Half-Life and Radiometric Dating Worksheet Generator
Remaining fraction and amount, age from a measured ratio, decay curves. No AI, no credits.
Grades 8 – 12No account needed
Remaining fraction and amount, age from a measured ratio, and decay curves drawn by code, using sourced half-lives. Every answer is computed by code. No AI, so it never uses a generation credit.
What students practice
- Earth and Space
- Half-life
- Radiometric dating
Live sample sheet
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Name: ____________________Date: ____________
Half-Life and Radiometric Dating
1. After 24.06 days, what fraction of Iodine-131 remains? (Half-life of Iodine-131 = 8.02 days.)
2. A sample contains 338 g of Rubidium-87. After 48,800,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
3. After 16.04 days, what fraction of Iodine-131 remains? (Half-life of Iodine-131 = 8.02 days.)
4. A sample contains 434 g of Potassium-40. After 3,753,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
5. After 26,808,000,000 years, what fraction of Uranium-238 remains? (Half-life of Uranium-238 = 4,468,000,000 years.)
6. A sample contains 160 g of Potassium-40. After 1,251,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
7. After 40.1 days, what fraction of Iodine-131 remains? (Half-life of Iodine-131 = 8.02 days.)
8. A sample contains 11 g of Potassium-40. After 3,753,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
9. After 6.01 hours, what fraction of Technetium-99m remains? (Half-life of Technetium-99m = 6.01 hours.)
10. A sample contains 25 g of Potassium-40. After 2,502,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
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Answer Key — Half-Life and Radiometric Dating
1. After 24.06 days, what fraction of Iodine-131 remains? (Half-life of Iodine-131 = 8.02 days.)
Solution:
Number of half-lives = 24.06 / 8.02 = 3
Remaining fraction = (1/2)^3 = 0.1250
As a percentage: 12.50%
Answer: 0.1250 (12.50%)
2. A sample contains 338 g of Rubidium-87. After 48,800,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
Solution:
Number of half-lives = 48,800,000,000 / 48,800,000,000 = 1
Remaining = 338 g × (1/2)^1 = 338 × 0.5000
Remaining = 169 g
Answer: 169 g
3. After 16.04 days, what fraction of Iodine-131 remains? (Half-life of Iodine-131 = 8.02 days.)
Solution:
Number of half-lives = 16.04 / 8.02 = 2
Remaining fraction = (1/2)^2 = 0.2500
As a percentage: 25.00%
Answer: 0.2500 (25.00%)
4. A sample contains 434 g of Potassium-40. After 3,753,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
Solution:
Number of half-lives = 3,753,000,000 / 1,251,000,000 = 3
Remaining = 434 g × (1/2)^3 = 434 × 0.1250
Remaining = 54.25 g
Answer: 54.25 g
5. After 26,808,000,000 years, what fraction of Uranium-238 remains? (Half-life of Uranium-238 = 4,468,000,000 years.)
Solution:
Number of half-lives = 26,808,000,000 / 4,468,000,000 = 6
Remaining fraction = (1/2)^6 = 0.0156
As a percentage: 1.56%
Answer: 0.0156 (1.56%)
6. A sample contains 160 g of Potassium-40. After 1,251,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
Solution:
Number of half-lives = 1,251,000,000 / 1,251,000,000 = 1
Remaining = 160 g × (1/2)^1 = 160 × 0.5000
Remaining = 80 g
Answer: 80 g
7. After 40.1 days, what fraction of Iodine-131 remains? (Half-life of Iodine-131 = 8.02 days.)
Solution:
Number of half-lives = 40.1 / 8.02 = 5
Remaining fraction = (1/2)^5 = 0.0313
As a percentage: 3.13%
Answer: 0.0313 (3.13%)
8. A sample contains 11 g of Potassium-40. After 3,753,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
Solution:
Number of half-lives = 3,753,000,000 / 1,251,000,000 = 3
Remaining = 11 g × (1/2)^3 = 11 × 0.1250
Remaining = 1.375 g
Answer: 1.375 g
9. After 6.01 hours, what fraction of Technetium-99m remains? (Half-life of Technetium-99m = 6.01 hours.)
Solution:
Number of half-lives = 6.01 / 6.01 = 1
Remaining fraction = (1/2)^1 = 0.5000
As a percentage: 50.00%
Answer: 0.5000 (50.00%)
10. A sample contains 25 g of Potassium-40. After 2,502,000,000 years, how much remains? (Half-life = 1,251,000,000 years.)
Solution:
Number of half-lives = 2,502,000,000 / 1,251,000,000 = 2
Remaining = 25 g × (1/2)^2 = 25 × 0.2500
Remaining = 6.25 g
Answer: 6.25 g
Answers computed by code. No AI, no credits.
Assumptions and Conventions
Assumptions:
- Remaining fraction = (1/2)^(elapsed time / half-life).
- Remaining amount = initial amount × (1/2)^(elapsed time / half-life).
- Age from ratio: age = -halfLife / ln(2) × ln(parent fraction).
- Parent fraction + daughter fraction = 1.
Conventions:
- Half-lives are given in the problem.
- All half-life data is sourced from nuclear physics reference data.
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Frequently asked questions
Do students need an account to use the Half-Life and Radiometric Dating?
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Can I print the Half-Life and Radiometric Dating without signing up?
Yes. This tool computes answers by code, so you can generate, preview and print worksheet without an account. A free account adds saving and student links.
How are the answers computed?
