2: The ratio of carbon-14 to carbon-12 in a living organism matches that of the atmosphere: about 1 part per trillion. After the organism dies, there is no longer any intake of carbon from the environment. Whatever amount of carbon-14 that is present in the organism when it dies undergoes beta-minus decay with a half-life of 5,730 years. On the other hand, the carbon-12 is stable and remains intact in the organism. (a) What is the decay constant of carbon-14? (b) An anthropologist is studying the remains of a neanderthal, and measures the 14C/12C ratio from a bone sample to be 14 parts per quadrillion. How long ago did this neanderthal die? (c) After about 8 half-lives have passed, there is typically not enough radioactive material left for the carbon-14 dating method to be accurate. What fraction of the original carbon-14 remains undecayed after 8 half-lives? (d) What is the oldest sample that could be reliably dated using the carbon-14 method? (Other methods of radioactive dating, such as potassium-argon dating, have a range of billions of years into the past.)