<p> Name______</p><p>GES 4 Extinction of the Dinosaurs: An Introduction to the Study of Earth History</p><p>Activity 5: Absolute Dating</p><p>OBJECTIVES Upon completion of this exercise students will be able to:</p><p>1. Model the statistics used to date rocks with the decay of radioactive isotopes. 2. Distinguish which decay schemes are most effective for dating different kinds of materials. 3. Correlate relative time boundaries established by the fossil record with absolute dates.</p><p>MATERIALS Pencil, paper, graph paper, straight edge, bucket, dice</p><p>INTRODUCTION</p><p>You may remember from an introductory chemistry class that several elements that occur on earth have more than one isotope. That is, although the number of protons and electrons which define the element are constant, the number of neutrons in an atom of that element can vary to a limited extent. For example, the element carbon (C), has three isotopes: 12C, 13C and 14C.</p><p>Some naturally occurring isotopes are radioactive – that is they spontaneously decay (e.g. lose one or more protons, neutrons or electrons) into a more stable form, either a different isotope of the same element, or a new element. What is useful about these isotopes is that the rate at which they decay is constant, and that rate is measureable. Therefore, if a geoscientist knows how much of a radioactive isotope (or parent isotope) is present in a rock, as well as the amount of the isotope that is produced (or daughter isotope) from radioactive decay of the parent, and finally the rate at which that decay occurred, they can calculate the age of that rock. Although several complexities can arise with this method in the real world, the mathematics behind the process is fairly straightforward and will be addressed in the first part of this lab. You will then take advantage of your new expertise on radiometric dating to solve some geologic problems.</p><p>1. A thought exercise on probability</p><p>Imagine flipping 100 coins – how many would you expect to be heads? Why is that?</p><p>1 If you were to remove all the coins that were tails, and then re-flip all the coins that were heads how many coins would you expect to have that were showing heads this time??</p><p>You could mentally (or physically) repeat this process several times, and see that the number of coins you would flip in each iteration should be about half the number of coins you flipped in the last iteration. This is because the probability of flipping a head is .5 (or you have a 50% chance of flipping a head). If these coins were radioactive isotopes, the coin would be the parent isotope, the tail coins (those you no longer flip) would be the daughter isotopes, and the decay rate, or the half-life of this isotope would be one flip.</p><p>Now we are going to actually try another, more complex, simulation of radioactive decay in order to calculate the half-life.</p><p>2. Radioactively decaying dice</p><p>In a group of 3 or 4, take one of the buckets from the front of the class containing a large number of dice. CAREFULLY pour your dice out on the table and count how many you have. This is the number of starting parent isotopes you have in your geologic system (the bucket). Record your parent number here ______.</p><p>Follow the directions below carefully and record your results on the page provided.</p><p>1. Place all of your parent dice in the bucket. </p><p>2. Shake somewhat vigorously, and again CAREFULLY pour your dice out on the table.</p><p>3. Remove all the dice that have a 1 showing on top (these are your daughter isotopes).</p><p>4. Count the number of daughter isotopes you removed, and record that in your table.</p><p>5. Count the number of parent isotopes you have remaining and also record this in your table, in the column for the next roll.</p><p>6. Repeat steps 1 through 5 twenty-five times, or until you run out of dice.</p><p>Once you have finished your experiment and recorded your data, make a graph of number of parent dice relative to the role number. Then, upload your data into Coursework, in the “Activity 5” section, with the members of your group listed. When the entire class has uploaded their data, make another graph, similar to your first using the combined class data, and answer the following questions. </p><p>2 Roll # Number of Parent dice Number of Daughter dice 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25</p><p>What is the half-life of your dice (e.g. how many rolls should it take to end up with half the parent dice that you started with)? Calculate this based on the probability of rolling a daughter cell (P = 1/6), on any given roll. Also, look at your class data set – is the half-life shown in your graph the same as the one you calculate?</p><p>3 Compare your data to the class data. Is it similar? If not, why not? When calculating your half-life which of these data sets would be better to use and why?</p><p>Say you find an outcrop of granite containing a radioactive element with the same half- life as your dice. You perform a careful chemical analysis and find that the ratio of parent to daughter atoms is 6:94. How old is this rock in terms of half-life (how many half-lives has the parent undergone?), and in terms of iterations of dice-rolls? Remember to start by determining the original number of parent atoms.</p><p>3. Geochronology: the absolute dating of rocks</p><p>Geochronology is a subdiscipline within geology that deals with the absolute dating of rocks and minerals. The techniques employed in this discipline are effectively the same as what you did in your dice exercise. However, geochronologists use the decay equation, which relates the proportion of daughter and parent atoms to time using the known half-life:</p><p>D = P(et – 1) (1) Where: D is the number of radioactive daughters present P is the number of radioactive parents present  is the decay constant which is a function of the half-life t is the time elapsed in years</p><p>The decay constant () is used instead of the half-life, and is defined as:</p><p> = ln2/t1/2 (2) Where:  is the decay constant t1/2 is the half-life of the nuclide</p><p>4 During alpha () decay, the nuclide loses a bundle of 2 protons and 2 neutrons, called an alpha particle. Thus, an atom’s mass is reduced by 4 when an atom undergoes alpha decay. During beta () decay, a nuclide loses a  particle, which can be either a nuclear electron (-) or a positron (+). The mass of atoms that undergo  decay does not change significantly since electrons have such a small mass. Some nuclides, like Uranium-238, undergo a series of decays before ending up as a stable daughter. This is called chain decay and can include both  and  decays.