An artifact has a carbon-14 to carbon-12 ratio that is one-fourth the carbon-14 to carbon-12 ratio of a similar modern object. How old is the artifact? (The half-life of carbon-14 is 5,715 years.)
See your post above on the wood. This is the same kind of problem.
To determine the age of the artifact, we can use the concept of carbon dating. Carbon-14 is an isotope of carbon that is used for dating organic materials that are up to around 50,000 years old. It decays at a constant rate over time, with a half-life of 5,715 years.
The ratio of carbon-14 to carbon-12 in a living organism is the same as in the atmosphere. However, once the organism dies, it no longer takes in new carbon-14, and the existing carbon-14 begins to decay.
In this case, the artifact has a carbon-14 to carbon-12 ratio that is one-fourth the ratio in a similar modern object. This means that only 1/4th of the original carbon-14 atoms remain compared to a modern sample.
To calculate the age of the artifact, we can use the concept of half-life.
1. Start by determining how many half-lives have passed since the artifact died.
Since the ratio of carbon-14 to carbon-12 is 1:4 compared to a modern sample, this means that only 1/4th of the original carbon-14 atoms remain. Therefore, it has gone through one half-life.
2. Calculate the number of years per half-life.
The half-life of carbon-14 is 5,715 years. This means that every 5,715 years, half of the original carbon-14 atoms decay.
3. Multiply the number of half-lives by the number of years per half-life.
In this case, since the artifact has gone through one half-life, we multiply 1 by 5,715 years.
1 * 5,715 = 5,715 years
Therefore, the artifact is approximately 5,715 years old.