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Radioactive Decay

 

#

Isotope

Decay-product

Disintegration Formula

Half-life

1

Bismuth-210

Polonium-210

Bi210 Po210

5.0 days

2

Carbon-14

Nitrogen-14

C14 N14

5,700 years

3

Polonium-218

Lead-214

Po214 Pb214

2 x 10-4 seconds

4

Potassium-40

Argon-40 & Calcium-40

K40 Ar40 & Ca40

1.3 x 109 years

5

Radium-226

Radon-222

Ra226 Rn222

1.62 x 103 years

6

Rubidium-87

Strontium-87

Rb87 Sr87

4.9 x 1010 years

7

Thorium-230

Radium-226

Th230 Ra226

8.0 x 104 years

8

Uranium-238

Lead-206

U238 Pb206

4.5 x 109 years

9

Imaginatium-123

Fantasium-123

Im123 Fa123

1 second

10

Earthsciencium-204

Studentogen-199

Ea204 St199

10 minutes

 

On a separate piece of paper, answer the seven questions, draw the chart below and fill it in all of the information for each isotope in the table above (all 10 of them). If it helps, draw the block to represent the sample. Then, answer the additional questions.

 

1. Note: 20 gram sample.

 

1.       What is the radioactive isotope? Bismuth-210

5. What is the decay-product? Polonium-210

2.       What is its chemical symbol of the isotope? Bi210

 

6. What is its chemical symbol of the decay-product? Po210

3.       What is its atomic mass of the isotope? 210

 

7. What is its atomic mass of the decay-product? 210

4.       How much time does one half-life take? (Include the units.)

5.0 days

 

 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in _Days_)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Decay-Product Ratio*

0

100%

0%

0

20

0

1/1

0:1

1

50%

50%

5.0

10

10

1/2

1:2

2

25%

75%

10.0

5

15

1/4

3:4

3

12.5%

87.5%

15.0

2.5

17.5

1/8

7:8

4

6.25%

93.75%

20.0

1.25

18.75

1/16

15:16

5

3.125%

96.875%

25.0

0.625

19.375

1/32

31:32

6

1.5625%

98.4375%

30.0

0.3125

19.6875

1/64

63:64

7

0.78125%

99.21875%

35.0

0.15625

19.84375

1/128

127:128

8

0.390625%

99.609375%

40.0

0.078125

19.921875

1/256

255:256

* The ratio between decay-product compared to the whole sample.

 

 

 

2. Note: 10 gram sample.

1.       What is the radioactive isotope? Carbon-14

5. What is the decay-product? Nitrogen-14

2.       What is its chemical symbol of the isotope? C14

 

6. What is its chemical symbol of the decay-product? N14

3.       What is its atomic mass of the isotope? 14

 

7. What is its atomic mass of the decay-product? 14

4.       How much time does one half-life take? (Include the units.)

5,700 years

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in _years_)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Decay-Product Ratio*

0

100%

0%

0

10

0

1/1

0:1

1

50%

50%

5,700

5

5

1/2

1:2

2

25%

75%

11,400

2.5

7.5

1/4

3:4

3

12.5%

87.5%

17,100

1.25

8.75

1/8

7:8

4

6.25%

93.75%

22,800

0.625

9.375

1/16

15:16

5

3.125%

96.875%

28,500

0.3125

9.6875

1/32

31:32

6

1.5625%

98.4375%

34,200

0.15625

9.84375

1/64

63:64

7

0.78125%

99.21875%

39,900

0.078125

9.921875

1/128

127:128

8

0.390625%

99.609375%

45,600

0.0390625

9.9609375

1/256

255:256

* The ratio between decay-product compared to the whole sample.

 

 

3. Note: 50 gram sample

 

1.       What is the radioactive isotope? Polonium-218

5. What is the decay-product? Lead-214

2.       What is its chemical symbol of the isotope? Po214

 

6. What is its chemical symbol of the decay-product? Pb214

3.       What is its atomic mass of the isotope? 218

 

7. What is its atomic mass of the decay-product? 214

4.       How much time does one half-life take? (Include the units.)

2 x 10-4 seconds

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in seconds)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Decay-Product Ratio**

0

100%

0%

0

50

0

1/1

0:1

1

50%

50%

2 x 10-4

25

25

1/2

1:1

2

25%

75%

4 x 10-4

12.5

37.5

1/4

3:1

3

12.5%

87.5%

6 x 10-4

6.25

43.75

1/8

7:1

4

6.25%

93.75%

8 x 10-4

3.125

46.875

1/16

15:1

5

3.125%

96.875%

10 x 10-4

1.5625

48.4375

1/32

31:1

6

1.5625%

98.4375%

12 x 10-4

0.78125

49.21875

1/64

63:1

7

0.78125%

99.21875%

14 x 10-4

0.390625

49.609375

1/128

127:1

8

0.390625%

99.609375%

16 x 10-4

0.1953125

49.8046875

1/256

255:1

 

** Ratio between decay-product and isotope.

 

 

4. Note: 100 gram sample. Also note: This is a tough one!!! For this one, we will pretend that both decay-products are perfectly equal.

