Half-Life Reasoning Problems for Chemistry and Physics

1. If an isotope’s half-life is 6 hours, after 18 hours the remaining fraction is:

1/2

1/4

1/8

1/16

Concept: converting time to half-lives. 18 hours = 3 half-lives → (1/2)^3 = 1/8. Three halvings reduce the original to one eighth.

Explanation

Concept: converting time to half-lives. 18 hours = 3 half-lives → (1/2)^3 = 1/8. Three halvings reduce the original to one eighth.

2. If 1/32 remains, 5 half-lives have passed.

True

False

Concept: powers of 1/2. (1/2)^5 = 1/32. Each half-life adds one more factor of 1/2 to the remaining fraction.

Explanation

Concept: powers of 1/2. (1/2)^5 = 1/32. Each half-life adds one more factor of 1/2 to the remaining fraction.

3. Starting with 48 g, after 1 half-life you have 24 g. How much after 3 half-lives?

12 g

8 g

6 g

3 g

Concept: applying three halvings. 48 → 24 → 12 → 6. Three half-lives means halve the amount three times.

Explanation

Concept: applying three halvings. 48 → 24 → 12 → 6. Three half-lives means halve the amount three times.

4. In equal time intervals of one half-life, the amount decreases by equal fractions, not equal amounts.

True

False

Concept: fractional vs absolute change. Exponential decay means constant fraction decrease.

Explanation

Concept: fractional vs absolute change. Exponential decay means constant fraction decrease.

5. If you know half-life and the number of half-lives passed, you can estimate remaining fraction using (1/2)^n.

True

False

Concept: mathematical model for half-life. That’s the core half-life model.

Explanation

Concept: mathematical model for half-life. That’s the core half-life model.

6. Half-life is useful for predicting how activity changes over time.

True

False

Concept: activity follows the same decay law. Activity is linked to the number of undecayed nuclei.

Explanation

Concept: activity follows the same decay law. Activity is linked to the number of undecayed nuclei.

7. Best grade 11 summary: half-life lets you estimate remaining amount by:

Subtracting a constant amount each step

Multiplying by 1/2 for each half-life and counting how many half-lives passed

Adding a constant percentage each step

Using temperature and pressure tables

Concept: half-life method. Half-life uses repeated halving.

Explanation

Concept: half-life method. Half-life uses repeated halving.

8. Half-life = 10 years. Starting with 800 g, after 30 years you have:

400 g

200 g

100 g

50 g

Concept: stepwise halving over multiple half-lives. 30 years = 3 half-lives → 800 → 400 → 200 → 100. Three equal halving intervals reduce the amount to one eighth.

Explanation

Concept: stepwise halving over multiple half-lives. 30 years = 3 half-lives → 800 → 400 → 200 → 100. Three equal halving intervals reduce the amount to one eighth.

9. A sample goes from 1600 bq to 200 bq. How many half-lives is that?

1

2

3

4

Concept: counting halvings in activity. 1600 → 800 → 400 → 200 (3 halvings). Each halving is one half-life, so this is three half-lives.

Explanation

Concept: counting halvings in activity. 1600 → 800 → 400 → 200 (3 halvings). Each halving is one half-life, so this is three half-lives.

10. Half-life is 4 days. If 3 half-lives pass, time is:

4 days

8 days

12 days

16 days

Concept: time = number of half-lives × half-life. 3 × 4 = 12 days. You multiply the count of half-life intervals by the half-life duration.

Explanation

Concept: time = number of half-lives × half-life. 3 × 4 = 12 days. You multiply the count of half-life intervals by the half-life duration.

11. If half-life = 2 hours, how many hours to go from 100% to 6.25%?

4 hours

6 hours

8 hours

10 hours

Concept: converting percent to number of half-lives. 6.25% = 1/16 = 4 half-lives → 4 × 2 = 8 hours.

Explanation

Concept: converting percent to number of half-lives. 6.25% = 1/16 = 4 half-lives → 4 × 2 = 8 hours.

12. Going from 1/2 to 1/8 takes ______ additional half-lives.

Concept: counting steps between fractions. 1/2 → 1/4 (1), → 1/8 (2). Each halving is one additional half-life.

Explanation

Concept: counting steps between fractions. 1/2 → 1/4 (1), → 1/8 (2). Each halving is one additional half-life.

Submit

13. A sample has half-life 5 minutes. How long to decrease from 80 units to 10 units?

10 minutes

15 minutes

20 minutes

25 minutes

Concept: stepwise halving with time. 80 → 40 (5 min) → 20 (10 min) → 10 (15 min). That is three half-lives, so 3 × 5 = 15 minutes.

