Arrange the following in order of decreasing N - O bond length `NO_(2)^(-),NO_(2)^(-),NO_(3)^(-)`

Explanation

The bond length of a covalent bond is inversely proportional to bond order. Let us caluclate the bond orders for `NO_(3)^(-) " and " NO_(2)^(-)` ions which exhibit resonance.

In the `NO_(3)^(-)` ion, each nitrogen atom is sharing one double bond (B.O.=2) and two single bonds (B.O.=1) `therefore` The resultant B.O. `=12//9=4//3=1.33`

In the `No_(2)^(-)` ion, each nitrogen atom is sharing one double bond and one single bond.
`therefore` The resulatant `B.O.=6//4=1.5`
Since B.O. of `NO_(2)^(-)` ion is more than that of `NO_(3)^(-)` ion, its bond length is, therefore, less.