Half-life (T): The half-life of a radioactive isotope is the time taken for the mass of the isotope to decrease to half its initial mass. (s)
Activity (A): The activity of a radioactive isotope is the number of nuclei of the isotope to decay per second. (Bq)
Decay constant (λ): The decay constant (λ) is the probability of an individual nucleus decaying per second. (s^-1)
The energy transfer per second from a radioactive source = AE (W)
Uses for radioactive decay:
Carbon dating: Living plants contain small amount of carbon-14 with is created in the atmosphere by cosmic rays knocking out neutrons from nitrogen-14 nuclei.
CO2 is taken up by the plant during photosynthesis and some of this CO2 contains carbon-14. Carbon-14 has a half-life of 5570 years so does not decay a lot during the plants lifetime. Once the plant has died, it no longer takes in CO2 so the proportion of C-14 decreases in the dead plant as the C-14 nuclei decays. This allows us to calculate the age.
Assumptions: The rate of production of C-14 is constant