OCR A-Level Physics/Fields, Particles and Frontiers of Physics/Radioactivity

Carbon dating
When a tree is living, it take carbon dioxide from the atmosphere to produce cellulose. The vast majority of carbon is carbon-12 which isn't radioactive, however a small fraction of the carbon atoms are carbon-14 which is radioactive. Once the tree dies, no more carbon-14 will be absorbed.

The ratio of carbon-14 to carbon-12 in dead organic matter decreases with time, so the ratio can be used for dating.

Limitations of carbon dating
Because the quantity of carbon-14 is very small, count rates are correspondingly small and after a few-half lives it may be indistinguishable from the background count rate.

The ratio of carbon-14 to carbon-12 in the air and in all living things is assumed to be constant, this may not be true if there have been changes in the rate at which carbon-14 is produced in the atmosphere.

Dating Rocks
Other methods of dating are used for non-living things, such as rocks. Rocks contain tiny amounts of radioactive isotopes which have very long half-lives. Different isotopes with different half-lives can used to find the since the formation of rock of different ages using the relative proportions of the parent atoms and decay products in the rock.

Radioactive decay
In radioactive decay, energy is released in the form of the kinetic energy of the fast moving $$\alpha$$ or $$\beta$$ particles, and may be also released as gamma ray photons. The origin of this energy is the conversion of some masses of the particles transferred into energy.