What causes an element to become radioactive?

First, we need to talk isotopes rather than elements. An element is defined by the number of protons in its nucleus. Isotopes of an element have the same number of protons, but a different number of neutrons in the nucleus. If a nucleus has more neutrons in its nucleus than it wants (the neutron/proton ratio is too high), it will try to get to a stable state by emitting some form of radiation (alpha, beta, gamma, nuetron). Some isotopes that occur naturally are radioactive. Most products resulting from the fission process are radioactive. A stable nucleus can be made radioactive by bombarding it with sub-atomic particles - usually alpha, neutron, or proton. The fission process releases a lot of neutrons. In a nuclear reactor some of these neutrons are absorbed by nuclei used in the structure of the reactor. These then become radioactive. In some reactors, materials are purposely inserted into the reactor to make them radioactive. This is how most radioactive isotopes used for medical purposes is produced.