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First, I need to define what an isotope is. An isotope of an element has the same number of protons, but a different number of neutrons. So, for example, Carbon-12 has 6 protons (which is why its atomic number on the table of elements is 6), and 6 neutrons. Carbon-14 also has 6 protons, but 8 neutrons. A radioactive isotope, or radioisotope, is one that is unstable and decays over time into another isotope or even another element that has a stable configuration.

Carbon-14 is what they use in "Carbon dating"; it has a half-life of 5,730 years. This means that if you had 10 pounds of carbon-14, at the end of 5,730 years, roughly half of it will have decayed into nitrogen-14. Some elements have an extremely long half-life; Uranium-235 has a half-life of 700 million years. Others have a half-life measured in a fraction of a second, like the man-made element Ununnilium-272, which has a half-life of only 10 milliseconds. For comparison, it takes 300 to 400 milliseconds to blink. This means Uun-272 has a half-life that is 30 to 40 times faster than a single blink!

At this point I could go into even more detail about the different types of radioactive decay (alpha-, beta-, and gamma-), which types of decay are dangerous to human life, and so on; but this is supposed to be an answer, not a chemistry book! I will, however, point out that the average American absorbs 360 mrem's of radiation per year. Your chance of dying from cancer increases 10% if you accumulate a total of 250,000 mrems - which means you'd have to live about 695 years to accumulate that much radiation! Not much to worry about...

Most elements, but not all, have at least one radioisotope.

All elements with an atomic number of 80 or higher have at least one radioisotope.

All isotopes of elements with an atomic number of 84 or higher are radioisotopes.

Therefore, Mercury (atomic number 80) is not normally radioactive, but some isotopes of it (Hg-194, Hg-197, Hg-203, and Hg-206) are radioactive; while all isotopes of Polonium (atomic number 84) are radioactive.

The total number of elements that have NO stable isotopes, including naturally-occurring and man-made elements, is about 37. If you add elements with naturally-occurring radioisotopes, that number will be significantly higher. (Carbon-14, for example, is naturally occurring.)

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