Different molecules can absorb different wavelengths of light, and if a molecule happens to absorb light in the ultraviolet or the visible region of the electromagnetic spectrum, we can find the wavelength or wavelengths of light that are absorbed by that compound by using a... UV-Vis spectrophotometer. Essentially what that does is it shines light with a range of wavelengths. So the wavelengths range from approximately 200 nanometers all the way up to 800 nanometers.
And so we shine that a range of wavelengths of light through a sample of the compound, and you get an absorption spectrum. And so here is an absorption spectrum for this molecule, for 1,3-butadiene. If we look over here, we can see that this molecule absorbs most strongly right about here, and if we drop down, we can see what wavelength of light is absorbed most strongly by the compound, and so we see that's just under 220 nanometers.
And it turns out to be 200 nanometers. 217 nanometers, so we call this lambda max. So wavelength, the wavelength of light absorbed by this molecule is about 217 nanometers.
It absorbs in the UV region, therefore, butadiene does not have any color, it's colorless. Alright, let's look at the dot structure a little bit more carefully here. So we have four carbons, and all four of these carbons, each one is sp2 hybridized, which means which means each one of those carbons has a p orbital.
So we're talking about four p orbitals here, or four atomic orbitals. And when you're dealing with molecular orbital theory, four atomic orbitals recombine to form four molecular orbitals. Two bonding molecular orbitals and two anti-bonding molecular orbitals. So let's go over here and let's look at the four molecular orbitals, and we're gonna focus in.
on the left side first. The bonding molecular orbitals are lower in energy than the anti-bonding ones. So this orbital and this orbital, these are our bonding molecular orbitals here. And this one and this one are the anti-bonding molecular orbitals.
And you can see energy, right? So energy is increasing. And so the anti-bonding molecular orbitals are higher in energy.
Let's look at the dot structure again. for butadiene, and let's see how many pi electrons we have. So here are two pi electrons, and here are two pi electrons. So a total of four pi electrons. And when you're thinking about molecular orbitals, you can think about electron configurations.
So we have four electrons, and where do we put those electrons? We're gonna put them in the lowest energy orbitals first. And we're also going to pair our spins.
So four electrons. So we're gonna... We're gonna put two into this bonding molecular orbital, and we paired our spins, and then two into this bonding molecular orbitals.
So the four pi electrons go into the bonding molecular orbitals when you're talking about the ground state. So here's the ground state, the ground state of butadiene. So next we shine light on butadiene, and the molecule is going to absorb energy.
from the light, and let's look at that here. So there's a difference in energy, right? There's a difference in energy between the orbitals, and in particular, we're concerned about these two orbitals right here. So there's a difference in energy between these two orbitals. This orbital down here, right, this is occupied by electrons, and it's higher in energy than this orbital.
So this is the highest occupied molecular orbital. So highest occupied molecular orbital. orbital, or HOMO.
This orbital right here is unoccupied. The antibonding molecular orbital right now is unoccupied, and it's lower in energy than this antibonding molecular orbital. So this is the lowest unoccupied molecular orbital.
So when you're talking about a molecule absorbing energy, we're concerned about the HOMO, the highest occupied molecular orbital, and the LUMO, the lowest unoccupied molecular orbital. The energy difference between those two orbitals is what what we're thinking about. So the molecule absorbs energy, and a pi electron absorbs energy from the light and is promoted to a higher energy level. So let me go ahead and right over here.
Now we're talking about the excited state. So we shine light on the molecule. So this is the excited state of butadiene. And these two pi electrons stay there. One of these pi electrons stays here.
And one of the pi electrons absorbs the energy from the light. is promoted to a higher energy level. So I'm saying this one right here was promoted to a higher energy level.
It goes from the HOMO to the LUMO. And it had to absorb a specific amount of energy in order to do that, right? So it had to absorb... the right amount of energy in order to make that transition. And we know that energy came from the light.