Every answer is computed by code and verified by a second independent method. No AI is used.
What grades is the Half-Life and Radiometric Dating for?
This tool fits Grades 8 – 12.
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Name: ____________________Date: ____________
Half-Life and Radiometric Dating
1. After 7.64 days, what fraction of Radon-222 remains? (Half-life of Radon-222 = 3.82 days.)
2. A sample contains 411 g of Uranium-238. After 13,404,000,000 years, how much remains? (Half-life = 4,468,000,000 years.)
3. After 1,251,000,000 years, what fraction of Potassium-40 remains? (Half-life of Potassium-40 = 1,251,000,000 years.)
4. A sample contains 499 g of Rubidium-87. After 244,000,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
5. After 292,800,000,000 years, what fraction of Rubidium-87 remains? (Half-life of Rubidium-87 = 48,800,000,000 years.)
6. A sample contains 485 g of Rubidium-87. After 195,200,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
7. After 13,404,000,000 years, what fraction of Uranium-238 remains? (Half-life of Uranium-238 = 4,468,000,000 years.)
8. A sample contains 389 g of Uranium-238. After 22,340,000,000 years, how much remains? (Half-life = 4,468,000,000 years.)
9. After 26.35 years, what fraction of Cobalt-60 remains? (Half-life of Cobalt-60 = 5.27 years.)
10. A sample contains 330 g of Rubidium-87. After 146,400,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
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Answer Key — Half-Life and Radiometric Dating
1. After 7.64 days, what fraction of Radon-222 remains? (Half-life of Radon-222 = 3.82 days.)
Solution:
Number of half-lives = 7.64 / 3.82 = 2
Remaining fraction = (1/2)^2 = 0.2500
As a percentage: 25.00%
Answer: 0.2500 (25.00%)
2. A sample contains 411 g of Uranium-238. After 13,404,000,000 years, how much remains? (Half-life = 4,468,000,000 years.)
Solution:
Number of half-lives = 13,404,000,000 / 4,468,000,000 = 3
Remaining = 411 g × (1/2)^3 = 411 × 0.1250
Remaining = 51.375 g
Answer: 51.375 g
3. After 1,251,000,000 years, what fraction of Potassium-40 remains? (Half-life of Potassium-40 = 1,251,000,000 years.)
Solution:
Number of half-lives = 1,251,000,000 / 1,251,000,000 = 1
Remaining fraction = (1/2)^1 = 0.5000
As a percentage: 50.00%
Answer: 0.5000 (50.00%)
4. A sample contains 499 g of Rubidium-87. After 244,000,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
Solution:
Number of half-lives = 244,000,000,000 / 48,800,000,000 = 5
Remaining = 499 g × (1/2)^5 = 499 × 0.0313
Remaining = 15.594 g
Answer: 15.594 g
5. After 292,800,000,000 years, what fraction of Rubidium-87 remains? (Half-life of Rubidium-87 = 48,800,000,000 years.)
Solution:
Number of half-lives = 292,800,000,000 / 48,800,000,000 = 6
Remaining fraction = (1/2)^6 = 0.0156
As a percentage: 1.56%
Answer: 0.0156 (1.56%)
6. A sample contains 485 g of Rubidium-87. After 195,200,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
Solution:
Number of half-lives = 195,200,000,000 / 48,800,000,000 = 4
Remaining = 485 g × (1/2)^4 = 485 × 0.0625
Remaining = 30.313 g
Answer: 30.313 g
7. After 13,404,000,000 years, what fraction of Uranium-238 remains? (Half-life of Uranium-238 = 4,468,000,000 years.)
Solution:
Number of half-lives = 13,404,000,000 / 4,468,000,000 = 3
Remaining fraction = (1/2)^3 = 0.1250
As a percentage: 12.50%
Answer: 0.1250 (12.50%)
8. A sample contains 389 g of Uranium-238. After 22,340,000,000 years, how much remains? (Half-life = 4,468,000,000 years.)
Solution:
Number of half-lives = 22,340,000,000 / 4,468,000,000 = 5
Remaining = 389 g × (1/2)^5 = 389 × 0.0313
Remaining = 12.156 g
Answer: 12.156 g
9. After 26.35 years, what fraction of Cobalt-60 remains? (Half-life of Cobalt-60 = 5.27 years.)
Solution:
Number of half-lives = 26.35 / 5.27 = 5
Remaining fraction = (1/2)^5 = 0.0313
As a percentage: 3.13%
Answer: 0.0313 (3.13%)
10. A sample contains 330 g of Rubidium-87. After 146,400,000,000 years, how much remains? (Half-life = 48,800,000,000 years.)
Solution:
Number of half-lives = 146,400,000,000 / 48,800,000,000 = 3
Remaining = 330 g × (1/2)^3 = 330 × 0.1250
Remaining = 41.25 g
Answer: 41.25 g
Answers computed by code. No AI, no credits.
Assumptions and Conventions
Assumptions:
- Remaining fraction = (1/2)^(elapsed time / half-life).
- Remaining amount = initial amount × (1/2)^(elapsed time / half-life).
- Age from ratio: age = -halfLife / ln(2) × ln(parent fraction).
- Parent fraction + daughter fraction = 1.
Conventions:
- Half-lives are given in the problem.
- All half-life data is sourced from nuclear physics reference data.
Made with TeachSpark
Half-Life and Radiometric Dating - General earth and space - Mixed half-life practice
Remaining fraction and amount, age from a measured ratio, decay curves. No AI, no credits.