A fossil is found to have a 14C level of 75.0% compared to living organisms. How old is the fossil?
The correct answer and explanation is:
To find the age of the fossil using carbon-14 dating, use the formula based on exponential decay:
Age = (t₁/₂ / ln2) × ln(N₀/N)
Where:
- t₁/₂ is the half-life of carbon-14 (5730 years)
- N₀ is the original amount of carbon-14 (100%)
- N is the current amount of carbon-14 (75.0%)
- ln is the natural logarithm
Step-by-step calculation:
- Use the formula:
Age = (5730 / ln2) × ln(100 / 75) - Calculate ln2:
ln2 ≈ 0.693 - Calculate 100 / 75 = 1.333
- Calculate ln(1.333):
ln(1.333) ≈ 0.2877 - Now plug into the formula:
Age = (5730 / 0.693) × 0.2877
Age ≈ 8267.97 × 0.2877
Age ≈ 2379 years
Correct Answer: Approximately 2379 years old
Explanation:
Carbon-14 dating is a method used to determine the age of once-living materials based on the decay of carbon-14, a radioactive isotope. Living organisms constantly exchange carbon with the environment, keeping their carbon-14 levels in equilibrium with the atmosphere. When an organism dies, it stops absorbing carbon, and the carbon-14 inside begins to decay at a known rate called the half-life.
In this case, the fossil retains 75% of the original carbon-14. This means one full half-life has not passed, but some decay has occurred. The calculation uses logarithms to reverse-engineer how much time must have passed for the original 100% to decrease to 75%.
This technique is highly effective for dating fossils up to about 50,000 years old and is widely used in archaeology and geology. The result of 2379 years suggests the organism died about that long ago.