Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (b) How many nodes are in the lowest-energy molecular orbital? (c) How many nodes are in the highestenergy 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)?

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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 eight lithium atom chain. So let's go down to our statements, we have a through D where a majority of these statements are in reference to something known as nodes and whether these nodes are located in each of the different types of orbital's. We have we have lower energy molecular orbital, lower in our diagram and then the higher energy molecular orbital's more upward in our diagram. And so we can see that in our lowest energy molecular orbital we have zero notes. We want to recall that node is going to be a plane of zero electron density in an orbital. And so when we move up higher in energy, we see this space between our two orbital's and this space here would represent our first note. So here we can count one note. Moving up we see we have now two spaces where we have a count of two notes and then where we have our highest occupied energy molecular orbital which is this orbital. Here we have a total of 123 spaces. So we would count three notes. And so for our final answer, we can agree that the only correct statement is going to be choice B, which states that there are three nodes in the highest energy occupied molecular orbital short for homo So B is our final answer. I hope everything I explained was clear. If you have any questions, leave them down below and I'll see everyone in the next practice video.

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Key Concepts

Molecular Orbitals

Nodes in Molecular Orbitals

HOMO and LUMO