Molecular orbital MO theory is a method for describing the electronic structure of molecules using quantum mechanics. It involves the combination of atomic orbitals to form molecular orbitals, which are then filled with electrons according to the Aufbau principle and Hund's rule. Bond order is a measure of the number of chemical bonds between a pair of atoms and can be used to predict the stability of a molecule.To determine the bond order of the oxygen molecule O2 , we first need to consider the electronic configuration of an oxygen atom. Oxygen has 8 electrons, with the electronic configuration 1s 2s 2p.In O2, there are two oxygen atoms, so there are a total of 16 electrons. We will now distribute these electrons into the molecular orbitals formed by the combination of atomic orbitals. The order of energy levels for molecular orbitals in O2 is as follows:1. 1s 2. * 1s 3. 2s 4. * 2s 5. 2p 6. 2p 7. * 2p Now, we fill the molecular orbitals with the 16 electrons, following the Aufbau principle and Hund's rule:1. 1s - 2 electrons2. * 1s - 2 electrons3. 2s - 2 electrons4. * 2s - 2 electrons5. 2p - 2 electrons6. 2p - 4 electrons 2 electrons in each degenerate orbital 7. * 2p - 2 electrons 1 electron in each degenerate orbital The bond order can be calculated using the formula:Bond order = number of electrons in bonding orbitals - number of electrons in antibonding orbitals / 2In the case of O2:Bond order = 2 + 2 + 2 + 4 - 2 - 2 / 2 = 10 - 4 / 2 = 6 / 2 = 3The bond order of the oxygen molecule O2 is 2, which indicates that there is a double bond between the two oxygen atoms.The bond order is related to the molecule's stability because a higher bond order generally corresponds to a stronger and more stable bond. In the case of O2, the bond order of 2 suggests that the molecule is relatively stable, with a bond strength between that of a single bond and a triple bond. The MO theory also helps to explain the paramagnetic nature of O2, as there are two unpaired electrons in the * 2p orbitals.