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: (c) How many nodes are in the highest-energy molecular orbital?

Verified step by step guidance

1. Identify the number of lithium atoms in the chain, which is six.
2. Recognize that each lithium atom contributes one valence electron, resulting in a total of six valence electrons for the chain.
3. Construct the molecular orbital diagram by arranging the molecular orbitals in order of increasing energy, as shown in the provided image.
4. Determine the highest-energy molecular orbital by locating the topmost orbital in the diagram.
5. Count the number of nodes (regions where the probability of finding an electron is zero) in this highest-energy molecular orbital.

Key Concepts

Molecular Orbitals

Molecular orbitals (MOs) are formed by the linear combination of atomic orbitals (LCAO) when atoms bond together. In a molecular orbital diagram, these orbitals are depicted with their energy levels, showing how electrons are distributed among them. The number of MOs corresponds to the number of atomic orbitals combined, and they can be classified as bonding, antibonding, or non-bonding based on their energy and stability.

Nodes in Molecular Orbitals

Nodes are regions in a molecular orbital where the probability of finding an electron is zero. The number of nodes in a molecular orbital is related to its energy level; specifically, the highest-energy molecular orbital will have the most nodes. For a linear chain of atoms, the number of nodes can be calculated using the formula: number of nodes = n - 1, where n is the number of atomic orbitals contributing to the molecular orbital.

Energy Levels in Molecular Chains

In a molecular chain, the energy levels of molecular orbitals are influenced by the number of atoms in the chain. As more atoms are added, the energy levels become more closely spaced, leading to a greater number of available molecular orbitals. This affects the distribution of electrons and the overall stability of the molecule, as well as the characteristics of the highest-energy molecular orbital, which is crucial for understanding electronic transitions and reactivity.