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7.2 What is Half Life?

7.2 What is Half Life?. Half Life is the time required for half of the radioactive sample to decay. Half-life. Half-life is constant for any radioisotope and can be used to measure the rate of radioactive decay for that isotope. Strontium-90 has a half-life of 29 years.

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7.2 What is Half Life?

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  1. 7.2 What is Half Life? • Half Life is the time required for half of the radioactive sample to decay. (c) McGraw Hill Ryerson 2007

  2. Half-life • Half-life is constant for any radioisotope and can be used to measure the rate of radioactive decay for that isotope. • Strontium-90 has a half-life of 29 years. • If you have 100 g of strontium-90 today, there will be 50 g remaining in 29 years. • Different isotopes have different rates of decay and therefore different half-lives. • The shorter the half-life, the faster the decay rate. (c) McGraw Hill Ryerson 2007

  3. Half-life • All radioactive decay rates follow a similar pattern called a decay curve (c) McGraw Hill Ryerson 2007

  4. Uses for Half Life: Geologic Dating Geological dating is a method of determining the age of rocks and fossils by measuring the radioactive decay radioactive isotopes embedded in the rocks. Methuselah: World’s Oldest Tree ~4780 years old. Gorgosaurus ~75 million years old. (c) McGraw Hill Ryerson 2007

  5. Determining Age with Carbon Dating • Radioactive isotopes decay into stable atoms over time. We can measure relative amounts of remaining radioactive material to the stable products that are formed. • By measuring this ratio, we can determine the age of the organic remains. See pages 302 - 304 (c) McGraw Hill Ryerson 2007

  6. Carbon Dating (c) McGraw Hill Ryerson 2007

  7. Carbon Dating • Carbon dating measures the ratio of carbon-12 and carbon-14. • Stable carbon-12 and (unstable) radioactive carbon-14 exist naturally in a constant ratio. • All animals obtain equal proportions of carbon-14 and carbon-12 by eating plants. • When the organism dies, Carbon-12, being stable, remains unchanged while unstable, radioactive carbon-14 decays into nitrogen-14 at a fixed rate. (c) McGraw Hill Ryerson 2007

  8. Carbon Dating • As neither carbons are being replenished, the ratio of carbon-14 to carbon-12 changes. (c) McGraw Hill Ryerson 2007

  9. 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

  10. Rate of Radioactive Decay • Decay curve is the graph showing the rate of decay of a radioisotope The decay curve for strontium-90 (c) McGraw Hill Ryerson 2007

  11. Decay Curve • After each half-life, amount of radioisotope drops by half. • The curve shows the relationship between half-life and percentage of original substance remaining. (c) McGraw Hill Ryerson 2007

  12. Decay Curve Example • Iodine-131 is used for treating thyroid cancer • It has a half-life of 8 days • Suppose you have 20g of iodine-131 • You can find out how much will remain after 16: 16 days = 2 half-lives 20g x ½ x ½ = 5 See pages 305 - 306 The decay curve for strontium-90 (c) McGraw Hill Ryerson 2007

  13. Decay Curve Practice • Do Practice Problems p306 (c) McGraw Hill Ryerson 2007

  14. Common Isotope Pairs • Many radioisotopes can be used for dating. • Isotope that decays is called the Parent isotope • Stable product(s) of parent isotope’s decay is called Daughter isotope. See page 307 (c) McGraw Hill Ryerson 2007

  15. Common Isotope Pairs • 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

  16. The Potassium-40 Clock • Radioisotopes with very long half-lives can help determine the age of very old things. • Potassium-40 has a half life of 1.3 billion years. • Its daughter isotope is argon-40. • When rock is created from lava, the daughter isotope argon-40 is forced out leaving only the parent potassium-40. • (the rock is starting with 0% daughter, 100% parent) See pages 307 - 308 Take the Section 7.2 Quiz (c) McGraw Hill Ryerson 2007

  17. The Potassium-40 Clock • Over time the potassium-40 decays and creates argon-40 which remains trapped in the rock. • As the amount of potassium-40 decreases, the amount of argon-40 increases. • Using the graph and the ratio of potassium-40 to argon-40 scientists can find how old the rock is. See pages 307 - 308 Take the Section 7.2 Quiz (c) McGraw Hill Ryerson 2007

  18. Since these rocks were probably formed at the beginning of the earth’s life, the age of the rock is close to the age of the earth. (c) McGraw Hill Ryerson 2007

  19. Check your understanding • Which two isotopes get compared in radiocarbon dating? • What is used to measure readioactive decay rate? • Does a half-life change for a given radioisotope? • What is a decay curve? • What is the daughter isotope of uranium-235 • What happens to the amount of argon-40 as the amount of potassium-40 decreases? (c) McGraw Hill Ryerson 2007

  20. Check your understanding • Carbon-12 and carbon-14 • Half-life • No • A graph of the ddecay of a radioisotope • Lead-207 • The amount of argon-40 increases (c) McGraw Hill Ryerson 2007

  21. Crash Course: Nuclear Chemistry • http://www.youtube.com/watch?v=KWAsz59F8gA (c) McGraw Hill Ryerson 2007

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

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