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 year
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 = 4 × 2 years = 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 2 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 = 3 × 1 year = 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 years
15. After 1 hour, four half-lives have passed. Therefore, the remaining number of atoms can be
Parent Tip: Review the logic above to help your child master the concept of half life calculations worksheet.
