The best-known radioactive isotope of carbon is carbon-14, which is used for dating (calculating the age) of organic materials. However, carbon has several other isotopes, both stable and unstable: http://en.wikipedia.org/wiki/Isotopes_of_carbon
A stable nucleus is one which will not decay, whereas an unstable nucleus will decay at some point, which cannot be predicted as decay is a random process, by alpha or beta decay.
Decay
Magnesium
An unstable nucleus, which can be caused by:excess of neutronsshortage of neutronsmetastable excited state of nucleus
the unstable nucleus will decay into smaller, stable particles.
Atomic nuclei that are unstable and decaying are said to be radioactive. Radioactive decay involves alpha, beta and gamma particle emissions.
When a nucleus is unstable it has either too many or too few neutrons in the nucleus. This is what causes nuclear decay as the nucleus needs to have the correct ratio of neutrons to protons to be stable. It may be triggered by an outside force, such as a colliding particle, or simply by chance.
Too many or too few neutrons.
It is true that unstable nuclei will undergo radioactive decay in order to gain stability. These include nuclei of #43 Technitium (Tc), any nucleus containing more that 83 protons and any nucleus with a high neutron-to-proton ratio, such as carbon-14. The most common forms of decay are by emission of an alpha particle (2 protons and 2 neutrons ... a helium nucleus!) or a beta-negative decay in which a neutron bcomes a proton by emitting an electron and an antineutrino.
The process of a radioactive decay is atomic nucleus of an unstable atom loses energy by emitting ionizing particles
You will have an unstable carbon atom. The result will be carbon
Instability is due to a certain ratio between neutrons and protons in the atomic nucleus.