A question regarding oxidation numbers

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Atoms have a limited range of oxidation numbers due to energetic favorability. For chlorine, which has seven valence electrons, achieving oxidation states of 2 or 4 would result in a radical, as it would involve gaining or losing an even number of electrons, leaving it with an odd number. Radicals are typically high in energy and less stable. While chlorine can theoretically have oxidation numbers of 2 and 4, such states are not commonly encountered because they are energetically unfavorable. The concept of oxidation numbers is a tool for balancing redox reactions and does not reflect a measurable property of the atom itself.
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How come atoms have only a few oxidation numbers they can assume? For example, Cl can have the oxidation numbers -1, 1, 3, 5, 7. What prevents it from having an oxidation number of say, 2 or 4?
 
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Nothing prevents it. It's just energetically unfavorable. That is, the other states have significantly lower energy.

You can really dive in here with how 'deeply' you want to explain it, but to just give the cursory, simplest answer: Chlorine has an odd number of valence electrons (7). If it gained or lost an even number, it'd still have an odd number. The resulting compound would be a radical, which are generally high in energy.
 
Who told you chlorine doesn't have compounds with ON 2 and 4?

http://en.wikipedia.org/wiki/Chlorine_monoxide

http://en.wikipedia.org/wiki/Chlorine_dioxide

Just remember that oxidation number is just a number assigned to atoms using some simple rules to help in balancing redox reactions. There is a logic behind, but there is no measurable property of the atom that reflects assigned oxidation numbers.

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I get it now. Thanks for the help.
 
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