Isotopes containing 83 protons or more are radioactive, although same may take billions of years before they decay, they will decay. These isotopes are called unstable.
By http://www.dictionary.com/ the chemistry definition of unstable is, "noting compounds that readily decompose or change into other compounds." This means that an unstable atom will eventually decompose and give off radioactive decay.
What makes an isotope radioactive?
-->Well first, as described earlier isotopes cantain 83 or more protons are radioactive. This is because the strong force (an attractive force that holds the protons and neutrons together in a nucleus) only works at very short distances. A nucleus with 83 or more protons is too big for the strong force to keep the protons together, so sooner or later the nucleus will decompose.
ex. Polonium has an atomic number of 84. All the isotopes of polonium are radioactive/
-->Another way for a nucleus to be unstable is if it contains too many or too few neutrons. It all depends on ratios. When nuclei have more than 60 protons they need a ratio of neutrons to protons of 3 to 2 to be stable. When nuclei have less than 20 protons they need a ratio of 1 to 1 to be stable.
ex. Hydrogen-3 has a ratio of 2 neutrons to 1 proton. Because there are less than 20 protons it needs a ratio of 1 to 1 to be stable. The ratio is greater so this means Hydrogen-3 is unstable and therefore radioactive.
ex. Beryllium-10 has a ratio of 3 to 2. It has 6 neutrons and 4 protons. This isotope is radioactive because its ratio is greater than 1 to 1.
Holt , Rinehart, and Winston. Interactions of Matter. 2002 (book)
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