wikiHow Calculating Half-Life Practice Answers 1. t1/2 = (ln 2) / λ = (ln 2) / 0.02 ≈ 34.65 years 2. λ = (ln 2) / t1/2 = (ln 2) / 5 ≈ 0.1386 per day 3. t1/2 = 1 hour 4. After 30 minutes, three half-lives have passed. Therefore, the remaining mass can be calculated as: Remaining mass = Initial mass × (1/2)^3 = 200 grams × (1/2)^3 = 25 grams 5. t1/2 = (ln 2) / λ = (ln 2) / 0.05 ≈ 13.86 days 6. t1/2 = 24 hours 7. To find the time it takes for 1/16 of the initial amount to remain, four half-lives need to pass: Time = 2 years × 4 = 8 years 8. After 9 hours, three half-lives have passed. Therefore, the number of remaining atoms can be calculated as: Remaining atoms = Initial atoms × (1/2)^3 = 1000 atoms × (1/2)^3 = 125 atoms 9. t1/2 = (ln 2) / λ = (ln 2) / 0.1 = 6.93 minutes 10. After 21 days, three half-lives have passed. Therefore, the remaining mass can be calculated as: Remaining mass = Initial mass × (1/2)^3 = 500 grams × (1/2)^3 = 62.5 grams 11. t1/2 = 30 minutes 12. To find the time it takes for the initial amount to decrease to 1/8, three half-lives need to pass: Time = 1 year × 3 = 3 years 13. After 6 hours, three half-lives have passed. Therefore, the remaining mass can be calculated as: Remaining mass = Initial mass × (1/2)^3 = 800 grams × (1/2)^3 = 100 grams 14. t1/2 = (ln 2) / λ = (ln 2) / 0.03 ≈ 23.1 days 15. After 1 hour, four half-lives have passed. Therefore, the remaining number of atoms can be calculated as: Remaining atoms = Initial atoms × (1/2)^4 = 2000 atoms × (1/2)^4 = 125 atoms 16. t1/2 = 40 minutes 17. To find the time it takes for 1/32 of the initial amount to remain, five half-lives need to pass: Time = 5 years × 5 = 25 years 18. After 18 hours, three half-lives have passed. Therefore, the remaining number of atoms can be calculated as: Remaining atoms = Initial atoms × (1/2)^3 = 500 atoms × (1/2)^3 = 62.5 atoms 19. t1/2 = (ln 2) / λ = (ln 2) / 0.05 = 13.86 minutes 20. After 30 days, three half-lives have passed. Therefore, the remaining mass can be calculated as: Remaining mass = Initial mass × (1/2)^3 = 100 grams × (1/2)^3 = 12.5 grams Page