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Geology 8.4: Absolute Dating of Rocks Fossils December 7, 2020 This document is intended to be for educational purposes only. In addition, By using any part of this document, you agree to pay it forward for any future Hunter student seeking help. Problem A 1. About how many half-lives of uranium-235 to lead-207 decay pair have elapsed in the zircon-crystals? A: As radioactive isotopes decay, they randomly decay into another isotope. We call the first isotope a parent isotope and the second isotope a daughter isotope. The time it takes for half of the parent isotope to decay is called the half-life. By now, we know the half-life’s of most of the common radioactive isotopes. As a result, if we can figure out how much of each isotope exists in rocks, we can calculate the age of the rock by using the half-life of the isotopes. In this problem: Parent = Uranium-235 (71%) Daughter = Lead-207 (29%) Some Intuition: Since we know that more than 50% of the uranium-235 still exists, we know that the amount of half-lives that have elapsed must be less than 1 (because if 1 half-life did elapse then we’d have 50% of uranium-235 and 50% of lead-207). There’s not a lot more that needs to be done here, since it’s asking for ”about how many” instead of something exact. Looking at the table on Figure 8.11, we can see that when 0.5 half lives have elapsed, there is roughly 7!% of the parent isotope remaining and 29% of the daughter isotope remaining. So the answer is 0.500 half-lives 1 2. What is the absolute age of the lava flow based on the zircon crystals? Show your calculations. A: For this question, you need to know the age formula which is as follows: age = # of half lives * half life of isotope In this case, we calculated the # of half lives from the previous question, all we need to know is the half-life of uranium-235, which is 7.038×108 (This is also in Figure 8.11). So we get: age = 0.500 ∗ (7.038 × 108 ) age = 351 million years 3. What is the age of the rock layers above the lava flow? A: If the age of the lava flow is around 351 million years, then anything above that rock should be younger. 4. What is the age of the rock layers beneath the lava flow? A: If the age of the lava flow is around 351 million years, then anything beneath that rock should be older. Problem B 1. Astronomers think that Earth probably formed at the same time as all other rocky materials in our solar system, including the oldest meteorites. The oldest meteorites ever found on Earth contain nearly equal amounts of both uranium-238 and lead-206. Based on Figure 8.11 what is the presumed age of the Earth? A: The key part of this question is the fact that they found equal parts of uranium-238 and lead-206. If they found equal parts, that means 1 half-life has passed ever since the formation of that rock. Using Figure 8.11, we see that uranium-238 has a half-life of 4.468 billion years. Using the age formula is overkill here but I’ll use it to be precise: age = # of half lives * half life of isotope age = 1 ∗ (4.468 × 109 ) age = 4.468 billion years 2 Problem C 1. The carbon in a buried peat has about 6% of the carbon-14 of modern shells. what is the age of the peat? A: Peat is soil-like, partially decaying plant material. Did you need to know that seem- ingly useless fact to answer the question? Absolutely not. But I included it just for you. :) By now, alarm bells should be going off every time you see a question about age. You should be busting out the age formula. Here it is again: age = # of half lives * half life of isotope The isotope in question is carbon-14 and according to the ever-so useful Figure 8.11, its half life is (a measly) 5,730 years. Meaning every 5,730 years, half of the atoms of carbon-14 decay into nitrogen. Since there’s about 6% of carbon-14 remaining, we can use this to figure out the other piece of information we need, the # of half lives, to calculate the age. If we start with 100%, how many times do we have to divide in half until we get to something around 6%? 1—2—3—4— 100, 50, 25, 12.5, 6.25 If we have 6% of carbon-14 remaining, then roughly 4 half-lives have passed. age = 4 ∗ (5730) age = 22920 years 2. In sampling the peat bed, you must be careful to avoid any young plant roots or old limestone. Why? A: Young plant roots have more carbon-14 than the peat bed, while old limestone has even less carbon-14 than the peat bed. As a result, if we accidentally sample these, then our carbon dating of the peat bed will be off. Problem D 1. If you walk on a modern New Jersey beach, then you will walk on some zircon sand grains. Yet if you determine the absolute age of the zircons, it does not indicate a modern age (zero years) for the beach. Why? 3 A: If the zircon forms in magma, then all of its crystals were formed during the time of when it was in magma and lava (which may have happened a long time ago). As a result, the zircon sand grains are much older than the other sand grains. 2. Suggest a rule that geologists should follow when they date rocks based on the radio- metric ages of crystals inside the rocks. A: To properly date rocks with crystals, make sure that the crystal and the rock were formed at the same time, otherwise do not use the radiometric ages of the crystals to date the rocks (and vice versa). Problem E 1. An ”authentic dinosaur bone” is being offered for sale on the Internet. The seller claims that he had it analyzed by scientists who confirmed that it is a dinosaur bone and used carbon dating to determine that it is 400 million years old. Should you be suspicious of this bone’s authenticity? A: HELL yes, you should be suspicious. Dinosaurs started to come about around the beginning of the Triassic period, which was the first of three periods that dinosaurs roamed the earth (the other two being the Mesozoic and Jurassic periods). The Triassic period started 243 million years ago, which is very far off from this seller’s 400 million claim. This is as fake as those secret shopper emails. 4