1. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Earth Systems 3209 Unit: 2 Historical Geology Reference: Chapters 6, 8; Appendix A & B

2. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems Unit 2: Topic 2.5 Focus on...  d  determining the age of a sample using radiometric data.  d  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. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems  These questions could make reference to the radioactive parent isotope in; 1.Fraction Form (ex. 1/16 th ) 2.Percent Form (ex. 25%) 3.Remaining Parent in Grams (ex. 512 grams)

4. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador 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: 1.Fraction (ex. 1/16 th ) 2.Percent (ex. 25%) 3.Ratio (1:7)

5. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems (Fraction) 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 Problem Type #1: Fraction of parent material remaining

6. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems (Percent) 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% Problem Type #2: Percent of parent material remaining

7. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems (Percent) 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” = ______ Problem Type #2: Percent of parent material remaining

8. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems (Percent) To calculate the Age of the radioactive sample, use the following formula; Age = “N” x # of years per half-lifeWhere: N = Number of half-lives Age = Half-life = 1.3 B.yrs. Age = Problem Type #2: Percent of parent material remaining

9. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador 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 =

10. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador 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. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador 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. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador 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. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador 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. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Solutions... Question: 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. Given: HL = 250 Million yrs Parent Isotope remaining = 12.5% Age = ???? # of Half Lives = 3HL 100% ➔ 50% ➔ 25% ➔ 12.5% Age = # HL x Time of HL Age = 3 HL x 250 Million years Age = 750 Million Years

15. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Radioactive Dating Problems  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. A “common error” students make when calculating this type of problem is;

16. Copyright © 2014 All rights reserved, Government of Newfoundland and Labrador Summary... Overview of Points covered:  First find the number of half lives.  Then you calculate the unknown, for example; 1)Age 2)Mass Remaining