A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min?

Question

A radioactive sample has a half-life of 10 min.  What fraction of the sample is left after 40 min?

BlackTom AI · Accepted Answer

To solve this, we use the concept of half-life: after each half-life period the amount remaining is halved. Since the half-life is 10 minutes, 40 minutes corresponds to four half-lives (40 / 10 = 4).
Option 1: 1/16. This matches (1/2)^4 = 1/16, so this is consistent with the half-life decay model.
Option 2: 1/8. If the sample were reduced to 1/8, that would imply three half-lives have passed (since (1/2)^3 = 1/8). Four half-lives are required to reach 1/16, so this is not correct for 40 minutes.
Option 3: 1/4. This would correspond to two half-lives (40 minutes would be 4 half-lives, not 2). Therefore this undervalues the decay.
Option 4: 1/32. This would be five half-lives (since (1/2)^5 = 1/32). That would require 50 minutes, not 40, so it overestimates the decay.
Option 5: 1/2. This would mean zero half-lives have occurred, i.e., no decay, which is incorrect for 40 minutes at a 10-minute half-life.
In summary, the decay pattern for four half-lives yields 1/16, while the other fractions correspond to fewer or more half-lives than the 40-minute interval specifies.

PHYSICS 1201 SU2025 (10585) Final Exam- Requires Respondus LockDown Browser

A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min?

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