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Electronic Transitions
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- Intro
- Electronic Transitions
- Electronic State & Transition
- Total Energy of the Diatomic Molecule
- Vibronic Transitions
- Selection Rule for Vibronic Transitions
- More on Vibronic Transitions
- Frequencies in the Spectrum
- Difference of the Minima of the 2 Potential Curves
- Anharmonic Zero-point Vibrational Energies of the 2 States
- Frequency of the 0 → 0 Vibronic Transition
- Making the Equation More Compact
- Spectroscopic Parameters
- Franck-Condon Principle
- Example I: Find the Values of the Spectroscopic Parameters for the Upper Excited State
- Table of Electronic States and Parameters
- Intro 0:00
- Electronic Transitions 0:16
- Electronic State & Transition
- Total Energy of the Diatomic Molecule
- Vibronic Transitions
- Selection Rule for Vibronic Transitions
- More on Vibronic Transitions
- Frequencies in the Spectrum
- Difference of the Minima of the 2 Potential Curves
- Anharmonic Zero-point Vibrational Energies of the 2 States
- Frequency of the 0 → 0 Vibronic Transition
- Making the Equation More Compact
- Spectroscopic Parameters
- Franck-Condon Principle
- Example I: Find the Values of the Spectroscopic Parameters for the Upper Excited State 47:27
- Table of Electronic States and Parameters 56:41
Physical Chemistry Online Course
Transcription: Electronic Transitions
Hello, welcome back to www.educator.com, welcome back to Physical Chemistry.0000
In the last four lessons, we have been discussing vibration spectroscopy, rotational spectroscopy, vibration rotation spectroscopy.0004
Today, we will talk about electronic transitions.0011
Let us get started.0016
Let us go ahead and do blue today.0020
Diatomic molecules absorbing radiation in the visible ultraviolet range.0032
They experience transitions to excited electronic states.0053
We call these electronic transactions.0072
We send the electronic up to a higher level of energy.0081
Electronic transmissions, remember when we did vibrational transition,0087
we had just rotational transitions that is the microwave range.0094
The infrared range, we have vibrational transitions.0098
But with the vibrational, you got the rotational also.0101
With electronic transitions, you get the vibrational and rotational also.0104
Electronic transitions are accompanied by both vibrational and rotational transitions.0111
In general, the rotational transitions we are not going to worry about because there are reasonably insignificant.0136
It is the vibration transitions that we are going to be concerned with.0141
Each electronic state has its own potential energy curve.0146
That is what you see here.0163
This is the ground state, this is the first excited state, or they say E1 could be any of the excited states.0164
Anything above the ground state has a potential energy curve that has is a set of vibrational energy states.0171
And the excited electronic state, this one right here on top, it has its own set of vibrational energy levels.0180
Each electronic state has its own potential energy curve.0188
They do not necessarily need to look alike.0194
One is not a copy of the other.0201
It might look like it here but they are not.0204
Let me see, should I do it on this page?0213
The total energy than of the molecule, the diatomic molecule leaving off the transitional energy,0223
leaving off the energy of motion.0237
We are just going to be concerned with the electronic energy, the vibrational energy, the rotational energy.0240
The molecule is a total, it = the electronic energy + the vibrational energy + the rotational energy.0246
That simple.0267
E total = electronic + ν sub E × R + ½ - X sub E ν sub E × R + ½².0274
This is the vibrational energy under the anharmonic oscillator + B × J × J + 1 - D × J² × J + 1².0295
This is the rotational energy in non rigid rotator that accounts for the centrifugal distortion.0320
This one right here, E electronic is the energy at the minimum of the potential energy curve of the potential energy curve.0331
In other words, in the ground vibrational state is that energy right there.0362
Whatever that happens to be.0367
In the first excited state, it is that right there.0368
It is the energy at the minimum of the potential energy curve.0372
That is what the electronic energy is.0376
Transitions between the vibrational states during electronic transitions,0388
