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?

Verified step by step guidance

1. insert step 1: Understand that each lithium atom contributes one atomic orbital to the molecular orbital (MO) diagram.
2. insert step 2: Recognize that for a chain of six lithium atoms, each atom contributes one atomic orbital, resulting in six atomic orbitals.
3. insert step 3: Recall that the number of molecular orbitals formed is equal to the number of atomic orbitals combined.
4. insert step 4: Construct the molecular orbital diagram by arranging the six molecular orbitals in order of increasing energy.
5. insert step 5: Conclude that there are six molecular orbitals in the diagram for a chain of six lithium atoms.

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 based on their energy levels and the number of atomic orbitals involved. Each molecular orbital can hold a maximum of two electrons with opposite spins, and they are categorized as bonding, antibonding, or non-bonding based on their energy and stability.

Linear Chains of Atoms

In a linear chain of atoms, such as lithium, the atomic orbitals combine to form molecular orbitals that extend over the entire chain. The number of molecular orbitals produced is equal to the number of atomic orbitals contributed by the atoms in the chain. For a chain of six lithium atoms, each contributing one atomic orbital, there will be six molecular orbitals in total, reflecting the collective behavior of the electrons in the chain.

Energy Levels and Orbital Filling

Molecular orbitals are filled according to the Aufbau principle, where lower-energy orbitals are filled before higher-energy ones. The energy levels of the molecular orbitals in a chain can be visualized in a diagram, where bonding orbitals are lower in energy and antibonding orbitals are higher. Understanding how to fill these orbitals helps predict the stability and reactivity of the molecule, as well as the total number of orbitals present in the system.