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?

Question

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?

Molecular orbital diagram for six lithium atoms showing energy levels and nodes.

Accepted Answer

Welcome back everyone in this example. We need to determine which of the below statement is correct. Based on the given molecular orbital diagram for a six lithium atom chain. So looking at our statements below, we can see that they're all in reference to notes and which ones occupy the lowest energy unoccupied molecular orbital. So we want to recall what a note is and we're going to recall that this is a region of zero electron density in an orbital and we can have more than one of these regions. So we can find multiple notes for various orbital's. And according to the prompt, we need to focus on the lowest energy unoccupied molecular orbital. And so this means that as we can see in our diagram, energy is increasing as we go up in our molecular orbital diagram. And so the unoccupied molecular orbital are going to be the molecular orbital's that are empty with no electrons filled in. So these three electrons here are all representative of filled electron molecular orbital's. So we want to look at these blank ones and we want to focus on the lowest energy molecular orbital. So that would be this one here. This is the lowest unoccupied, specifically lowest energy unoccupied molecular orbital. And so we would count the total number of notes here. So starting with the bottom of our diagram, we have the lowest energy occupied molecular orbital where we have a count of zero nodes moving up higher in energy we have two more electrons filled in where we have a total of one little space here that we can count as a region of zero electron density. So this represents one node moving up to our higher energy occupied molecular orbital. We count a total of two spaces which represent a total of two notes. Now moving to our unoccupied molecular orbital, which is first lowest in energy. We would count a total of 123 spaces, meaning in this lowest energy unoccupied molecular orbital. We count a total of three notes because again, we have these three spaces or these three regions of zero electron density, meaning that the only correct answer choice to complete this example is going to be choice B. As our final answer. There are three notes in the lowest energy unoccupied molecular orbital. So B is our final answer. I hope everything I reviewed was clear. If you have any questions, leave them down below and I'll see everyone in the next practice video.

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 Solution

Key Concepts

Molecular Orbitals

Nodes in Molecular Orbitals

Energy Levels in Molecular Chains