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It is because radicals are so unstable that they will only exist for a very short time before reacting with something else in an effort to regain stability. This intense reactivity is what makes them dangerous to things like the body's cells, for example.
Radicals would occur if an atom becomes an ion and has an odd number of electrons. In addition, in the bonding of a particular molecule with an odd number of atoms, radicals frequently occur. It is standard procedure to assign radical electrons to an element in a particular molecule that would lessen the resulting formal charges and the overall formal charge of that molecule.
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