Explanation

Concept: stepwise halving with time. 80 → 40 (5 min) → 20 (10 min) → 10 (15 min). That is three half-lives, so 3 × 5 = 15 minutes.

14. If 1/4 remains, what percent remains?

4%

25%

50%

75%

Concept: converting fractions to percent. 1/4 = 0.25 = 25%. This corresponds to two half-lives because (1/2)^2 = 1/4.

Explanation

Concept: converting fractions to percent. 1/4 = 0.25 = 25%. This corresponds to two half-lives because (1/2)^2 = 1/4.

15. Which are equivalent statements?

2 half-lives have passed

25% remains

50% remains

Remaining fraction is 1/4

Concept: equivalent representations. a, b, d match. Two half-lives means two halvings, leaving one quarter (25%) of the original.

Explanation

Concept: equivalent representations. a, b, d match. Two half-lives means two halvings, leaving one quarter (25%) of the original.

Submit

16. An isotope has half-life 3 days. How long to drop from 1/2 to 1/16?

3 days

6 days

9 days

12 days

Concept: additional half-lives from a starting fraction. 1/2 → 1/4 (1), → 1/8 (2), → 1/16 (3) = 3 half-lives. Each half-life is 3 days, so 3 × 3 = 9 days.

Explanation

Concept: additional half-lives from a starting fraction. 1/2 → 1/4 (1), → 1/8 (2), → 1/16 (3) = 3 half-lives. Each half-life is 3 days, so 3 × 3 = 9 days.

17. Half-life is 1 hour. Starting at 320 bq, after 5 hours activity is:

160 bq

80 bq

20 bq

10 bq

Concept: repeated halving over multiple intervals. 320 → 160 → 80 → 40 → 20 → 10 (5 half-lives). Each hour is one half-life.

Explanation

Concept: repeated halving over multiple intervals. 320 → 160 → 80 → 40 → 20 → 10 (5 half-lives). Each hour is one half-life.

18. If the amount drops to 12.5%, that is the same as ______ of the original.

Concept: percent to fraction conversion. 12.5% = 0.125 = 1/8. This corresponds to three halvings because (1/2)^3 = 1/8.

Explanation

Concept: percent to fraction conversion. 12.5% = 0.125 = 1/8. This corresponds to three halvings because (1/2)^3 = 1/8.

Submit

19. If a sample has a higher initial amount, it will take longer to reach zero.

True

False

Concept: exponential decay never truly hits zero. It never truly reaches zero; decay rate depends on half-life, not initial amount.

Explanation

Concept: exponential decay never truly hits zero. It never truly reaches zero; decay rate depends on half-life, not initial amount.

20. Exponential decay means the amount is multiplied by the same ______ each half-life.

Concept: exponential change. It’s always ×1/2 per half-life.

Explanation

Concept: exponential change. It’s always ×1/2 per half-life.

Submit

Half-Life Reasoning Problems Quiz

1. If an isotope’s half-life is 6 hours, after 18 hours the remaining fraction is:

2.

What first name or nickname would you like us to use?

2. If 1/32 remains, 5 half-lives have passed.

3. Starting with 48 g, after 1 half-life you have 24 g. How much after 3 half-lives?

4. In equal time intervals of one half-life, the amount decreases by equal fractions, not equal amounts.

5. If you know half-life and the number of half-lives passed, you can estimate remaining fraction using (1/2)^n.

6. Half-life is useful for predicting how activity changes over time.

7. Best grade 11 summary: half-life lets you estimate remaining amount by:

8. Half-life = 10 years. Starting with 800 g, after 30 years you have:

9. A sample goes from 1600 bq to 200 bq. How many half-lives is that?

10. Half-life is 4 days. If 3 half-lives pass, time is:

11. If half-life = 2 hours, how many hours to go from 100% to 6.25%?

12. Going from 1/2 to 1/8 takes ______ additional half-lives.

13. A sample has half-life 5 minutes. How long to decrease from 80 units to 10 units?

14. If 1/4 remains, what percent remains?

15. Which are equivalent statements?

16. An isotope has half-life 3 days. How long to drop from 1/2 to 1/16?

17. Half-life is 1 hour. Starting at 320 bq, after 5 hours activity is:

18. If the amount drops to 12.5%, that is the same as ______ of the original.

19. If a sample has a higher initial amount, it will take longer to reach zero.

20. Exponential decay means the amount is multiplied by the same ______ each half-life.