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7.2 Half Life

7.2 Half Life. A half life can be used to compare the rate of radioactive decay for an isotope. The shorter the half-life, the faster the decay rate. All radioactive decay rates follow a similar pattern called a decay curve.

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7.2 Half Life

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  1. 7.2 Half Life • A half life can be used to compare the rate of radioactive decay for an isotope. • The shorter the half-life, the faster the decay rate. • All radioactive decay rates follow a similar pattern called a decay curve. • The difference between the different isotopes is the length of their half-lives. (c) McGraw Hill Ryerson 2007

  2. Geologic Dating Methuselah: World’s Oldest Tree ~4780 years old. Gorgosaurus ~75 million years old. (c) McGraw Hill Ryerson 2007

  3. Determining Age with Carbon Dating Radioactive isotopes decay into a stable atom over time. We can measure relative amounts of remaining radioactive material to the stable products that are formed. • This decay rate is not affected by environmental factors and is always consistent. • Carbon dating measures the ratio of carbon-12 and carbon-14. • Stable carbon-12 and radioactive carbon-14 exist naturally in a constant ratio. See pages 302 - 304 (c) McGraw Hill Ryerson 2007

  4. Carbon Dating • All animals obtain equal proportions of carbon-14 and carbon-12 by eating plants. • However, when the organism dies carbon-14 radioactively decays into nitrogen-14 at a fixed rate without being replaced (no more plants are ingested). (c) McGraw Hill Ryerson 2007

  5. Decay This means that the ratio of carbon-14 to carbon-12 changes. By measuring this ratio, we can determine the age of the organic remains. (c) McGraw Hill Ryerson 2007

  6. Carbon Dating Carbon dating only works for organisms less than 50 000 years old. Using carbon dating, these cave paintings of horses, from France, were drawn 30 000 years ago. (c) McGraw Hill Ryerson 2007

  7. The Rate of Radioactive Decay • Half-life measures the rate of radioactive decay. • Half-life = time required for half of the radioactive sample to decay. • is a constant rate of decay. • Strontium-90 has a half-life of 29 years. If you have 10 g of strontium-90 today, there will be 5.0 g remaining in 29 years. • Decay curves show the rate of decay for radioactive elements. • The curve shows the relationship between half-life and percentage of original substance remaining. See pages 305 - 306 The decay curve for strontium-90 (c) McGraw Hill Ryerson 2007

  8. Common Isotope Pairs • There are many radioisotopes that can be used for dating. • Parent isotope = the original, radioactive material • Daughter isotope = the stable product of the radioactive decay • The rate of decay remains constant, but some elements require one step to decay while others decay over many steps before reaching a stable daughter isotope. • Carbon-14 decays into nitrogen-14 in one step. • Uranium-235 decays into lead-207 in 15 steps. • Thorium-235 decays into lead-208 in 10 steps. See page 307 (c) McGraw Hill Ryerson 2007

  9. The Potassium-40 Clock • Radioisotopes with very long half-lives can help determine the age of very old things. • The potassium-40/argon-40 clock has a half-life of 1.3 billion years. • Argon-40 produced by the decay of potassium-40 becomes trapped in rock. • Ratio of potassium-40 : argon-40 shows age of rock. See pages 307 - 308 Take the Section 7.2 Quiz (c) McGraw Hill Ryerson 2007

  10. Here’s how it works: • a) Radioactive isotope decay is measured as a half-life. • One half-life is equal to the amount of time required for half of the parent isotope present in a sample to decay into the daughter isotope. This length of time varies depending on the parent isotope being analyzed. • b) By multiplying the half-life time for the parent isotope by the number of half-lives elapsed, you can determine how old the sample is. (c) McGraw Hill Ryerson 2007

  11. Radioactive Decay of Potassium-40 • The Potassium-40 Clock is the use of this radioactive isotope’s half-life to determine the age of very old rocks. (c) McGraw Hill Ryerson 2007

  12. Radioactive Decay of Potassium-40 • a) Using the Potassium-40 decay curve, determine the age of a rock with 25% Potassium-40 and 75% Argon-40. • b) What is ratio of argon-40 to potassium-40 remains 3.9 billion years after the rock has formed? • *Complete Check Your Understanding Questions 6, 7, 9-12 on page 311. (c) McGraw Hill Ryerson 2007

