Final answer:
To calculate the age of a fossil with 1.25 grams of carbon-14 and 3.75 grams of nitrogen-14, we determine that two half-lives of carbon-14 have passed, which equals approximately 11,460 years. Therefore, the fossil is around 11,460 years old.
Step-by-step explanation:
The question involves using the half-life of carbon-14 to determine the age of a fossil. The isotope carbon-14 decays into nitrogen-14, and by measuring the ratio of the two substances in the fossil, we can estimate how many half-lives have passed since the organism died. Given that the half-life of carbon-14 is approximately 5,730 years, and the fossil contains 1.25 grams of carbon-14 and 3.75 grams of nitrogen-14, we can infer that for every gram of carbon-14 that has decayed, a gram of nitrogen-14 has been formed.
Initially, there would have been 5 grams of carbon-14 and zero grams of nitrogen-14. After one half-life (5,730 years), half of the carbon-14 would have decayed, leaving us with 2.5 grams of carbon-14 and 2.5 grams of nitrogen-14. Since we now have 1.25 grams of carbon-14 remaining, another half-life has passed, meaning the total time elapsed is two half-lives or 11,460 years. Therefore, the fossil is approximately 11,460 years old.