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Bond orders can give you an indication of the stability of a bond. A high bond order indicates more attraction between electrons, so the atoms are held together more tightly. With a lower bond order, there is less attraction between electrons so the atoms are held together more loosely. The higher the bond order, the more electrons holding the atoms together, and therefore the greater the stability.
Based on my understanding, bond order is the measurement of the stability of chemical bonds. For a chemical between two atoms, the larger bond order is, the stabler the chemical bond is; the smaller bond order is, the weaker the chemical bond is. When the bond order is zero, the chemical bond cannot exist.
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