A wooden artifact from an ancient tomb contains 45 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made
6601 years
To determine the approximate age of the wooden artifact, we can use the concept of carbon dating. Carbon-14 (C-14) is an unstable isotope of carbon that is present in the Earth's atmosphere. Living organisms, including trees, constantly absorb carbon, and the ratio of C-14 to stable carbon-12 (C-12) remains relatively constant in their bodies.
However, when an organism dies, it no longer takes in new carbon-14, and the existing C-14 starts to decay at a known rate. By measuring the remaining C-14 in a sample, scientists can estimate how long it has been since the organism died and ceased replenishing its C-14 levels.
In this case, the artifact contains 45 percent of the C-14 found in living trees. By comparing this percentage to the known half-life of C-14, we can calculate the age of the artifact. The half-life of C-14 is approximately 5730 years, which means that every 5730 years, half of the C-14 in a sample decays.
To calculate the age of the wooden artifact:
1. Determine the number of half-lives that have occurred:
- Divide 100% by 45% to find the fraction remaining: 45%/100% = 0.45.
- Take the logarithm base 2 of the fraction remaining: log2(0.45) ≈ -0.153.
- Divide the result by the logarithm base 2 of 0.5 (representing one half-life): -0.153 / log2(0.5) ≈ 0.266.
2. Multiply the number of half-lives by the C-14 half-life (5730 years): 0.266 * 5730 ≈ 1523 years.
Therefore, the artifact was made approximately 1523 years ago to the nearest year.