  13. Radioactive Decay of Potassium-40 • a) Using the Potassium-40 decay curve, determine the age of a rock with 25% Potassium-40 and 75% Argon-40. • 25% Potassium-40 = 2 half-lives • 2 x 1.3 billion years = 2.6 byo. • b) What is ratio of argon-40 to potassium-40 remains 3.9 billion years after the rock has formed? • *Complete Check Your Understanding Questions 6, 7, 9-12 on page 311. (c) McGraw Hill Ryerson 2007

  14. Radioactive Decay of Potassium-40 • a) Using the Potassium-40 decay curve, determine the age of a rock with 25% Potassium-40 and 75% Argon-40. • 25% Potassium-40 = 2 half-lives • 2 x 1.3 billion years = 2.6 byo. • b) What is ratio of argon-40 to potassium-40 remains 3.9 billion years after the rock has formed? • 3.9b / 1.3 b = 3 Half-Lives = 12.5% parent isotope remains • 1000g x 0.125 = 125 g • *Complete Check Your Understanding Questions 6, 7, 9-12 on page 311. (c) McGraw Hill Ryerson 2007

  15. Example 1 An archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14. • -How many half-lives have elapsed since the Rhino died? • -What is the time required for one half-life to elapse for carbon-14? • -How long ago did the Rhino die? (c) McGraw Hill Ryerson 2007

  16. Example • For example, an archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14. • -How many half-lives have elapsed since the Rhino died? • 2 • -What is the time required for one half-life to elapse for carbon-14? (c) McGraw Hill Ryerson 2007

  17. Example • For example, an archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14. • -How many half-lives have elapsed since the Rhino died? • 2 • -What is the time required for one half-life to elapse for carbon-14? • 5730 years • -How long ago did the Rhino die? (c) McGraw Hill Ryerson 2007

  18. Example • For example, an archaeologist finds a Woolly Rhinoceros and through testing discovers that of the carbon present in the skeleton, 25% is carbon-14. • -How many half-lives have elapsed since the Rhino died? • 2 • -What is the time required for one half-life to elapse for carbon-14? • 5730 years • -How long ago did the Rhino die? • 5730 x 2 = 11,460 years ago. (c) McGraw Hill Ryerson 2007

  19. Example 2 • If a Neanderthal skeleton starts with 1000 grams of carbon-14, how much would remain 17,190 years after the organism died? (c) McGraw Hill Ryerson 2007

  20. a) How many half-lives have elapsed? • b) What percentage of the parent isotope remains? • c) After 17,190 yrs, how much of the parent isotope is remaining? • d) How many grams of Nitrogen-14 have been produced over 17,190 years of Carbon-14’s radioactive decay? (c) McGraw Hill Ryerson 2007

  21. a) How many half-lives have elapsed? • 17,190 / 5,730 = 3 half-lives (c) McGraw Hill Ryerson 2007

  22. b) What percentage of the parent isotope remains? • 12.5% (½ x ½ x ½) • c) After 17,190 yrs, how much of the parent isotope is remaining? • 1000 x 0.125 = 125 grams of Carbon-14 after 17,190 years (or 3 half-lives) (c) McGraw Hill Ryerson 2007

  23. b) What percentage of the parent isotope remains? • 12.5% (½ x ½ x ½) • c) After 17,190 yrs, how much of the parent isotope is remaining? • 1000 x 0.125 = 125 grams of Carbon-14 after 17,190 years (or 3 half-lives) • d) How many grams of Nitrogen-14 have been produced over 17,190 years of Carbon-14’s radioactive decay? • 1000 g – 125g = 875 grams of Nitrogen-14 • 1000 grams x 0.875 = 875 grams of Nitrogen-14 (c) McGraw Hill Ryerson 2007

  24. e) What percentage of the Carbon-14 is remaining after 2 half-lives? • f) What is the ratio of Carbon-14 to Nitrogen-14 after 4 half-lives? (c) McGraw Hill Ryerson 2007

  25. e) What percentage of the Carbon-14 is remaining after 2 half-lives? • 25% • f) What is the ratio of Carbon-14 to Nitrogen-14 after 4 half-lives? (c) McGraw Hill Ryerson 2007

  26. e) What percentage of the Carbon-14 is remaining after 2 half-lives? • 25% • f) What is the ratio of Carbon-14 to Nitrogen-14 after 4 half-lives? • Four half-lives: 6.25% Carbon-14 remaining, 93.75% N-14 formed (c) McGraw Hill Ryerson 2007

  27. (c) McGraw Hill Ryerson 2007

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