# Why are there multiple oxidation states?

The oxides of nitrogen provide a nice array of oxidation states. $N O$, i.e. $N \left(+ I I\right)$; $N {O}_{2}$, i.e. $N \left(+ I V\right)$, ${N}_{2} {O}_{5}$, $N \left(+ V\right)$, $N {O}_{3}^{-}$, $N \left(+ V\right)$...$N {O}_{2}^{-}$, $N \left(+ I I I\right)$...
And of course in this series the oxidation number of oxygen is constant at $- I I$...oxygen can exhibit the $- I$ oxidation state peroxides. Elemental dioxygen and dinitrogen each have formal $0$ oxidation states..