A radioactive isotope has a half-life of 6.0 hours. If a sample initially contains 80 mg of this isotope, how much of the isotope remains after 18 hours?
Show the answer and explanation
Correct answer
A. 10 mg
Principle or equation
After n half-lives, the remaining amount is the initial amount multiplied by (1/2)^n.
Why this answer is correct
18 hours is 3 half-lives (18/6 = 3). Remaining = 80 mg × (1/2)^3 = 80 × 1/8 = 10 mg.
Example
If a sample has a half-life of 2 years, after 6 years (3 half-lives) only 1/8 of the original remains.
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