Nuclear energy is obtained through fission and fusion reactions. Fission reactions require splitting up of atoms with a result to release enormous amounts of energy. The conversion of mass to energy can be explained by Einsteins relation of relativity E = MC^2. However the energy required for fusion is enormous as well and makes it impractical. Scientists for many years have entertained the idea of "cold fusion" which entertains the possibility of causing a fusion reaction at room temperature, so far there's been little advancement on that. However, in nuclear reactors it's fission reaction that is used to produce electricity which entails splitting of atoms of radioactive elements.
