Question

If a fossil that has been discovered recently contains 0.2% of the \(^{14}C\) (t₁/₂ = 5,730 years) that was present when the fossil was formed, then the age of the fossil in years is likely to fall in the range of

• A. 25,000 – 35,000
• B. 35,000 – 45,000
• C. 45,000 – 55,000
• D. 55,000 – 65,000

Hint:

For carbon dating, use the half-life formula and the percentage of \(^{14}C\) remaining to calculate the age of a fossil.

Answer 1

The Correct Option is C

Step 1: Understanding Carbon Dating.
The age of a fossil can be determined using radiocarbon dating, where the amount of \(^{14}C\) remaining in a sample is compared to its original amount. The half-life of \(^{14}C\) is 5,730 years.
Step 2: Applying the formula.
We use the formula for the remaining percentage of \(^{14}C\): \[ N = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} \] Where \(N_0\) is the original amount of \(^{14}C\), \(N\) is the remaining amount, \(t\) is the time elapsed, and \(t_{1/2}\) is the half-life.
Given that the remaining amount is 0.2%, we calculate the corresponding age, which is closest to 50,000 years.
Step 3: Conclusion.
Therefore, the age of the fossil is likely to fall in the range of 45,000 – 55,000 years (C).