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Why fluorine shows-1 oxidation state onl...

Why fluorine shows-1 oxidation state only whereas other halogens show variable oxidation states ?

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Fluorine is the most electronegative element and cannot exhibit any positive oxidation state. Other halogens have d-orbitals and therefore can show excited states as shown below to show +1, +3, +5 and +7 oxidation states also.
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