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Bond order is the number of chemical bonds between a pair of atoms. So for example, C-H has a bond order of 1 because it has a single bond. A double bond has a bond order of 2 and a triple bond has a bond order of 3. So, yes, when the bond order is greater than 0 then it is stable because if it were 0 it would not form the molecule. Also, higher bonds indicate a greater stability of the molecule.
The greater the bond order, the greater the stability of the molecule. For example, O2+ has a bond order of 2.5. When drawing out the Lewis structure for O2+, the 2 indicates a double bond and the .5 indicates a resonance structure. Double bonds are shorter, and thus stronger. If the bond order was 3.0, the Lewis structure would have a triple bond, and thus a shorter and stronger bond.
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