A piece of ancient wood has carbon-14 activity equal to 35% of the activity in living wood having the same amount of carbon. The half-life of carbon-14 is 5730 years. The age of the sample is closest to:
Options

Question

A piece of ancient wood has carbon-14 activity equal to 35% of the activity in living wood having the same amount of carbon. The half-life of carbon-14 is 5730 years. The age of the sample is closest to:

Options

G1 Physics · Accepted Answer

Activity is proportional to the number of carbon-14 nuclei, so A(t) ÷ A₀ = 0.35. Decay law: 0.35 = exp(−λt). Therefore, t = −ln(0.35) ÷ λ. Using λ = ln2 ÷ 5730, we get t = 5730×[−ln(0.35)] ÷ ln2. With −ln(0.35) ≈ 1.0498 and ln2 ≈ 0.693, t ≈ 5730×1.0498 ÷ 0.693 ≈ 8680 years. Thus the closest option is 8.68×10³ years. Correct option: B.