A radioactive isotope has a half-life of 12 hours. If a sample initially contains 64 mg of this isotope, how much of the isotope remains after 36 hours?
Show the answer and explanation
Correct answer
B. 8 mg
Principle or equation
Radioactive decay: remaining amount = initial amount × (1/2)^(t / half-life).
Why this answer is correct
The half-life is 12 hours, and the elapsed time is 36 hours, which is 3 half-lives. After each half-life, the amount halves: 64 mg → 32 mg → 16 mg → 8 mg. So after 36 hours, 8 mg remains.
Example
If a sample has half-life 2 days and initial 100 mg, after 6 days (3 half-lives) it becomes 12.5 mg.
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