A radioactive isotope has a half-life of 8.0 days. If an initial sample contains 80 mg of this isotope, how much of the original isotope remains undecayed after 24 days?

Answer and explanation

Correct answer: A. 10 mg

  1. Step 1: Calculate the number of elapsed half-lives: n = total time / half-life = 24 days / 8.0 days = 3 half-lives.
  2. Step 2: The remaining mass is: m = m_0 * (1/2)^n.
  3. Step 3: Substitute values: m = 80 mg (1/2)^3 = 80 mg (1/8) = 10 mg.
Answer
10 mg.
Why not the others: '20 mg' represents the remaining amount after only 2 half-lives (16 days); '5.0 mg' represents 4 half-lives (32 days); '40 mg' is after 1 half-life (8 days).

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