The radiocarbon dating method is based on the fact that radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
Alpha decay typically occurs in nuclei that are so big that they can’t be stable.
In alpha decay, the nucleus ejects a helium nucleus (alpha particle) composed of two neutrons and two protons, dropping the mass of the original nucleus by four mass units.
Other corrections must be made to account for the proportion of throughout the biosphere (reservoir effects).
Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s.
More information is available on this project's attribution page.