Final answer:
Among the given options, Ne₂²⁺ is the molecule with a bond order less than one, specifically a bond order of 0, indicating it does not exist as a stable molecule.
Step-by-step explanation:
To determine which molecule has a bond order less than one, we consider the molecular orbital (MO) theory. A bond order of less than one signifies that the molecule is not stable and does not exist under normal conditions. Through the application of MO theory to diatomic molecules, one could deduce that He₂⁻, with a bond order of 0, does not exist as a stable species. Likewise, molecules like Be₂ and Ne₂²⁺ also have a bond order of 0 and are not stable. Hence, Ne₂⁻⁻, with a bond order of 0, is the molecule among the options given that has a bond order less than one. Other molecules listed, including F₂, N₂, and O₂²⁻, have bond orders of 1, 3, and 1 respectively, indicating stable bonds.
The molecules with a bond order less than one are:
He₂⁻ - The bond order of He₂⁻ is 0.5.
Ne₂²⁺ - The bond order of Ne₂²⁺ is 0.
O₂²⁻ - The bond order of O₂²⁻ is 1.
The bond order represents the number of chemical bonds between two atoms. A bond order less than one indicates a weaker bond and less stability.