Final answer:
Radiocarbon dating is the radiometric dating method that can date materials up to 75,000 years old by measuring the remaining radioactive carbon (carbon-14) in organic material.
Step-by-step explanation:
The radiometric dating method popular with archaeologists that can be used to date materials up to 75,000 years old is known as radiocarbon dating, or carbon-14 dating. This method is used to determine the absolute age of organic materials by measuring the amount of radioactive carbon (carbon-14) remaining in a sample. When a living organism dies, its intake of carbon-14 stops, and the isotope begins to decay at a known rate, called its half-life. By measuring the remaining carbon-14 in a sample, scientists can calculate when the organism died, within a margin of error. However, radiocarbon dating is effective only for samples that are between 300 and 50,000 years old, with the most accurate results for samples no older than 50,000 years.