in other words during the transition from one electronic state to another, are called vibronic transitions.0405
In general, we will ignore the rotational term.0429
It makes our equations a little bit easier to deal with.0442
Ignore the rotational terms in the above equation.0449
The reason is because on the scale of electronic energies, when we are talking about 10⁻¹⁸ J,0467
the rotational energies are insignificant.0486
The rotational energies 10⁻²⁴ J are very small.0494
For the most part, we can just ignore them.0504
We have E total = electronic E × R + ½ ν sub E × R + ½².0532
This is the total energy of molecule.0557
Our selection rule for the vibronic transitions, δ R = + or -1, + or -2, + or -3, and so on.0562
You can jump from 0 to 1, 0 to 2, 0 to 3.0586
You can jump from 1 to 2, 1 to 3, 1 to 4, 1 to 5.0595
You have to go just from one level at the time.0601
As we said before, at normal temperatures most molecules are in the R = 0 vibrational state.0608
Most of the vibronic transitions would happen from the ground state, the R = 0.0639
It happen from the 0 vibrational state.0648
Most of the vibronic transitions originate there.0654
In other words, R = 0.0670
You are going to have the 0 to 1 transition.0673
You are going to have 0 to 2.0676
You are going to have 0 to 3.0678
You are going to have 0 to 1, 0 to 2, 0 to 3, 0 to 4.0682
Those are the transitions that are going to take place.0690
As we said before, each electronic state has its own potential energy curve.0705
That is the potential energy curve for the upper state.0710
That is the potential energy curve for the lower state.0714
In general, the ground state.0717
It is not necessary to write this down.0733
I will just go ahead and tell you.0735
The upper states are usually designated with a single prime.0738
You are going to see it right there.0762
The lower energy states, they are usually designated with a double prime.0768
Personally, I prefer the designations U for upper and L for lower.0786
The primes tend to confuse me especially when you start taking the difference between energy levels.0791
All of the sudden you have got single primes and double primes.0796
We have already seen symbolism heavy.0799
Primes and double primes, it is just a personal thing.0802
In general, in your book more than likely you are going to see single primes and double primes.0805
Single for upper and double for lower.0809
For my notation, I will just use U and L.0811
Sometimes I will go ahead and use 0 for the ground state.0815
We are going to investigate the vibronic transitions from the lower R value of 0 to the upper R value 1, 2, 3, and so on.0821
We are going to go from the ground vibrational state up.0858
In the upper electronic state, we would be hitting the 1, 2, 3, 4, 5 vibrational states.0861
That is what we are going to actually look at.0867
Each transition 0 to 1, 0 to 2, 0 to 3, 0 to 4, represents a line in the spectrum.0869
Each transition is a line in the spectrum.0878
Actually in the case of electronic spectrum, you are not going to see necessarily a line.0889
What you are going to see is a peak.0893
In electronic spectrum, under visible UV spectroscopy, you are going to see just a bunch of peaks.0895
Those represent the lines, the absorption, the transmission, things like that.0905
This set of transitions 0 to 1, 0 to 2, 0 to 3, 0 to 4, 0 to 5, it is called a progression.0912
This collection of transitions 0 to 1, 0 to 2, 0 to 3, there a lot of them by the way, not just 1, 2, 3, 4, 5.0930
We are talking 60 or 70 sometimes.0943
This collection of transitions is called a progression.0947
0 to 1, 0 to 2, 0 to 3, 0 to 4, 0 to 5, that is a question that we see on the actual spectrum that we take.0961
Each one of those peaks represents a vibronic transition.0972
When you look in your spectrum, that is what you are going to be seeing.0976
We have the energy total is equal to the electronic energy + that × R + ½ - X sub E ν sub E R + ½², that gives us the energy.0981
The frequencies that we observe in the spectrum, the peaks that we see,1006
the frequencies we see in the electronic spectrum of a particular diatomic molecule is going to be,1012
We will call it ν observed.1024
Ν observed, I will specify that we are talking about vibronic, although we should know that because that is the lesson we are in.1029
Again, the observed frequency that we see in the spectrum is going to be the difference between one energy level and another.1037
The upper - the lower.1043
It is going to be the total energy of the upper level - the total energy of the lower level.1045
