1. Radioactive Decay and Half-Life

2. The isotope Radium–228 undergoes beta decay as shown in the following equation:

3. As time goes on, the amount of Radium that is still present decreases, as the nuclei decay.

4. The isotope Radium–228 undergoes beta decay as shown in the following equation: Start with 5.0 g of radium–228

6. Mass

7. Time

8. t Time t

9. t The mass of radium–228 remaining at time t = 3.4 g

10. t 3.4

11. t The mass of radium–228 remaining at time t = 3.4 g 3.4

12. Time “0”

13. The mass of radium–228 remaining at time 0 = 5.0 g Time “0”

14. The mass of radium–228 remaining at time 5.8 y = 2.5 g

15. 2.5

16. The mass of radium–228 remaining (2.5 g) is exactly one-half its initial value of 5.0 g 2.5

17. The mass of radium–228 remaining (2.5 g) is exactly one-half its initial value of 5.0 g 2.5

18. The mass of radium–228 remaining (2.5 g) is exactly one-half its initial value of 5.0 g 2.5 Half-Life The time it takes for a radioactive isotope to decay to half the mass it started with.

19. 2.5

20. 1.25 g 2.5 g In the second 5.8 years, the mass halved again from 2.5 g to 1.25 g

21. 2.5 1.25 g 0.625 g In the third 5.8 years, the mass halved again from 1.25 g to 0.625 g

22. 2.5 Every time one half-life passes, the mass of the parent isotope drops to one-half of what is was before that half-life.

23. 2.5 1 2 3 4 5 6 7 8 Half-Lives 0.3125 g 0.625 g 0.1563 g

24. 2.5 1 2 3 4 5 6 7 8 Half-Lives

25. 2.5 1 2 3 4 5 6 7 8 Half-Lives

26. 2.5

28. How many half-lives would pass for the amount of a parent isotope to drop to 30% of its initial mass?

31. 1.7

32. How many half-lives would pass for the amount of a parent isotope to drop to 30% of its initial mass? Answer: 1.7 Half-lives 1.7

34. What is the half-life of lead-210?

38. 22 years

39. What is the half-life of lead-210? Answer: 22 years 22 years

40. What percent of the original lead–210 remains after 80 years?

43. 8%

44. What percent of the original lead–210 remains after 80 years? Answer: 8% 8%

45. What percentage of the total possible bismuth-210 will be produced after 60 years?

47. 15%

48. What percentage of the total possible bismuth-210 will be produced after 60 years? 15% When 0% of the lead–210 remains, the maximum total possible bismuth–210 will be formed. So if 15% of the lead–210 remains, that means (100-15) = 85% of the maximum bismuth–210 will be formed.

49. What percentage of the total possible bismuth-210 will be produced after 60 years? 15% When 0% of the lead–210 remains, the maximum total possible bismuth–210 will be formed. So if 15% of the lead–210 remains, that means (100-15) = 85% of the maximum bismuth–210 will be formed.

50. What percentage of the total possible bismuth-210 will be produced after 60 years? 15% When 0% of the lead–210 remains, the maximum total possible bismuth–210 will be formed. So if 15% of the lead–210 remains, that means (100-15) = 85% of the maximum bismuth–210 will be formed.

51. What percentage of the total possible bismuth-210 will be produced after 60 years? 15% When 0% of the lead–210 remains, the maximum total possible bismuth–210 will be formed. So if 15% of the lead–210 remains, that means (100-15) = 85% of the maximum bismuth–210 will be formed.

52. If one starts out with a 3.50 g sample of lead–210, what mass of lead–210 will be left after 45 years?

56. 24%

57. If one starts out with a 3.50 g sample of lead–210, what mass of lead–210 will be left after 45 years? 24%

58. If one starts out with a 3.50 g sample of lead–210, what mass of lead–210 will be left after 45 years? 24%

59. If one starts out with a 3.50 g sample of lead–210, what mass of lead–210 will be left after 45 years? 24%

60. If one starts out with a 3.50 g sample of lead–210, what mass of lead–210 will be left after 45 years? Ans: 0.84 g 24%

61. Using Equations to Do Radioactivity Problems

62. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

63. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

64. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

65. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

66. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

67. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

68. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

69. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

70. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

71. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours?

72. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours? (3 half-lives)

73. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours? (3 half-lives)

74. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours? (3 half-lives) Multiply by ½ for each half-life.

75. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours? (3 half-lives)

76. The half-life of the isotope is 66.0 hours. An initial sample contains 2.00 grams of molybdenum–99. What mass of molybdenum–99 will be left in the sample after 8 days and 6 hours? (3 half-lives) Answer: 0.25 g

77. An Equation We Can Use:

79. Where n = the # of half-lives that have passed

80. Here’s an example question:

81. The radioisotope thorium–234 has a half-life of 24 days.

82. Here’s an example question: The radioisotope thorium–234 has a half-life of 24 days. A sample initially contains 5.000 g of thorium–234.

83. Here’s an example question: The radioisotope thorium–234 has a half-life of 24 days. A sample initially contains 5.000 g of thorium–234. What mass of thorium–234 will be left in the sample after 120 days?

89. The radioisotope thorium–234 has a half-life of 24 days. A sample initially contains 5.000 g of thorium–234. What mass of thorium–234 will be left in the sample after 120 days? Answer: 0.156 g