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Earth Systems 3209

Earth Systems 3209. Reference: Chapters 6, 8; Appendix A & B. Unit: 2 Historical Geology . Unit 2: Topic 2.5. Radioactive Dating Problems. Focus on . . . d etermining the age of a sample using radiometric data.

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Earth Systems 3209

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  1. Earth Systems 3209 Reference: Chapters 6, 8; Appendix A & B Unit: 2Historical Geology

  2. Unit 2: Topic 2.5 Radioactive Dating Problems Focus on . . . • determining the age of a sample using radiometric data. • demonstrating scenarios that include calculations to determine;1) the fraction or percent of parent and daughter material,2) the number of half-lives,3) the ratios of parent to daughter materials, and 4) changing masses.

  3. Radioactive Dating Problems • These questions could make reference to the radioactive parent isotope in; • FractionForm (ex. 1/16th) • Percent Form (ex. 25%) • Remaining Parent in Grams (ex. 512 grams)

  4. Radioactive Dating Problems • Note:When calculating any radioactive dating problem, you first need to calculate the number of half lives that has passed!!! • One piece of information given in the problem will allow you to do this. • Example: • Fraction (ex. 1/16th) • Percent (ex. 25%) • Ratio (1:7)

  5. Radioactive Dating Problems (Fraction) Problem Type #1: Fraction of parent material remaining Given the half-life of U-235 is 0.7 billion years, determine the age of a sample of U-235 if 1/16 of the starting material remains. Given:Half-life = 0.7 billion years Fraction of parent (U-235) remaining = 1/16 • You must first find out how many half-lives have passed if 1/16 of the parent (U-235) remains. Age = # of Half-lives x Time for 1 Half-life

  6. Radioactive Dating Problems (Percent) Problem Type #2: Percent of parent material remaining Question: Calculate the age of a rock using the K - 40 Ar – 40 dating method (which has a half – life of 1.3 billion years), if you know that 12.5% of the parent material now remains in the rock sample. Information Given in Problem: Half-life of radioactive sample  1.3 Billion Years Parent material remaining  12.5%

  7. Radioactive Dating Problems (Percent) Problem Type #2: Percent of parent material remaining The key to solving radioactive problems is that the number of half-lives (represented by “N”) must be found. To find the number of half-lives (N) that passed when 12.5% of the radioactive sample remains we can use a chart and follow the following steps: • Note: • The original amount before any radioactive material decayed was 100% • This is represented in the chart as zero half-lives. • Find how many half-lives the radioactive sample has to go through so that 12.5% remains. After 3 half-lives Thus,“N” = ______

  8. Radioactive Dating Problems (Percent) Problem Type #2: Percent of parent material remaining To calculate theAgeof the radioactive sample, use the following formula; Age = “N” x # of years per half-life Where: N = Number of half-livesAge = Half-life = 1.3 B.yrs. Age =

  9. Radioactive Dating Problems (Mass Remaining) Problem Type #3: Mass of parent material remaining 1200 g of a radioactive element has decayed to produce 150 g of the element. If the half-life of the mineral is 0.40 billion years, what is the age of the sample? Given: 1200 grams decays to 150 grams & Half-life = 0.4 Billion years First find out how many half-lives have passed when 1200g decays to form 150g # of Half LivesAge of Sample Age = Number of HL X Time of HL Age = Age =

  10. Example 1: What is the age of the rock described below? (A) 2.6 billion years(B) 3.9 billion years (C) 4.2 billion years(D) 5.5 billion years A granite sample is dated using the radioactive isotope K-40, which has a half-life of 1.3 billion years. The rock contains 1/8 of the original K-40.

  11. Your Turn . . . Take the time and complete the following questions . . .(Solutions to follow) Question: The half-life of element X is 200 000 years. If a sample originally held 256 g of parent isotope and the rock sample has been determined to be 1 million years old, what mass of parent now remains? Show calculations. Given:

  12. Solutions . . . Question: • The half-life of element X is 200 000 years. If a sample originally held 256 g of parent isotope and the rock sample has been determined to be 1 million years old, what mass of parent now remains? Show calculations. • Number of Half-lives: • Half-life = 1,000,000 years = 5 HL • 200,000 years • Mass of parent remaining: • 256g ➜ 128g ➜ 64g ➜ 32g ➜ 16g ➜ 8g

  13. Your Turn . . . Take the time and complete the following questions . . .(Solutions to follow) Questions: The parent isotope of a radioactive element has a half-life of 250 million years. If a sample contains 12.5% of the parent isotope, how old is the rock?Show all workings.

  14. Solutions . . . Question:

  15. Radioactive Dating Problems A “common error” students make when calculating this type of problem is; • Students when calculating the number of half-lives, as previously shown, count the “0" which implies 100% of the sample, as one of the half-lives. • This would give an incorrect number of half-lives (N = 4), which results in an incorrect answer.

  16. Summary . . . Overview of Points covered: • First find the number of half lives. • Then you calculate the unknown, for example; • 1) Age • 2) Mass Remaining

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