The Geologic Time Scale (from the Geological Society of America); this is the same one that I handed out in class. You will be responsible for the following information:

• all the eras - Precambrian, Paleozoic, Mesozoic, and Cenozoic;
• all the periods - Cambrian, Orodovician, Silurian, Devonian, Carboniferous (Mississippian, Pennsylvannian), Permian, Triassic, Jurassic, Cretaceous, Tertiary, and Quaternary;
• epochs of the Cenozoic - Paleocene, Eocene, Oligocene, Miocene, Pliocene, Pleistocene, and Holocene;
• and the following dates:
• 543 Ma - Precambrian/Paleozoic boundary
• 248 Ma - Paleozoic/Mesozoic boundary
• 65 Ma - Mesozoic/Cenozoic boundary
• 1.8 Ma - Tertiary/Quaternary boundary
• 10 ka - Pleistocene/Holocene boundary

*In millions of years before the present

The University of California at Berkeley's Museum of Paleontology has an excellent web page concerning the geologic time scale and its organization and development.

The question you should now ask, is how exactly did geologists develop the time scale and how did they assign the dates to the various subdivions.

Geologists and paleontologists divided the Earth's geologic history into sections that had similar life forms and the breaks between divisions were based on major changes in life. Most of the divisions were made during the late 1800s. The bounding dates, however weren't added until much later - after the advent of radiometeric age techniques.

As mentioned during the first lecture or two, there are several different radiometric age dating techniques that can be used. All of these techniques rely on the fact that unstable isotopes of elements will decay at constant rates. Measuring the quantities of the radioactive element (the parent or the one that decays) and the stable end-product (the daughter), as well as knowing the decay factor, allows geologist to calculate the age of the material.

Isotope: a form of an element which has the same number of protons and electrons in it, but a different number of neutrons.

E.g., all isotopes of carbon have 6 protons and 6 electrons. The various isotopes have different numbers of neutrons giving rise to the various isotopes, C¹², C¹³, and C¹⁴ which have different atomic mass.

Isotopes are either stable (they do not spontaneously decay) or unstable (they will spontaneously decay by some type of nuclear decay process). C¹², which is stable, comprises 98.89% of all carbon; 1.11% of all carbon is stable C¹³; the remain trace amount of carbon is radioactive (unstable) C¹⁴ which is produced high in Earth's atmosphere when N¹⁴ gains one neutron after being hit by cosmic rays. The free C¹⁴ is quickly combined with oxygen to form CO₂ which is used in respiration and food uptake by all organisms.

The C¹⁴ is unstable and will spontaneously break down into N¹⁴ and release energy. This relationship between unstable parent isotope and stable daughter occurrs at a specific rate. For the C¹⁴ decay scheme, this happens once every 5730 years. This constant decay is known as the half-life of the isotope. Different unstable isotopes have different half-lives that are constant for that particular isotope.

1. C¹⁴: Living organisms continually exchange carbon with the atmosphere through the process of photosynthesis. When the organism dies, however, exchange of carbon ceases and the carbon present in the organism becomes isolated. This event (death of the organism) marks the effective starting of the C¹⁴ clock. One of the most common types of material used in C¹⁴ dating is charcoal (e.g., trees burned during a volcanic eruption).
2. Igneous Rocks:  These rocks form by the cooling and crystallization of magma or lava.  As cooling proceeds crystals grow. A growing crystal may trap small amounts of a radioactive isotope within its structure. When this occurs, the radioactive atoms become effectively isolated or trapped. Subsequent disintegration will produce daughter atoms replacing the original radioactive parents. Consequently, the process of cooling and crystallization starts the clock for igneous rocks. In many respects, igneous rocks are the easiest to date because the starting of the clocks are unambiguous.
3. Sedimentary Rocks: Sedimentary rocks are, to a large degree, made from fragments of pre-existing rocks that have been broken, weathered, transported and ultimately deposited in ocean basins. These fragments (e.g., sand or mud) may become cemented together to form sedimentary rocks. The original source for the sediment may have been diverse, consisting of different rock types of different ages. Consequently, a sedimentary rock such as a sandstone or a shale is likely to consist of framgents of different age. Radiometric dating of sedimentary rocks is, therefore, not common.
4. Metamorphic Rocks: These rocks typically form in deep levels of the crust, and consist of minerals that have formed in response to increasing temperature and pressure. If a new mineral grows in a metamorphic rock, and if that mineral incorporates radioactive isotopes in its crystal structure, then dating of that mineral can provide an estimate of the time of mineral growth (metamorphism). Most metamorphic rocks are very complex, and many have undergone several episodes of metamorphism and/or mineral growth over protracted periods of time. Radiometric dating of metamorphic rocks can be successful, but often the results are difficult to interpret, and in many cases are ambiguous.

