Carbon-14 has a half-life of 5730 years. In a plant fossil, you find that the 14C14C has decayed to 1/4.00 of the original amount. How long ago was this plant alive?
The Correct Answer and Explanation is:
To determine how long ago the plant was alive, we use the concept of half-life. A half-life is the time it takes for half of a radioactive substance to decay. In this case, the half-life of Carbon-14 is 5730 years.
The problem tells us that only one-quarter (1/4) of the original Carbon-14 remains in the plant fossil. That means the carbon has gone through two half-lives:
- After one half-life (5730 years), 1/2 of the original Carbon-14 remains.
- After two half-lives (5730 × 2 = 11,460 years), 1/2 of 1/2 = 1/4 of the original Carbon-14 remains.
Answer: 11,460 years ago
Explanation
Carbon-14 dating is a method used to estimate the age of organic materials by measuring the remaining amount of Carbon-14 in a sample. Carbon-14 is a radioactive isotope that is absorbed by living organisms. When the organism dies, it stops absorbing Carbon-14 and the existing Carbon-14 in its body starts to decay at a known rate. This decay follows a pattern known as exponential decay.
The half-life of Carbon-14 is 5730 years. That means every 5730 years, half of the existing Carbon-14 decays into nitrogen-14. This process continues in halves with time. So if we start with a certain amount of Carbon-14, after one half-life only half remains. After two half-lives, only one-quarter of the original Carbon-14 remains, and so on.
In this problem, the fossilized plant contains only one-quarter of its original Carbon-14. Since each half-life reduces the amount by half, this means it has gone through two half-lives. First, the amount dropped to one-half, then to one-quarter. We can multiply the half-life by the number of half-lives to find out the total time that has passed.
So we multiply 5730 years by 2, giving 11,460 years. This means the plant died approximately 11,460 years ago. This method is reliable for dating specimens up to about 50,000 years old and is commonly used in archaeology and geology to date organic remains.
