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Write resonance structure of $NO_{3}^{-}$ and $N{{O}_{2}}$

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Hint: All non-metals form metal oxides with oxygen, which reacts with water that will form acids or with bases forms salts. Most nonmetals form oxyacid’s from their acidic oxides. A set of two or Lewis structures collectively describes the electronic bonding of a single polyatomic species including fractional charges are resonance structures.

Complete step by step answer:
Based on resonance structures of single polyatomic species are capable of describing delocalized electrons that cannot be expressed by a single Lewis formula with an integer number of covalent bonds.
The nitrate ($NO_{3}^{-}$ ) ion:
Count the valence electrons $=$ no of nitrogen atoms $\times 5$electrons $+$ no of oxygen atoms $\times 6$ electrons $+$ one electron.
\[=1\times 5+3\times 6+1=24electrons\]
The below diagram shows the bond connectivity and octet electrons to the atoms bonded to the central atom which is the trigonal planar and the possible resonance structures are:
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Nitrogen dioxide ($N{{O}_{2}}$ ): Nitrogen dioxide contains an odd number of $17$ valence electrons and it behaves as a typical odd molecule. It exhibits a resonance structure on dimerization, Nitrogen dioxide converted to stable dinitrogen tetraoxide molecule with an even number of molecules.
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Note: Sometimes Lewis structure is not enough for explaining bonding in some molecules or ions and a single Lewis formula is not sufficient to describe the delocalized electrons within certain molecules or polyatomic ions. A molecule or ion with such delocalized electrons is represented by several structures. For example, ozone is an allotrope of oxygen with a V-shaped structure with an $O-O-O$ bond angle of $117.5{}^\circ $