To determine the bond order for the oxygen molecule O2 using molecular orbital theory, we need to first understand the molecular orbital diagram for oxygen. Oxygen has a total of 12 valence electrons 6 from each oxygen atom . The molecular orbitals are formed by the combination of atomic orbitals from each oxygen atom.The molecular orbital diagram for O2 is as follows:1. Two 2s orbitals from each oxygen atom combine to form one sigma 2s bonding orbital and one sigma* 2s antibonding orbital.2. Two 2px orbitals from each oxygen atom combine to form one sigma 2px bonding orbital and one sigma* 2px antibonding orbital.3. Four 2py and 2pz orbitals from each oxygen atom combine to form two pi 2py, 2pz bonding orbitals and two pi* 2py, 2pz antibonding orbitals.Now, we need to fill the molecular orbitals with the 12 valence electrons. The order of filling is:1. sigma 2s 2. sigma* 2s 3. sigma 2px 4. pi 2py, 2pz 5. pi* 2py, 2pz 6. sigma* 2px Filling the orbitals, we get:1. sigma 2s - 2 electrons2. sigma* 2s - 2 electrons3. sigma 2px - 2 electrons4. pi 2py, 2pz - 4 electrons 2 in each 5. pi* 2py, 2pz - 2 electrons 1 in each 6. sigma* 2px - 0 electronsNow, we can calculate the bond order using the formula:Bond order = number of electrons in bonding orbitals - number of electrons in antibonding orbitals / 2Bond order = 2 + 2 + 4 - 2 - 2 / 2 = 8 - 4 / 2 = 4 / 2 = 2So, the bond order of the oxygen molecule O2 is 2.The bond order is directly related to the stability of the molecule. A higher bond order indicates a stronger bond and greater stability. In the case of O2, a bond order of 2 suggests a relatively stable molecule with a double bond between the two oxygen atoms. This double bond results in a shorter bond length and higher bond energy, contributing to the overall stability of the oxygen molecule.