Chapter 2, Problem 14PS

Interpreting Data As discussed in the text and shown in Figure 2.17, radiometric dating can be used to determine the age of biological materials. The calculation of age depends on the half-life of the radioisotope under consideration For example, carbon-14 makes up about 1 part per trillion of naturally occurring carbon When an organism dies, its body contains 1 carbon-14 atom per trillion total carbon atoms. After 5,700 years (the half-life of carbon-14), its body contains one-half as much carbon-14; the other half has decayed and is no longer present. French scientists used carbon-14 dating to determine the age of prehistoric wall paintings in the Niaux caves They determined that the paintings were made using natural dyes approximately 13,000 years ago Using your knowledge of radiometric dating, how much carbon-14 must the scientists have found in the cave paintings to support this result? Express your answer in both percentage of carbon-14 remaining and in parts of carbon-14 per trillion.