Radiocarbon Dating with Carbon-14

Steps:

• Wooden objects are organic, so age is determined by radiocarbon dating.
• Radiocarbon dating measures decay of radioactive Carbon-14 isotope absorbed during life.
• Half-life of Carbon-14 is 5730 years, suitable for 6000-year-old samples.
• Stable carbon isotopes do not decay and cannot date objects.

Why A is correct:

• ^{14}C is the radioactive isotope whose decay rate follows the exponential decay formula N = N_0 e^{-\lambda t}, enabling age calculation for organic remains.

Why the others are wrong:

• B. ^{12}C is stable and non-radioactive, providing no decay information for dating.
• C. ^{13}C is stable, used for isotopic fractionation corrections but not age determination.
• D. ^{12}C is identical to B, stable and unsuitable for radioactive dating.

Final answer: A