1.       What is the radioactive isotope? Potassium-40

5. What is the decay-product? Argon-40 & Calcium-40

2.       What is its chemical symbol of the isotope? K40

 

6. What is its chemical symbols of the decay-products? Ar40 & Ca40

3.       What is its atomic mass of the isotope? 40

 

7. What is its atomic mass of the decay-product? 40 (for both)

4.       How much time does one half-life take? (Include the units.) 1.3 x 109 years

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of Decay-product

Amount of Time Passed

(in _years_)

Amount of Isotope

Amount of Decay-Product (of each)

Isotope Fraction

Ca40

Ar40

0

100%

0%

0%

0

100

0

1/1

1

50%

0.25%

0.25%

1.3 x 109

50

0.25

1/2

2

25%

0.375%

0.375%

2.6 x 109

25

0.375

1/4

3

12.5%

0.4375%

0.4375%

3.9 x 109

12.5

0.4375

1/8

4

6.25%

0.46875%

0.46875%

5.2 x 109

6.25

0.46875

1/16

5

3.125%

0.484375%

0.484375%

6.5 x 109

3.125

0.484375

1/32

6

1.5625%

0.4921875%

0.4921875%

7.8 x 109

1.5625

0.4921875

1/64

7

0.78125%

0.49609375%

0.49609375%

9.1 x 109

0.78125

0.49609375

1/128

8

0.390625%

0.498046875%

0.498046875%

10.4 x 109

0.390625

0.498046875

1/256

 

 

 

5. Note: 100 grams of sample.

1.       What is the radioactive isotope? Radium-226

5. What is the decay-product? Radon-222

2.       What is its chemical symbol of the isotope? Ra226

 

6. What is its chemical symbol of the decay-product? Rn222

3.       What is its atomic mass of the isotope? 226

 

7. What is its atomic mass of the decay-product? 222

4.       How much time does one half-life take? (Include the units.) 1.62 x 103 years

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in _years_)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Decay-Product Ratio**

0

100%

0%

0

100

0

1/1

0:1

1

50%

50%

1.62 x 103

50

50

1/2

1:1

2

25%

75%

3.24 x 103

25

75

1/4

3:1

3

12.5%

87.5%

4.86 x 103

12.5

87.5

1/8

7:1

4

6.25%

93.75%

6.48 x 103

6.25

93.75

1/16

15:1

5

3.125%

96.875%

8.1 x 103

3.125

96.875

1/32

31:1

6

1.5625%

98.4375%

9.72 x 103

1.5625

98.4375

1/64

63:1

7

0.78125%

99.21875%

11.34 x 103

0.78125

99.21875

1/128

127:1

8

0.390625%

99.609375%

12.96 x 103

0.390625

99.609375

1/256

255:1

** Ratio between decay-product and isotope.

 

 

6. Note: 1,000 grams of sample.

1.       What is the radioactive isotope? Rubidium-87

5. What is the decay-product? Strontium-87

2.       What is its chemical symbol of the isotope? Rb87

 

6. What is its chemical symbol of the decay-product? Rn222

3.       What is its atomic mass of the isotope? 87

 

7. What is its atomic mass of the decay-product? 87

4.       How much time does one half-life take? (Include the units.) 4.9 x 1010 years

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in _years_)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Isotope Ratio***

0

100%

0%

0

1,000

0

1/1

1:1

1

50%

50%

4.9 x 1010

500

500

1/2

1:2

2

25%

75%

9.8 x 1010

250

750

1/4

1:4

3

12.5%

87.5%

14.7 x 1010

125

875

1/8

1:8

4

6.25%

93.75%

19.6 x 1010

62.5

937.5

1/16

1:16

5

3.125%

96.875%

24.5 x 1010

31.25

968.75

1/32

1:32

6

1.5625%

98.4375%

29.4 x 1010

15.625

984.375

1/64

1:64

7

0.78125%

99.21875%

34.3 x 1010

7.8125

992.1875

1/128

1:128

8

0.390625%

99.609375%

39.2 x 1010

3.90625

996.09375

1/256

1:256

*** Ratio between isotope and the whole sample.

 

 

7. 200 grams of sample.

1.       What is the radioactive isotope? Thorium-230

5. What is the decay-product? Radium-226

2.       What is its chemical symbol of the isotope? Th230

 

6. What is its chemical symbol of the decay-product? Ra226

3.       What is its atomic mass of the isotope? 230

 

7. What is its atomic mass of the decay-product? 226

4.       How much time does one half-life take? (Include the units.) 8.0 x 104 years

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in _years_)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Isotope Ratio***

0

100%

0%

0

200

0

1/1

1:1

1

50%

50%

8

100

100

1/2

1:2

2

25%

75%

16

50

150

1/4

1:4

3

12.5%

87.5%

24

25

175

1/8

1:8

4

6.25%

93.75%

32

12.5

187.5

1/16

1:16

5

3.125%

96.875%

40

6.25

193.8

1/32

1:32

6

1.5625%

98.4375%

48

3.125

196.9

1/64

1:64

7

0.78125%

99.21875%

56

1.563

198.4

1/128

1:128

8

0.390625%

99.609375%

64

0.781

199.2

1/256

1:256

*** Ratio between isotope and the whole sample.

 

 

 

 

8. 50 gram sample.

