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Using molecular orbital theory, calculate the bond order of the H2 molecule. Show all your calculations and explain what the bond order indicates about the stability of the molecule.

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Molecular orbital theory is a method for describing the electronic structure of molecules using quantum mechanics. In this theory, atomic orbitals from individual atoms combine to form molecular orbitals, which are associated with the entire molecule rather than a single atom. The molecular orbitals can be classified as bonding, non-bonding, or anti-bonding based on their energy levels and electron distribution.For the H2 molecule, we have two hydrogen atoms, each with one electron in the 1s orbital. When these two atoms come together to form a molecule, their atomic orbitals combine to form two molecular orbitals: one bonding  1s  and one anti-bonding  1s* .The bonding molecular orbital  1s  is lower in energy than the atomic orbitals and has a greater electron density between the two nuclei, which leads to an attractive force and bond formation. The anti-bonding molecular orbital  1s*  is higher in energy and has a node between the nuclei, leading to a repulsive force.To calculate the bond order, we use the following formula:Bond order =  Number of electrons in bonding orbitals - Number of electrons in anti-bonding orbitals  / 2For H2, there are two electrons in the bonding orbital  1s  and none in the anti-bonding orbital  1s* . So, the bond order is:Bond order =  2 - 0  / 2 = 1The bond order of H2 is 1, which indicates that there is a single bond between the two hydrogen atoms. A bond order of 1 or higher generally indicates that the molecule is stable, while a bond order of less than 1 indicates that the molecule is unstable and unlikely to exist. In the case of H2, the bond order of 1 suggests that the molecule is stable, and indeed, H2 is a stable diatomic molecule at room temperature and pressure.
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