A constant-rate process such as radioactive decay is described by the simple equation:

where N is the number of radioactive parent atoms present, t is time and l (Greek lambda) is the radioactive decay constant (a number defining the probability that an atom will spontaneously decay in a given time period). In order to use this equation for decay over a given time period, we simply integrate from t = 0 to t, and from N₀ to N (N₀ gives the number of parent atoms at time zero). Integrating, we have:

The equation above is known as the decay equation. It shows that at any time t, the number of parent atoms, N, is equal to the number of original parent atoms at time zero, multiplied by the natural exponent raised to the negative power of the decay constant (l) multiplied by the time (t).

The decay equation can be used to show the relationship of the decay constant l to the half-life of any unstable isotope. To do this we simply substitute (in the decay equation) t = t_1/2 and N = N₀/2:

Okay, so now that we know the decay equations, how do we date a rock?

The decay equation shown above constitutes the basis for determining the absolute ages of appropriate rocks and/or minerals. I use the term "appropriate" in the sense that the specimen to be dated must obviously contain isotopes of a well known radioactive decay series, and be suitable for precise chemical analysis. In the simplest ideal situation,the decay equation is utilized by making the following substitutions:

P = N (# of parent atoms currently present as measured in the lab)

P₀ = N₀ (# of original parents at time zero) Note that this is an unknown

D = P₀ - P (# of daughter atoms present as measured in the lab)

If we assume for the moment (more on this later) that no daughters were present at time zero, then:

P₀ = P + D and:

which can be arranged as:

Therefore, if we know the decay constant (l) and can accurately measure D and P, in principle, we can determine the absolute age.

Accurate measurement of either the absolute or relative abundance of trace quantities of radioactive isotopes requires sophisticated instruments, known as mass spectrometers, and instrument operators who really know what they are doing. The technique appears to be simple and straightforward, but is actually very difficult and time-consuming. Depending on the system and the specimens, reliable age determinations can take months to be made and can cost up to $1,000. It is not a trivial task!

The simplified application of the decay equation presented above, bases age determinations on measurement of the ratio of parent:daughter isotopes. The fundamental assumption in this simplified approach is that there existed no daughter atoms at the time the radiometric clock started. This assumption is in many cases not valid, as daughter atoms certainly existed in the mineral or rock at the time the radiometric clock started. The solution to this problem can be illustrated using the Rubidium (Rb) - Strontium (Sr) system.

Rubidium exists as stable Rb⁸⁵ and unstable Rb⁸⁷. Rb⁸⁷ decays to Sr⁸⁷ by beta decay (same as C¹⁴), with a half-life of 50Ga. Strontium has four isotopes [Sr⁸⁴, Sr⁸⁶, Sr⁸⁷ and Sr⁸⁸]. Sr⁸⁷ in a given rock may have been produced by the decay of Rb⁸⁷ or it may have been present initially as part of the total Sr incorporated before any radioactive decay.

With Sr⁸⁷ as the daughter and Rb⁸⁷ as the parent, the decay equation presented above is:

If some Sr⁸⁷ was initially present, the total amount of Sr⁸⁷ present is given by the following:

The solution around the problem can be attained by using ratios, instead of absolute abundance:

The figure to the left shows such an example of using the ratios of Sr⁸⁷/Sr⁸⁶ and Rb⁸⁷/Sr⁸⁶. The rock dated is from the Apollo Lunar mission, as is a basalt from a Mare basin. Three minerals were analyzed - ilmenite (Ilm), pyroxene (Px) and plagioclase feldspar (Plag). In addition the whole rock (WR) was analyzed. All four point fall on a straight line known as an isochron (meaning same age). The intercept on the Y axis gives the initial ratio of Sr⁸⁷/Sr⁸⁶. The slope of the isochron is given by (e^-lt -1), and from this slope the age is determined to be 3.09Ga.

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Last updated 22 February 2000

John Stimac (cfjps@eiu.edu)