The highest occupied molecular orbital of a molecule is abbreviated as the HOMO. The lowest unoccupied molecular orbital in a molecule is called the LUMO. Experimentally, one can measure the difference in energy between the HOMO and LUMO by taking the electronic absorption (UV-visible) spectrum of the molecule. Peaks in the electronic absorption spectrum can be labeled as p2p9p2p*, s2s9s2s*, and so on, corresponding to electrons being promoted from one orbital to another. The HOMO-LUMO transition corresponds to molecules going from their ground state to their first excited state. (c) The electronic absorption spectrum of the N2 molecule has the lowest energy peak at 170 nm. To what orbital transition does this correspond?

Question

Accepted Answer

Welcome back everyone in this example we're told that homo is the abbreviation for the highest occupied molecular orbital of a molecule and lou mo is the abbreviation for the lowest unoccupied molecular orbital. The difference in energy between homo and uomo can be determined by taking electronic absorption, UV visible spectrum of the molecule and the home Olmo transition corresponds to the molecules going from their ground state to their first excited state. We need to identify the orbital transition that the lowest energy peak of oxygen corresponds to. So this means that we need to draw out a molecular orbital diagram for oxygen and in order to do so we need to calculate the total valence electrons in oxygen. So we call that oxygen is located in Group six A on the periodic table. And so because we have two oxygen atoms, we're going to multiply by recalling that the group number that oxygen is in corresponds to the valence electrons. We're gonna multiply by six valence electrons And this gives us a total number of valence electrons equal to 12. So we have 12 valence electrons total and this is what we will use to draw out our orbital diagram. Now also recall that oxygen is located in group or across period two of our periodic tables. And so we're going to begin our molecular orbital diagram with the lowest energy orbital, which we recall is our sigma to us bonding molecular orbital where we have just one orbital which contains our first two electrons. Moving up higher in energy. We go to our anti bonding sigma to us. Molecular orbital which is also just one orbital containing our next two electrons and then moving up higher in energy, we have our bonding sigma p molecular orbital which is also just one orbital containing our next two electrons of opposite spins. I'm sorry that should be Sigma two p. Moving up higher in energy. We then go to our pie to p bonding molecular orbital which consists of a total of two orbital's. So we have one orbital here in the second here and we should recall Hunt's rule which states that we will occupy each orbital with each electron first before pairing these electrons up. So we're gonna occupy each orbital with one electron first and then we will pair them up with the opposite spin next. So we've so far filled in a total of 10 of our valence electrons leaving us with two more valence electrons to fill in. So moving up higher in energy, we have our pie anti bonding to p molecular orbital which is also to orbital's where we place our last two electrons according to Hunt's rule in each orbital. So one here and then the second electron here. Now higher up in energy, we should recall that even though we filled in all our vans electrons, we can go further up to our sigma anti bonding to p molecular orbital which consists of just one orbital which we're leaving empty because we filled in all 12 of our vans electrons in the preceding lower energy molecular orbital. And so based on our two valence electrons being in the pie to p molecular orbital, we can say that this would be the highest occupied molecular orbital or homo of our molecule of oxygen. So that would be this orbital rpai anti bonding to p molecular orbital. And we would say that our lowest unoccupied molecular orbital is going to be our molecular orbital for oxygen that is empty, which we can see is our sigma anti bonding to p molecular orbital. So, according to our prompt to label the lowest energy peak, we should recognize that this corresponds to going from ground state two. The electrons first excited state, meaning we are going through a transition of the highest occupied molecular orbital to the lowest occupied molecular orbital. And so therefore we would say that our orbital transition for the lowest energy peak of oxygen is going from our pie anti bonding to p molecular orbital to the sigma anti bonding to p molecular orbital. And so this will correspond to choice C in the multiple choice. So, this is our final answer to complete this example. So, I hope that everything I reviewed 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

HOMO and LUMO

Electronic Absorption Spectrum

Orbital Transitions