The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.21. 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?

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Identify the number of lithium atoms in the chain, which is six.

Recall that each lithium atom contributes one valence electron to the molecular orbitals.

Understand that the molecular orbitals are formed by the combination of atomic orbitals, and the number of molecular orbitals equals the number of atomic orbitals.

Recognize that the highest-energy molecular orbital will have the maximum number of nodes, which is one less than the number of atoms in the chain.

Determine the number of nodes in the highest-energy molecular orbital by subtracting one from the number of lithium atoms in the chain.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 according to their energy levels and the number of nodes they possess. The arrangement of MOs helps predict the electronic structure and stability of the molecule, as well as its magnetic properties.

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; higher energy orbitals have more nodes. For a linear chain of atoms, the number of nodes can be determined by the formula: number of nodes = n - 1, where n is the number of atomic orbitals combined to form the molecular orbital.

Linear Chains of Atoms

In a linear chain of atoms, such as lithium, the molecular orbitals are formed by the overlap of atomic orbitals from each atom in the chain. As the number of atoms increases, the number of available molecular orbitals also increases, leading to a more complex energy level structure. This affects the distribution of electrons and the overall properties of the material, including conductivity and reactivity.

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The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.21. 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?

Textbook Question

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.21. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: e. How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?

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