Final answer:
Carbon dating can be used to determine the age of fossils based on the amount of carbon-14 remaining in the sample. If a fossil contains 25 atoms of carbon and 25 atoms of nitrogen, it is estimated to be approximately 5,730 years old based on the half-life of carbon-14.
Step-by-step explanation:
Carbon dating, also known as radiocarbon dating, can be used to determine the age of fossils. Carbon-14 (¹⁴C) is a radioisotope that is present in all living organisms. When an organism dies, it no longer takes in carbon-14, and the amount of carbon-14 in its cells gradually decreases over time due to radioactive decay. By measuring the ratio of carbon-14 to carbon-12 in a fossil, scientists can calculate its age.
In the given scenario, if a fossil contains 25 atoms of carbon and 25 atoms of nitrogen, it means that half of the original carbon-14 has decayed into nitrogen-14. Based on the known half-life of carbon-14, which is 5,730 years, we can estimate that the fossil is approximately 5,730 years old.