what is meant when we say a nucleus is radioactive?

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Radioactivity is a property of certain isotopes of certain elements on the periodic table. What it means is that some isotopes of elements will spontaneously break apart into two smaller elements(decay) and at the same time release other smaller particles such as an electron or an alpha particle.  In addition, a certain amount of energy is also released. A well known example is Uranium 235 (U-235) which is uranium, element 92,with a mass of 235.  This isotope is used in nuclear power plants to produce electricity by using the energy that is released when it decays.

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