</p><p>Table 1: Important decay schemes used in geochronology Parent Daughter Decay Scheme Half Life (yrs) Decay Constant Mineral/Rock Locality (1/yrs) 238U 206Pb Chain 4.47 x 109 1.55125 x 10-10 Zircon/Apatite – Igneous 235U 207Pb Chain 704 x 106 9.8485 x 10-10 Zircon/Apatite – Igneous 232Th 208Pb Chain 14.01 x 109 0.49475 x 10-10 Zircon/Apatite – Igneous 40K 40Ar + 1.193 x 109 0.581 x 10-10 Micas/K-spar – Ign./Meta. 14C 14N - 5.73 x 103 1.209 x 10-4 Organic material 87Rb 87Sr - 49.4 x 109 1.402 x 10-11 Micas/K-spar – Meta. rocks 147Sm 143Nd  106 x 109 6.54 x 10-12 Pyroxene, Feldspar – Ign. 187Re 187Os - 4.56 x 1010 1.52 x 10-11 Pyroxene, Feldspar – Ign. 176Lu 176Hf - 35.7 x 109 1.94 x 10-11 Pyroxene, Feldspar – Ign.</p><p>Table 1. shows a list of common decay schemes used by geochronologists, and the rocktypes that they can be most effectively used to date. Using table 1, recommend a dating scheme that would work well for the following time scales.</p><p>Charcoal found in ancient campsites in North America.</p><p>Meteorites believed to be about the same age as the earth.</p><p>5 Although all of the decay schemes in geochronology have limitations in the rock types that they can date, the results of these dating techniques have an extremely broad range of geologic applications. A primary example is that it is now possible to attach a quantitative timeline to a stratigraphic timescale developed using relative dating methods. Additionally, stratigraphic sequences lacking dateable material can also be given absolute dates using graphic correlation.</p><p>Below is a graph correlating the two columns you looked at in your biostratigraphy lab. Luckily, there are actually several ashbeds that were deposited in Section 1, which were dated using the K-Ar method on the volcanic glass in the ash (Figure 1).</p><p>Geochronologists investigating these beds determined that Section 1 was deposited at a constant rate of 1m per every 1000 years (1ky). Given this information and your graphic correlation plot (shown below in Figure 3), estimate how old the contacts of each sedimentary unit are in Section 2 (the depth is shown below in Figure 2). Additionally, determine the sedimentation rate of each of these units using the dates you’ve estimated from your correlation graph and the given thicknesses of each unit. Show your work.</p><p>6 7 Another advantage of absolute dating is that it can place upper and lower boundaries on geologic events that may be undateable themselves. For example, evidence of the K-T boundary crater impact that has been shown to span the globe is limited to a few- centimeter thick bed of iridium-rich clay – material that is not easily dated. However, tektites, or glassy melt rock that often results as ejecta from an impact crater, can contain potassium-rich glass, which can be dated using the K-Ar method. Additionally sanidine- bearing bentonite (coal) beds have been found underlying or overlying the K-T boundary in several locations, and K-Ar dating of the sanidine minerals can also provide age limits on the K-T boundary. Tektites and bentonites have been found in several localities, and the resulting data are listed in the table below. Additional methods that have been used include dating nearby ash layers, or the bulk plagioclase minerals found in basalts from volcanic eruptions.</p><p>Location Age Rock Type Relative location to Source (Ma = million yrs) K-T boundary Chicxulub drillcore, 64.98 ± 0.05 Ma Tektite Co-eval 1 Mexico Beloc, Haiti 65.01 ± 0.08 Ma Tektite Co-eval 1 Arroyo el Mimbral, 65.07 ± 0.10 Ma Tektite Co-eval 1 NE Mexico Beloc, Haiti 64.5 ± 0.10 Ma Tektite Co-eval 2 Hell Creek, Montana 64.6 ± 0.20 Ma Sanidine Younger 2 (in Bentonite) Argentina 66.0  0.5 Ma Ash Layer Older/Co-eval 3 Anjar region, India ~ 65 Ma Basalt Younger 4 Anjar region, India ~ 66.5 Ma Basalt Older 4 Raton Basin, 65.87  0.11 Ma Sanidine Older 5 New Mexico (in Bentonite) Raton Basin, 65.5  0.3 Ma Shocked Co-eval 6 Colorado zircon ejecta Sources: 1. Swisher et al., 1992. Science, 257:954-958. 2. Izett et al., 1991. Science, 252:1539-1542. 3. Palamarczuk et al., 2002. GSA Abstracts with Programs, 34:137. 4. Courtillot et al., 2000. EPSL, 182:137- 156. 5. Pillmore and Miggins, 2000. GSA Abstracts with Programs, 32:452. 6. Krogh et al., 1993. EPSL, 119:425-429.</p><p>Notice there are a lot of discrepancies between the ages recorded above. What sources of error do you think there may be in these dating methods, and how might you go about reconciling them?</p><p>8 In the figure below, there are several geologic features that have been successfully dated, as well as some features that could not be dating using geochronologic methods. The ages of the dated units are listed in the table below, with an error range of  0.1Ma for all dates. List the possible age range for the following rock units or geologic features, using relative age dating methods and your knowledge of the ages of the surrounding geology:</p><p>G, O, E+F (these last two units can be combined as one estimate)</p><p>Dated units (in millions of years – Ma):</p><p>A (granite intrusion) 45.7 M (intermediate dike) 48.0 L (intermediate dike) 48.3 N (basalt dike) 49.5 D (ash bed) 52.0</p><p>Note that the constraints of your relative ages are limited by the amount, quality and time gap of units dated using absolute dating methods.</p><p>9</p>