In this particular case, it is the ground state 0.1055
Sometimes, I will use 0 instead of L but again we know what it is going to be upper – lower.1059
The energy of the upper, that is that one.1067
The energy of the lower, that is that one.1069
Let us go ahead and put these values in.1072
We are moving the lower level, it is the ground state.1074
It is going to be R = 0 vibrational state.1078
In this particular case, R is going to equal 0.1086
A lot of symbolism here, I apologize.1090
The electronic energy, the upper state + ν sub E upper × R upper + ½ -1099
X sub E upper ν sub E upper × R upper + ½² - the lower energy.1120
This is the upper energy - the lower energy.1137
The lower energy R value is equal to 0.1140
That is going to be the energy electronic 0 state + ½ ν 0 – X sub E 0 ν sub E.1143
I will stick with upper and lower so I’m not going to use the 0.1170
This is going to be the energy of the electronic of the lower state + ν sub E lower state × ½ - R 0 ½² is ¼.1173
Let us go ahead and do a little bit of algebra here.1215
I’m going to separate out the terms, multiply these out, put some terms together.1219
It is going to be, our ν observed for vibronic is going to be the electronic energy of1227
the upper state - the electronic energy of the lower state.1235
That takes care of the electronic energies.1240
+ ν sub E upper × R in the upper + ½ ν sub E of the upper.1244
It is not necessary for me to actually go through this algebra.1257
I could just write down the equation, but I think it is nice to go through them.1264
It is part of your scientific and your mathematical literacy here with physical chemistry1268
in quantum mechanics spectroscopy, whatever it is.1277
I just think it is nice to go through the mathematics, it makes it a lot more clear1280
instead of dropping down like a stone.1284
Some equation being dropped in your lab.1286
All we are doing is we are taking the upper energy - lower energy.1288
The rest is just very very careful algebra with this insane symbolism.1291
I apologize for that.1295
- X sub E upper ν sub E upper × R upper² – X sub E upper ν sub E upper.1300
That is crazy, I have no idea how they kept all of it straight all those years.1320
In some of the problems, you might be asked to derive these equations, - ½ ν sub E lower + ¼.1331
The negative × negative is positive.1351
¼ X sub E upper ν sub E upper.1355
Our final equation comes down to this.1366
When I put some things together here, I'm going to get ν observed equal1372
to the upper electronic state - the lower electronic state +,1381
I'm going to combine different terms, ½ ν sub E upper - 1/4 X sub E upper ν sub E upper - ½ ν sub E lower1395
- ¼ X sub E lower ν sub E lower + ν sub E upper × R - X sub E upper ν sub E upper.1421
This X sub E ν sub E, this is a single parameter.1445
We just write it together.1447
× R × R + 1.1450
This equation right here, this gives us the frequency of the line that we see.1454
Let us break this down even further.1461
The frequency of the transition 0 to 1, 0 to 2, things like that.1463
1, 2, 3, 4, 5, 6, there are 6 terms in this equation.1475
The difference of the first two terms, in other words the E upper - E lower electronic is sometimes called T sub E.1490
It is the difference of the minima of the two potential energy curves.1540
In other words, it is going to be this energy - this energy.1565
That is TE.1571
If you want to put a little line there, a little line here, go like this.1575
The difference between been the minima.1582
The third and fourth terms of the equation that we just had,1585
they are just the anharmonic 0 point vibrational energies of the two states.1598
In other words, the third term in that equation, that represents the energy of that level.1623
The fourth term represents the energy of that level.1629
The 0 point energy of the two states.1635
The ground state, in other words.1638
For the first 4 terms taken together, the difference between the energy minima and1657
the difference between these two ground state energies,1664
Let me go ahead and write this down.1669
The first 4 terms taken together represents the frequency of the 0 to 0 vibronic transition.1671
The transition that goes from this level 0 in the lower electronic state to the R = 0 of the upper electronic state.1715
That, the frequency of that transition, that is what those 4 terms taken together represent.1727
The E upper, the E lower, and that third term and that 4th term.1735
