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Radioactivity refers to the particles/energy which are emitted from nuclei as a result of nuclear instability.
Because the nucleus experiences the intense conflict between the two strongest forces in nature, the electromagnetic force that makes atoms stick together to form molecules and the strong nuclear force that holds the nucleus together, it should not be surprising that there are many nuclear isotopes which are unstable and emit some kind of radiation.
The most common types of radiation are called alpha, beta, and gamma radiation.