Carbon-dating is used to determine the age of -

Fossils

The correct answer is option 2. Fossils.

Carbon dating, also known as radiocarbon dating, is a method used to determine the age of organic materials, including fossils. This technique relies on measuring the amount of carbon-14 (\(^{14}C\)) isotope in the remains of once-living organisms. As living organisms absorb carbon from the atmosphere, the ratio of carbon-14 to carbon-12 remains relatively constant. However, once an organism dies, the carbon-14 begins to decay at a known rate.

By comparing the ratio of carbon-14 to carbon-12 in a sample to the known ratio in the atmosphere, scientists can estimate how long it has been since the death of the organism. This provides valuable information about the age of fossils, helping researchers understand the timing of events in Earth's history and the evolution of life.