Radioactive decay using half-life

Steps:

• Half-life is 7 years, so mass halves every 7 years.
• Initial mass 0.16 kg; target 0.02 kg.
• Number of half-lives n satisfies 0.16 / 2^n = 0.02, so 2^n = 8, n=3.
• Time = 3 × 7 = 21 years.

Why C is correct:

• The decay formula shows mass = initial × (1/2)^(t/T), where T=7 years; at t=21, (1/2)^3 = 1/8, so 0.16/8=0.02 kg.

Why the others are wrong:

• A: One half-life gives 0.16/2=0.08 kg, above target.
• B: Two half-lives give 0.16/4=0.04 kg, above target.
• D: Four half-lives give 0.16/16=0.01 kg, below target.

Final answer: C