Final answer:
All of the choices—wood, bones, and charcoal—can be dated using carbon-14 at archaeology sites. Radiocarbon dating is effective for dating organic materials up to around 50,000 years old.
Step-by-step explanation:
The materials that can be dated with carbon-14 at archaeology sites are: A. wood, B. bones, C. charcoal. The correct answer to the initial question is D. all of these choices are correct. Organic material, including these, contain carbon and can be radioactively dated using the long-lived nuclide of carbon, carbon-14 (¹⁴C). When an organism dies, the ratio of ¹⁴C to ¹²C decreases at a known rate, allowing the determination of the time since death. This method is called radiocarbon dating and is effective for artifacts up to 50,000 years old.
As for the piece of wood from an ancient Egyptian tomb with an activity per gram of carbon of A = 10 decay/min²g, to determine its age we compare the activity to that of a modern standard to calculate the number of half-lives that have passed and then multiply by the half-life of ¹⁴C, which is approximately 5,730 years. However, details for the complete calculation process are not provided here.
It is important to note that carbon dating would not be valid for a piece of wood claimed to be 3 billion years old, as the half-life of carbon-14 is such that after around 50,000 years there is too little ¹⁴C remaining to measure accurately.