And we also know the energy of a photon of light is equal to h, where h is Planck's constant, times the frequency of light, which is is new. And over here for the absorption spectrum, we have everything in wavelengths. So we need to write the energy in terms of a wavelength.
And we know that the frequency of light and the wavelength of light are related by the speed of light is equal to the wavelength times the frequency. And so the frequency is equal to the speed of light over the wavelength. And we can take that. So frequency is equal to c over lambda and plug it in.
into here, so now we have the energy, the energy is equal to h times c over lambda. And this is really important, right? So energy and wavelength are inversely proportional to each other. And you can think about one wavelength, right, giving you a specific amount of energy. And so this energy difference, right, this energy difference between the HOMO and the LUMO, right, this corresponds to a wavelength.
And And if we go over here to the absorption spectrum for butadiene, we're talking about a wavelength of 217 nanometers. And so at first it might be a little bit confusing because it looks like we have a very broad, it looks like we have a broad range of wavelengths that are absorbed here. And don't worry about that too much. This just results from the different vibrations and rotations of the molecule, which can change the energy differences slightly. And so we don't see one.
exact wavelength, we end up seeing this broad band of wavelengths being absorbed here. So what you do is you just look for the one that's absorbed most strongly, and think about that as being the wavelength that corresponds to the energy difference between these two orbitals here. So that's how to think about it. All right, let's look at another molecule here.
So instead of butadiene, let's look at this molecule. So we have ethanol. All right, so here's our dot structure. And And if we look at this molecule, we know we have two pi electrons here for ethanol. So two pi electrons.
We know that those electrons are going to go into the bonding molecular orbital. So let me draw a line right here on this diagram. So this is our bonding molecular orbital down here. And so we're talking about two pi electrons. So let's put in our two pi electrons.
two pi electrons into here. And then, let me just go ahead and change colors up here. So this up here is our anti-bonding molecular orbital, which we call pi star. So there's an energy difference between the bonding molecular orbital and the anti-bonding molecular orbital.
So this is delta E. And we talked about the fact that this corresponds to a certain wavelength of light. And so ethanol can have, when it promotes one of these pi electrons up, it can have a pi.
we call this a pi to pi star transition. So the molecule is going to absorb energy, and the energy, let me use a different color here, the energy corresponds to a wavelength of light. So this energy difference between our two orbitals.
And it turns out, that this pi to pi star transition is approximately 180 nanometers, which is below the range of what you're usually measuring when you're using a UV-Vis spectrophotometer. All right, but we have a We have another possibility here too. Let me go ahead and highlight a lone pair of electrons here on the oxygen. We have a lone pair, so we have non-bonding, non-bonding electrons. Non-bonding electrons occupy a non-bonding orbital, which is actually a little bit higher in energy than our bonding molecular orbital.
Another possibility, we call this n right here. This is a non-bonding orbital. And on the other side, we have a non-bonding orbital.
bonding orbital here, and we can put some electrons into that orbital, so we put those two electrons into the non-bonding orbital, and we can have a different type of transition. So we're still talking about a pi star, an anti-bonding molecular orbital right here. We can have a n to pi star transition, so we can have an n to pi star transition as well, since we have a carbonyl compound, so we're not just talking about pi electrons here. The carbonyl we can think about a non-bonding electron here.
And let's think about this energy difference. So this energy difference is smaller than before. So this energy difference is smaller than this energy difference.
And so what would happen to the wavelength of light that's absorbed? So if we have a smaller energy difference, energy and wavelength are inversely proportional, so this must be a longer wavelength. So this absorbs light at a different wavelength, so a higher wavelength. And if we have a smaller wavelength, And it turns out to be, let me go ahead and change colors here.
So this energy transition corresponds to a wavelength of light that's approximately 290 nanometers. And so this n to pi star transition, a lower difference, a smaller difference in energy, I should say, corresponding to a higher wavelength. This is an important concept. So as you decrease the energy difference between your orbitals, you're going to increase the wavelength of light.
that's absorbed, and we'll talk much more about that in the next few videos because that's where the idea of color comes in.