To calculate the bond order and bond length of the nitrogen-oxygen bond in the NO molecule using molecular orbital theory, we first need to determine the molecular orbital configuration of the molecule.1. Determine the total number of valence electrons in the NO molecule.Nitrogen N has 5 valence electrons, and oxygen O has 6 valence electrons. Therefore, the NO molecule has a total of 5 + 6 = 11 valence electrons.2. Fill the molecular orbitals following the aufbau principle, Pauli exclusion principle, and Hund's rule.The molecular orbitals for NO are filled in the following order: 1s , * 1s , 2s , * 2s , 2pz , 2px = 2py , * 2px = * 2py .With 11 valence electrons, the molecular orbital configuration for NO is: 1s ^2, * 1s ^2, 2s ^2, * 2s ^2, 2pz ^2, 2px ^1, 2py ^13. Calculate the bond order.Bond order = number of electrons in bonding orbitals - number of electrons in antibonding orbitals / 2Bond order = 2 + 2 + 1 + 1 - 2 - 2 / 2Bond order = 1The bond order of the nitrogen-oxygen bond in the NO molecule is 1.4. Estimate the bond length.The bond order is inversely proportional to the bond length. Since the bond order is 1, the bond length will be between the typical bond lengths of a single bond for N-N and O-O. The average bond length for N-N is approximately 1.45 , and for O-O is approximately 1.48 . The bond length for NO will be somewhere between these values, but closer to the N-N bond length since nitrogen is smaller than oxygen.A reasonable estimate for the bond length of the nitrogen-oxygen bond in the NO molecule would be around 1.45 . However, the exact bond length can be determined experimentally or through more advanced computational methods.