At an archaeologicalte you unearth a fire pit and take a carbon sample to determine the age 5370 years. of the burnt material. From a reference source, you know that the half-life of carbon-14 is (a) If we know the number of carbon atoms in a sample and the carbon-14 half-life, explain how we can estimate the age of the sample. (1 mark) (b) Another way to determine the age of an object comes from measuring the activity of the sample. Explain why measuring the activity is useful, by explaining how activity is connected to the number of carbon atoms in the sample. (1 mark) (C) As you keep digging at the site, you uncover another layer of burnt carbon. When you analyse this sample, you discover there is no carbon-14. What can you say about the age of this sample? (1 mark) (d) Radioactive isotopes are used in nuclear medicine to diagnose or treat certain conditions. Explain why radioactive isotopes found in the natural world are not used in nuclear medicine. That is, why do we use isotopes created in the lab? (2 marks)