We often symbolize this as ν 00 or sometimes ν 0 to 0, with a little arrow.1741
Some variation, thereof.1754
You put a comma, you do not put a comma, it is up to you.1756
Again, it represents the vibronic transition from the R = 0 state, ground state to the R = 0 state of the upper state.1761
The ground state of the upper electronic state, that is what that represents.1770
If we use the symbolism, either that one or this one, if we use the symbolism1776
to make our 6 term equation more compact, we get the following.1796
We get that the observed frequency of transition is equal to this ν 00 + ν sub E upper × R – X sub E upper ν sub E upper.1810
I think I should just put that is as 1, that is okay.1831
× R × R + 1.1834
Here, R is equal to 1, 2, 3, and so on.1838
Here, R is the vibration quantum number of the upper state, the one in that electronic state.1845
If we set R = 0 in this equation, we get the observed frequency of the 0 to 0 transition.1871
That is what we actually get.1902
The 0 to 0 vibronic transition, when we set R = 0 in this equation.1907
Let us see what we have got here.1925
Let us go ahead and go to blue.1933
Let me write it over here.1941
This is very very important, please make sure you understand that each electronic state, each potential energy curve,1944
it has its own set of spectroscopic parameters.1966
In other words, it has its own ν sub E, X sub E, ν sub E.1993
It has its own B sub E and so on.2003
It is very important.2006
Those are the parameters that we are actually going to be solving for many of the problems.2007
Let us talk about this thing called the Franck-Condon principle, which actually is what this image really represents.2013
We see a lower electronic state, we see an upper electronic state.2019
We should have the vibration levels but all the vibration levels, we also have the actual wave functions.2022
These wave functions right here.2031
This image shows the wave functions.2034
If we were to take the square of the wave function, ψ², what we would get is the probability density.2037
The only difference between the wave function of a probability density is the same exact picture.2051
All of these curves, they would all be above the axes.2055
In other words, like this one right here, it would be curved up.2059
Everything would be above the axis because you square something, you end up getting something positive.2066
Now, let us talk about the Franck Condon principle.2073
Let me go ahead and do this in red.2085
We see that each electronic state has its own potential energy curve.2090
The minima of each state, the minima of the various states, in this particular case2098
I have 2 electronic states but I will say various because it is more than one electronic state, many of them.2114
The minima of the various electronic states do not necessarily lie on top of each other.2120
In other words, you notice this minima is right here.2162
This minima is right here.2166
There is a difference between them.2169
That difference is very important and you will see in a minute.2172
Do not necessarily lie on top of each other.2174
In other words, the R sub E for this state is different than the R sub E for this state.2180
Again, we know that already, they have different parameters.2189
The Franck Condon principle says that the electronic transitions happens very fast2193
because the electronic transitions happen in time frames that are instantaneous,2216
compared to the motion of the nuclei of the atoms involved.2241
Let us go ahead and say that.2269
The much more massive nuclei, in other words the electrons can move a lot faster and2274
move to other states a lot faster than the nuclei can actually adjust to the new state.2280
That is what is happening, the electron is so much smaller than a nucleus.2286
When it moves to a higher electronic state, it is there in a minute.2291
It is going to take a lot longer, relatively speaking, for the nuclei to adjust to that new electronic state2295
compared to the motion of much more massive nuclei.2302
Because of that, we can represent vibronic transitions as vertical lines.2309
This is one electronic state, this is another electronic state.2314
It is already been adjusted.2317
One electron actually move from one state to the other.2321
It is just going to jump straight up.2325
This electronic state, these wave functions represent the different vibrational levels of that state.2329
Here, the wave functions represent the different vibration levels of that state.2338
