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Species with an odd number of electrons have an unpaired electron. Take CH3 for example: there are 7 electrons total, so carbon will have 3 pairs and 1 single electron. This, by definition, makes it a radical. The converse is true, as even numbers of electrons form pairs.
Radicals are defined as compounds with an unpaired e-, and the converse is true--that compounds with an even number of electrons are not radicals. Important to note that because of the one unpaired e-, radicals are highly reactive and exist for only a short time (because they are likely to react and form something more stable).
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