1.       What is the radioactive isotope? Uranium-238

5. What is the decay-product? Lead-206

2.       What is its chemical symbol of the isotope? U238

 

6. What is its chemical symbol of the decay-product? Pb206

3.       What is its atomic mass of the isotope? 238

 

7. What is its atomic mass of the decay-product? 206

4.       How much time does one half-life take? (Include the units.) 4.5 x 109 years

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in _years_)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

Isotope Ratio****

0

100%

0%

0

50

0

1/1

1:0

1

50%

50%

4.5

25

25

1/2

1:1

2

25%

75%

9

12.5

37.5

1/4

1:3

3

12.5%

87.5%

13.5

6.25

43.75

1/8

1:7

4

6.25%

93.75%

18

3.125

46.88

1/16

1:15

5

3.125%

96.875%

22.5

1.563

48.44

1/32

1:31

6

1.5625%

98.4375%

27

0.781

49.22

1/64

1:63

7

0.78125%

99.21875%

31.5

0.391

49.61

1/128

1:127

8

0.390625%

99.609375%

36

0.195

49.8

1/256

1:255

**** Ratio of isotope to decay-product.

 

 

 

9. 123 gram sample.

1.       What is the radioactive isotope? Imaginatium-123

5. What is the decay-product? Fantasium-123

2.       What is its chemical symbol of the isotope? Im123

 

6. What is its chemical symbol of the decay-product? Fa123

3.       What is its atomic mass of the isotope? 123

 

7. What is its atomic mass of the decay-product? 123

4.       How much time does one half-life take? (Include the units.) 1 second

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in seconds)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

0

100%

0%

0

123

0

1/1

1

50%

50%

1

61.5

61.5

1/2

2

25%

75%

2

30.75

92.25

1/4

3

12.5%

87.5%

3

15.38

107.6

1/8

4

6.25%

93.75%

4

7.688

115.3

1/16

5

3.125%

96.875%

5

3.844

119.2

1/32

6

1.5625%

98.4375%

6

1.922

121.1

1/64

7

0.78125%

99.21875%

7

0.961

122

1/128

8

0.390625%

99.609375%

8

0.48

122.5

1/256

 

 

 

 

10. 1 gram sample.

1.       What is the radioactive isotope? Earthsciencium-204

5. What is the decay-product? Studentogen-199

2.       What is its chemical symbol of the isotope? Ea204

 

6. What is its chemical symbol of the decay-product? St199

3.       What is its atomic mass of the isotope? 204

 

7. What is its atomic mass of the decay-product? 199

4.       How much time does one half-life take? (Include the units.) 10 minutes

 


 

Number of

Half-lives

Percentage of Radioactive Isotope

Percentage of

Decay-product

Amount of Time Passed

(in minutes)

Amount of Isotope

Amount of Decay-Product

Isotope Fraction

0

100%

0%

0

1

0

1/1

1

50%

50%

10

0.5

0.5

1/2

2

25%

75%

20

0.25

0.75

1/4

3

12.5%

87.5%

30

0.125

0.875

1/8

4

6.25%

93.75%

40

0.063

0.938

1/16

5

3.125%

96.875%

50

0.031

0.969

1/32

6

1.5625%

98.4375%

60

0.016

0.984

1/64

7

0.78125%

99.21875%

70

0.008

0.992

1/128

8

0.390625%

99.609375%

80

0.004

0.996

1/256

 

 

 

Additional questions:

1.       What is a half-life? (What does it mean?) The amount of time that it takes for half of the radioactive isotope to breakdown into its decay-product.

2.       What is an isotope? An unstable atom with too many or too few neutrons in its nucleus (compared to normal versions of the same atom).

3.       What is the decay-product? This is the stable atom that the isotope becomes after it undergoes radioactive decay.

4.       When filling the charts for each isotope, what information changes from chart to chart? The quantities of the samples (how many grams), the type of ratio that I was asking for, and (MOST IMPORTANTLY) THE AMOUNT OF TIME THAT IT TAKES FOR ONE HALF-LIFE TO OCCUR FOR EACH TYPE OF ISOTOPE.

5.       Does the amount of time for each half-life change throughout the decay of any one isotope? No. The amount of time needed for one half-life remains the same for the isotope. It only changes when you have a different isotope.

6.       What percentage of the sample do you have before any half-lives occur? 100%

7.       What percentage of the sample should you have after one million half-lives have passed? 100%. When adding the percentage of the remaining isotope to the amount of decay-product you should always have the answer of 100%.

8.       How do you calculate the percentage of the isotope and the percentage of the decay-product? The percentage of isotope starts at 100% and is divided in half for each half-life. The decay-product can be calculated in two ways: the easiest way is to subtract the amount of remaining isotope from 100%. The other way is to take the other half of the isotope and add it to the decay-product.