$^{14}c$, or carbon-14, is a radioactive isotope of carbon that is used in radiometric dating to determine the age of organic materials. It is formed in the atmosphere when cosmic rays collide with nitrogen-14, converting it into carbon-14, which then gets absorbed by living organisms. After an organism dies, the absorption stops, and the carbon-14 begins to decay at a known rate, allowing scientists to estimate the time since death.