To calculate the bond order of the nitrogen-oxygen bond in the NO molecule, we need to consider the molecular orbital MO theory. According to MO theory, bond order is calculated as:Bond order = number of electrons in bonding MOs - number of electrons in antibonding MOs / 2For the NO molecule, nitrogen has 7 electrons and oxygen has 8 electrons, giving a total of 15 electrons. The molecular orbital configuration for NO is:1 2 1 3 1* 2*Here, the bonding MOs are 1, 2, 1, and 3, while the antibonding MOs are 1* and 2*.Number of electrons in bonding MOs = 2 1 + 2 2 + 4 1 + 2 3 = 10Number of electrons in antibonding MOs = 4 1* + 1 2* = 5Now, we can calculate the bond order:Bond order = 10 - 5 / 2 = 2.5The bond order of the nitrogen-oxygen bond in the NO molecule is 2.5.To estimate the bond length, we can use the bond order and compare it to the known bond lengths of N-N, N=O, and O=O bonds. The bond order of 2.5 is between a double bond bond order 2 and a triple bond bond order 3 . The bond lengths for N-N, N=O, and O=O are approximately:N-N single bond : 1.45 N=O double bond : 1.21 O=O double bond : 1.21 NN triple bond : 1.10 OO triple bond : 1.12 Since the bond order of the nitrogen-oxygen bond in the NO molecule is 2.5, the bond length should be between the double bond and triple bond lengths. We can estimate the bond length to be around 1.15 . However, it's important to note that this is just an approximation, and more accurate bond lengths can be obtained through experimental methods or high-level quantum chemistry calculations.