Final answer:
The dating method based on the decay of radioactive carbon isotopes is known as radiocarbon dating which estimates the age of organic materials by measuring the remaining carbon-14.
Step-by-step explanation:
The method of dating fossils and artifacts based on the decay of radioactive carbon isotopes is called radiocarbon dating. This technique uses the principle that carbon-14 (C-14), a radioactive isotope of carbon, is continuously formed in the atmosphere and absorbed by living organisms. Once an organism dies, it no longer takes in C-14, and the isotope begins to decay at a known rate, known as its half-life, which is approximately 5,730 years. By measuring the amount of C-14 remaining in a sample and comparing it to the known rate of decay, scientists can estimate the time since the death of the organism, effectively dating the sample up to about 50,000 years old.