What percentage of a radioactive isotope would remain after three half-lives?

Question

BlackTom AI · Accepted Answer

To determine the remaining percentage after a number of half-lives, remember that each half-life halves the amount present.
Option 1: 6.3 percent. This would correspond to roughly 1/16 (6.25%) or a miscalculation of two and a half half-lives, which is not an integer number of half-lives. Since we’re told three half-lives have passed, this value is not correct.
Option 2: 12.5 percent. After one half-life you have 50%, after two you have 25%, and after three you have 12.5%. This is the exact result of applying three successive halvings: (1/2) × (1/2) × (1/2) = 1/8 = 12.5%. This option matches the mathematical progression.
Option 3: 50.0 percent. This would be the amount remaining after only one half-life, not after three. It ignores the subsequent halvings, so it does not reflect three half-lives.
Option 4: 25.0 percent. This value corresponds to after two half-lives (1/2 × 1/2 = 1/4 = 25%), not after three. It shows a common mix-up between the number of half-lives and the amount remaining.
In summary, the correct conceptual approach is to apply three successive halvings, yielding 12.5%, while the other options reflect either an earlier point in the decay sequence or a miscount of half-lives.

CHE 1V_SS1 2025 Final Exam_SS1_2025_Proctored

What percentage of a radioactive isotope would remain after three half-lives?

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