Radioactive half-life is independent of sample mass Steps:

• Half-life is the time for half of the radioactive nuclei to decay, a constant for the isotope.
• It does not change with sample size; the decay rate per nucleus is fixed.
• For radon-222, half-life is always 3.8 days, regardless of starting mass.
• Thus, for a 2.0 mg sample, the half-life remains 3.8 days. Why C is correct:
• Half-life is an intrinsic property of the isotope, defined independently of the amount of material present. Why the others are wrong:
• A: After 3.8 days (one half-life), 1.0 mg remains from 2.0 mg, not 0.5 mg.
• B: After 7.6 days (two half-lives), 0.5 mg remains, not 0.0 mg.
• D: After 7.6 days, 0.5 mg remains; decay is exponential, never exactly zero in finite time.

Final answer: C