What is the age in years of a bone in which the ratio 14C/ 12C is measured to be 2.3×10^−13?

I am confused on this question.

To determine the age in years of a bone using the ratio of 14C/12C, we need to understand the concept of radiocarbon dating. Radiocarbon dating is based on the fact that the ratio of radioactive carbon-14 (14C) to stable carbon-12 (12C) in the Earth's atmosphere is relatively constant.

However, when an organism, such as a plant or animal, dies, it no longer takes in any carbon from the atmosphere. Over time, the amount of 14C in the organism's remains decreases due to radioactive decay, while the amount of stable 12C remains constant. By measuring the ratio of 14C to 12C in a sample, scientists can estimate the age of the sample.

In this case, the given ratio of 14C/12C is 2.3x10^−13. To calculate the age in years, we need to use the decay constant of 14C, which is the rate at which 14C decays. The half-life of 14C is approximately 5730 years, meaning that after 5730 years, half of the 14C in a sample will have decayed.

The equation used to calculate the age is as follows:

Age (in years) = (ln (14C0/14C) / λ)

Where:
- λ is the decay constant of 14C (0.693 / half-life)
- 14C0 is the initial amount of 14C in the organism when it died
- 14C is the measured amount of 14C in the sample

To calculate the age, we need to know the initial amount of 14C in the organism when it died (14C0). This value would require additional information and understanding of the specific dating scenario. Without knowing this value, it is not possible to calculate the age based on the given ratio of 14C/12C alone.