00:01
For this question, the only thing that we need to remember is that the fundamental frequency for a diatomic molecule, taking into account the harmonic oscillator approximation, is equal to 1 over 2 pi square root of k over mu, where mu is going to be the reduced mass.
00:19
Remember that the reduced mass is equal to mass 1 times mass 2 divided by mass 1 plus mass 2.
00:33
So in this case we don't actually need to calculate the frequencies, we don't need to transform the masses of the atoms into kilograms and calculate the actual values, and we're told that k, we're assuming, is equal for all the cases.
00:52
So the only thing that we need to calculate is the reduced mass for each of the molecules that we have.
00:58
The larger the reduced mass of the molecule, of the diatomic molecule, the lower the frequency that we're going to get.
01:06
So in the case for carbon -oxygen, we can calculate the reduced mass as 12 times 16, of course this is atomic mass units instead of umas, atomic mass units, times 16, divided by 12 plus 16.
01:33
And of course here as well, atomic mass units, and here atomic mass units.
01:38
So the result is 6 .857 atomic mass units.
01:47
We're going to do the same with carbon -chlorine, the value over here of carbon -chlorine is equal to, now we're going to have 12 atomic mass units times, let's take 35 .45 atomic mass units, divided by the sum of both of these guys, which is going to be 47 .45 atomic mass units.
02:22
So now we're going to have 8 .96 atomic mass units, actually 9 .65, but it really doesn't matter.
02:34
And finally what we're going to get is carbon -carbon.
02:38
So the reduced mass for a carbon -carbon bond is going to be 12 times 12, again atomic mass units, atomic mass units, divided by the sum of the two, which is 24 atomic mass units.
02:54
As you can see, this is directly equal to 6 atomic mass units...