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

## Equations and Half-life

### 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.

## Mass-Energy Conservation

In radioactive decay, energy is released in the form of the kinetic energy of the fast moving ${\displaystyle \alpha }$  or ${\displaystyle \beta }$  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.