Half-lives determine fractional decay in radioactive isotopes

Steps:

• The half-life is 6000 years, meaning activity halves every 6000 years.
• 1/16 of initial activity equals (1/2)^4, requiring 4 half-lives.
• Multiply half-lives by time per half-life: 4 × 6000 years.
• Total time is 24000 years.

Why C is correct:

• Radioactive decay law states activity A = A0 × (1/2)^(t/T), where t/T = 4 gives A = A0/16 at t = 24000 years.

Why the others are wrong:

• A: One half-life reduces activity to 1/2, not 1/16.
• B: Three half-lives reduce to 1/8, not 1/16.
• D: Sixteen half-lives reduce to 1/65536, far below 1/16.

Final answer: C