To determine the state and relative ages of the organisms based on the given information about the [tex]\( \text{C-12/C-14} \)[/tex] ratios, we need to analyze how these ratios compare to the ratio in the atmosphere.
### Step-by-Step Analysis:
1. Understand the Atmospheric Ratio:
- The ratio of [tex]\( \text{C-12} \)[/tex] to [tex]\( \text{C-14} \)[/tex] in the atmosphere is [tex]\( 1 \times 10^{12} \)[/tex].
2. Ratios in Organisms:
- Organism A: [tex]\( 1 \times 10^{12} \)[/tex]
- Organism B: [tex]\( 2 \times 10^{12} \)[/tex]
- Organism C: [tex]\( 4 \times 10^{12} \)[/tex]
3. Determine if an Organism is Dead:
- When an organism dies, it stops taking in new carbon, so the [tex]\( \text{C-14} \)[/tex] starts to decay, increasing the [tex]\( \text{C-12/C-14} \)[/tex] ratio.
- Compare the ratios inside the organisms to the atmospheric ratio to check if each organism is dead:
- Organism A: [tex]\( 1 \times 10^{12} \)[/tex] (same as the atmosphere) -> Likely not dead.
- Organism B: [tex]\( 2 \times 10^{12} \)[/tex] (greater than the atmosphere) -> Dead, because the ratio is higher.
- Organism C: [tex]\( 4 \times 10^{12} \)[/tex] (greater than the atmosphere) -> Dead, because the ratio is higher.
4. Relative Age of Dead Organisms:
- Higher [tex]\( \text{C-12/C-14} \)[/tex] ratio indicates a longer time since death because more [tex]\( \text{C-14} \)[/tex] has decayed.
- Compare the ratios of the dead organisms B and C:
- Organism B has [tex]\( 2 \times 10^{12} \)[/tex].
- Organism C has [tex]\( 4 \times 10^{12} \)[/tex].
- Since [tex]\( 4 \times 10^{12} > 2 \times 10^{12} \)[/tex], Organism C has a ratio that indicates it might have been dead longer (more decay of [tex]\( \text{C-14} \)[/tex]).
### Conclusion:
Both Organism B and Organism C are dead. However, Organism C has a higher [tex]\( \text{C-12/C-14} \)[/tex] ratio than Organism B, implying that Organism C has been dead for a longer period than Organism B.
Thus, the conclusion is:
- Both Organism B and Organism C are dead, but Organism B has been dead longer than Organism C.
Therefore, the correct conclusion from the given information is:
- Both Organism B and Organism C are dead, but Organism B has been dead longer than Organism C.
