[Music] okay so with the level that we can understand infrared spectroscopy turns out we can answer a pretty fundamental question about water namely why water is blue so i can hear some of you telling me that that water is not blue you might be drinking water out of a bottle at your elbow or have recently poured water out of the tap and you'll tell me that water is clear not blue but it depends how much water you're looking at when you when you ask whether water has a color or not so if i bring up some illustrations just to be able to talk about the color of water these pictures will show us that depending on how much water we're talking about the color in fact does change a small amount of water like a glass of water does look clear hopefully if your water is good quality but if you have enough water to fill a bathtub it begins to take on a slightly bluish tint and a swimming pool has enough water to really begin to look blue and of course the ocean isn't clear at all it's it's quite blue at least if you're an area where there's not much uh muddy sediment clouding up the water so water is in fact blue in large quantities although it looks clear at smaller quantities and the reason for this boils down to the details of the infrared spectrum so if i take these pictures away and put up the infrared spectrum for water we've already seen that water absorbs light at several different frequencies at bands which are roughly 3650 wave numbers 3657 for the symmetric stretch 1595 inverse centimeters for the bending mode and 37.56 inverse centimeters for the asymmetric stretch so just as a reminder symmetric stretch bending mode asymmetric stretch we've seen the bending mode absorbs around here so this absorption is new sub 2. here's new sub 1 and new sub 3 a little above 3 500 wave numbers these peaks however water also absorbs away at frequencies of 5000 some wave numbers a little above 7000 wave numbers and what those are are the overtones water can in addition to these fundamental vibrational frequencies because water the vibrational modes in water are not perfectly harmonic that arma and harmonicity means the selection rules that we derive from the harmonic oscillator don't perfectly apply so the absorption is a little weaker but the molecule can absorb light at frequencies of new not new 3 but nu1 and nu2 combine nu3 and nu2 combined what that means is the molecule is simultaneously increasing by one quantum number in its symmetric stretch and by one quantum number and it's bend it's exciting both of those motions at the same time that costs an amount of energy equivalent to the energy of the bending mode plus the energy of the stretching mode whichever vibrational mode new one or new three is being increased so that 1500 plus about 3 500 adds up to a little above 5000 wave numbers so this would be the overtones associated with combining these two frequencies can also absorb at twice the symmetric stretch frequency or twice the asymmetric stretch frequency so that would be these peaks over here which are about twice the energy of the peaks at 3500 those peaks are weaker because although these overtones don't technically violate the selection rules because the vibrational motions are and harmonic they're still weaker than the front of the fundamental vibrational modes and what that means is further overtones further out at higher frequencies also absorb a little bit of light so if i replace this spectrum with one at a wider range of frequencies and the other thing i've done here is i've changed from a linear scale to a log scale so again we see if i label these this is the new two peak the second peak is either nu1 or nu3 symmetric or antisymmetric stretches those are the ones that are about 3500 wave numbers or so here's a non-ideal overtone new one plus nu2 or nu3 plus nu2 the ones that are double the symmetric and antisymmetric stretch that's this collection of peaks here twice new one or twice new three those are at a little above seven thousand wave numbers on the log scale notice on the log scale each line on the scale is is decreasing by a factor of 100 so these next few peaks that we can talk about those are roughly a hundred times weaker in intensity than the fundamental vibrational peaks so those are beginning to be quite minor peaks but those would be we won't label them all but this one here those would be the second overtones for the symmetric and anti-symmetric stretch that show up at three times the fundamental vibrational frequency here we've got four times the fundamental vibrational frequencies for the symmetric and anti-symmetric stretch and so on so there's overtones all the way out the the more the higher the overtone the less intense the peak is so by the time we're out here we're absorbing light with an intensity of maybe one millionth the intensity of the fundamental vibrational frequencies so what that means is water's pretty good at absorbing infrared light as i move to higher and higher frequencies however toward the visible portion of the spectrum it gets less good at absorbing that light the intensity is smaller in fact if i overlay on this graph the wavelengths or colors of the visible portion of the spectrum you can see that by the time we get up to a little above 14 000 wave numbers or so we've entered the visible portion of the spectrum so there is some in this region there isn't in fact some weak absorption in the the red the orange into the yellow even a little bit of the green parts of the spectrum are being absorbed by water not from its fundamental vibrational frequencies but from these weakly absorbing fourth fifth sixth overtone frequencies so what that means is if i have a large enough body of water that the photon can pass through quite a bit of the water some of those photons a small number of those photons will be absorbed but if i pass through enough molecules uh to eventually absorb most of the red orange yellow green parts of the spectrum then the part of the light that's left over after that absorption is blue the overtones there are no overtones or at least none with any significant absorption out beyond the blue portion of the spectrum so the reason water absorb the water looks blue even though water should only be absorbing in the infrared if it's a harmonic oscillator is because the bonds are not perfectly harmonic that non-ideality that anharmonicity causes the overtones to weakly absorb in the red side of the visible spectrum so turns out the spectroscopy of water is is quite complex but it gives rise to this perfectly ordinary everyday phenomenon this spectrum is complicated enough already even for a triatomic molecule like water as we move on to more larger more polyatomic molecules we'll see that the spectrum gets more complicated still and that's what we'll do next