the parent and therefore has a chance of being expelled.

3. Table 9.1: The Potassium-Argon (K-Ar) method of dating is especially prone to escape of the daughter isotope since the K parent is a metal whereas daughter Ar is a gas. Argon will escape if the mineral has been reheated after initial crystallization through burial or metamorphism to temperatures exceeding 150-200 ^oC.

4. As a result, a mineral may have its isotope clock reset by a metamorphic event that causes escape of the daughter isotopes into the surrounding rock matrix. Following closure of the mineral system after the metamorphic event, daughter isotopes will again accumulate in the mineral. The age given by the mineral therefore dates the last metamorphic event rather than the age of initial crystallization from magma.

5. Often this problem can be solved by crushing and analyzing the whole rock rather than analyzing individual minerals separately. If the rock only experienced a reheating event and was not extensively metamorphosed, than it may still contain the older daughter isotopes in the matrix, even though these isotopes have escaped the individual minerals. In this case, whole rock analysis can provide the initial crystallization age.

6. Ages obtained from individual minerals will therefore date the last metamorphic event. In the event that no metamorphism occurred, mineral ages will coincide with whole-rock ages and both will give the age of initial crystallization of the rock.

7. It’s best to analyze more than one isotopic series in a rock to constrain whether the ages represent crystallization or metamorphic dates.

1. In general, clastic sedimentary rocks do not give meaningful ages because the minerals contained in these rocks were derived from other sources. At best, detrital minerals can only provide the ages of their original source rocks.

2. Direct isotopic dating of a sedimentary rock is only possible if it contains an authigenic mineral (e.g. glauconite or K-feldspars) that crystallized in the environment of deposition.

3. The ages of sedimentary rock packages can be bracketed by dating underlying and/or overlying igneous and metamorphic rocks, inter-layered volcanic ash deposits and cross-cutting dikes.

1. Igneous rocks can provide an approximate crystallization age using whole rock analyses. Minerals also provide a crystallization age provided the rocks have not experienced subsequent metamorphism.

2. A metamorphic rock can provide an age for the last metamorphic event. If the rock experienced more than one episode of metamorphism, then usually only the most recent event can be dated.

3. In general, clastic sedimentary rocks do not give meaningful ages because the minerals contained in these rocks were derived from other sources. At best, detrital minerals can only provide the ages of their original source rocks.

4. Isotopic dating of a sedimentary rock is only possible if it contains an authigenic mineral (e.g. glauconite or K-feldspars) that crystallized in the environment of deposition.

5. The ages of sedimentary rock packages can be bracketed by dating underlying and/or overlying igneous and metamorphic rocks, inter-layered volcanic ash deposits and cross-cutting dikes.

Figure 9.13: Geologic Time Scale.