what is an unpaired electron?

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So following on from the definition of a radical as being a species with an unpaired electron, my question is what are these unpaired electrons? What does it mean for two electrons to be doubled up? Is this an observable effect or is it just a bookkeeping technique?

Won’t all the elements in group 1, 3,… 2n-1 have an unpaired electron? So Fluorine has 1s²2s²2p5 which is 9 electrons in total (an odd number, cannot all be paired) and this applies to half the elements in the periodic table. Another example is Lithium solids. Yet I know half of the elements are not radicals so I am confused.

In: Chemistry

I think flourine might naturally occur as F2 with a covalent bond?