The half-life of carbon-14 is about 6000 years. If the amount of carbon-14 remaining in a sample is 1/100 of the original amount, the atoms of the sample began decaying about
A) 20,000 years earlier.
B) 40,000 years earlier.
C) 60,000 years earlier.
D) 80,000 years earlier.

Question

Quizplus · Accepted Answer

The half-life formula is used to calculate the time it takes for a quantity to reduce to half its initial amount. Since the half-life of carbon-14 is about 6000 years, and the sample has reduced to 1/100 (or $1/2^{\text{n}}$, where n is the number of half-lives), we find n by solving $1/2^{\text{n}} = 1/100$. This gives $n \approx 6.64$, but since each half-life is 6000 years, we approximate to 7 half-lives for easier calculation, which gives us $7 \times 6000 = 42,000$ years. However, the closest answer choice to this calculation is 40,000 years, indicating that the sample began decaying about 40,000 years earlier.

The Half-Life of Carbon-14 Is About 6000 Years