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The isotope of hydrogen we call tritium is radioactive because all atoms of it have an unstable nucleus. Tritium, which is hydrogen-3, has a single proton in its nucleus (as you'd expect), and has two neutrons there as well. This combination of nucleons is not stable, and it will eventually decay (with a 12.32 year half-life). Said another way, the nuclear arrangement of a proton and two neutrons is not a stable one, so atoms of this isotope of hydrogen will be radioactive and will eventually decay.

When any atom is "created" by fusion or other means (including nuclear decay), the nucleons (the protons and neutrons that make up its nucleus) have to "make a deal" as to how they are going to get along in the tiny volume of space that the nucleus occupies. Some arrangements of protons and neutrons just "aren't right" and are unstable, and this gives rise to characterizing the isotope as being radioactive. Tritium (H-3) is one such isotope.

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