The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22 . Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (a) How many molecular orbitals are there in the diagram? (b) How many nodes are in the lowest-energy molecular orbital? (c) How many nodes are in the highest energy molecular orbital? (d) How many nodes are in the highest-energy occupied molecular orbital (HOMO)? (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)? (f) How does the HOMO-LUMO energy gap for this case compare to that of the four-atom case?