To determine the most likely conclusion based on the C12/C14 ratios for the given organisms, we need to understand the relationship between these ratios and the time since death.
The C12/C14 ratio is used in radiocarbon dating to determine the age of an organism since its death. Carbon-14 ([tex]\(^14C\)[/tex]) is a radioactive isotope that decays over time, while Carbon-12 ([tex]\(^12C\)[/tex]) is a stable isotope. When an organism dies, it stops absorbing [tex]\(^14C\)[/tex], and the existing [tex]\(^14C\)[/tex] begins to decay. Therefore, the higher the C12/C14 ratio, the longer the organism has been dead, because more [tex]\(^14C\)[/tex] has decayed relative to the amount of [tex]\(^12C\)[/tex].
Given the C12/C14 ratios:
- Organism X: [tex]\(8 \times 10^{12}\)[/tex]
- Organism Y: [tex]\(2 \times 10^{12}\)[/tex]
- Organism Z: [tex]\(1 \times 10^{12}\)[/tex]
We can conclude the following based on these ratios:
1. Organism Z has the smallest C12/C14 ratio of [tex]\(1 \times 10^{12}\)[/tex]. This implies that it has the highest amount of [tex]\(^14C\)[/tex] relative to [tex]\(^12C\)[/tex], meaning it is the most recently alive or still living.
2. Organism Y has a C12/C14 ratio of [tex]\(2 \times 10^{12}\)[/tex], which is higher than Z's ratio but lower than X's ratio. This implies that Y has been dead longer than Z but shorter than X.
3. Organism X has the highest C12/C14 ratio of [tex]\(8 \times 10^{12}\)[/tex]. This suggests that X has been dead the longest among the three organisms.
Therefore, from the given information, the most accurate conclusion is:
Only Organism Z is alive, and Organism Y has been dead longer than Organism X.
