Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (f) How does the HOMO–LUMO energy gap for this case compare to that of the four-atom case?

Video transcript

Hey everyone were asked which of the following statements is true regarding the comparison of the energy gap between the home alu mo for straight six chain lithium atoms and straight eight chain lithium atoms. Now, before we look at our answer choices, let's think about what we know regarding home Olmo energy gaps. So generally we've learned that the more atoms in the chain, the smaller the Homo lou mo energy gap. Now using this to answer a question, we can go ahead and look at our answer choices and see which matches our answer. Looking at our first one a, it says that the energy gap between the home a limo for a straight six chain lithium atom is smaller than that of an a chain lithium atom. This statement would be incorrect because we just stated that we need more atoms in the chain in order to have a smaller Home Olmo energy gap. Our next statement states the energy gap between the home a limo for a straight six chain lithium adam is larger than that of an eight chain lithium adam. This statement would be correct because our six chain will have a larger gap since it has less atoms in the chain. And we stated that the more atoms than chain, the smaller our home Olmo energy gap. So it looks like B is going to be our answer choice C would be incorrect because it states that the energy gap would be equal between the two Andy would also be incorrect. So I hope this made sense and let us know if you have any questions