When electron makes a jump to a higher electronic state, it is just going to jump time wise because it happened quickly.2342
Relative to the motion of the nuclei, we can represent them as just a vertical leap.2348
Graphically, we represent it as just a straight vertical line from the ground state .2353
Therefore, on a diagram like the one above, like the ones that you see in your book,2367
the transition from the lower state to the upper electronic state is represented vertically.2383
When we represent a vibronic transition, we are representing it vertically.2397
There is a state, there is another state, it is going to go this way.2401
Where it lands have a relative, based on the wave function is the extent to which we are actually going to see that line of the spectrum.2405
Therefore, on the diagram, the transition is represented vertically.2415
Let me write up here.2426
Each curve in these diagrams shows the wave function for each value of R, the probability density ψ² look the same.2433
Except all the shadings are above the X axis.2476
Nothing that we do not know from our previous work in quantum mechanics.2486
What the Franck Condon principle does is, it gives us the relative intensities of the vibronic transitions.2495
Let us say the vibronic transition lines.2535
The lines that we see, some of them are going to be very strong lines.2537
Some of them are going to be very weak lines.2541
The strength and the weakness of those lines depends on the probability density of the electron2543
is going to be in that particular state there.2551
Here is what is going on.2563
We would be going from, let us say to 0 to 1 transition.2565
You look over here, the 0 transition from the ground state R = 0 up to level 1.2569
First of all, notice that this particular transition.2582
Because this in this particular image, for this state E1 and E0, the R value of E1 is if a significantly larger than the RE value of the E sub 0.2587
They are not on top of each other.2606
The transition that takes place, the vibronic transition we said it was vertically,2607
it actually ends up passing the one level and go straight to the two level.2611
At the two level, notice where it hits.2617
It actually hits where the density is rather high.2620
In this particular case, we might not even see a line for the 0 to 1 transition.2623
Because it does not even touch the potential energy curve from here, the place of maximum density2629
and the 0 vibration state for the lower electronic state to a place of maximum density.2636
For the upper actually ends up hitting for the level 2, that is where it hits.2642
That particular line is going to be very intense.2649
Maximum intensity, maximum intensity.2652
Here, you may or may not see a line for the 0 to 1 transition.2656
You are definitely not going to see one for the 0 to 0 transition.2660
You may or may not.2662
Again, a little bit of density out here but it is outside of the potential energy curve so you might not see anything at all.2665
What about the 0 to 3 transition?2672
The 0 to 3 transition, if we go straight up, we hit right about there.2675
It is a place of minimum density.2682
We will still probably see one but it may not be very strong.2684
It may not be very intense.2689
How about the 0 to 4 transition?2691
Let us see, where 0 to 4?2693
Over here, 0 to 4 transition we would go straight up.2695
Sorry about that, the 0 to 4 transition straight up.2699
It is probably going to be a little bit more intense than the 0 to 3 but not quite as intense as the 0 to 2.2703
And that is what the Franck Condon principal says.2709
When you have one electronic state, you have another electronic state,2712
the transitions are going to take place vertically on these diagrams.2715
The intensity of the transition 0 to 1, 0 to 2, 0 to 3, depends on where you are actually going to hit2719
maximum probability density, minimum probability density, or somewhere in between.2727
You are just going to get a series of lines that have different intensities.2733
That is all the Franck Condon principle.2739
Let us see here.2745
Let me remind you.2752
It can happen that the upper states R sub E is significantly larger than the R sub E for the lower state.2757
In other words, the upper state can lie much further, not over but in a shifted away from the lower state,2791
such that the 00 transition may not even appear.2804
Sometimes the 0 to 1, 0 to 2 transitions do not even appear.2823
Sometimes the first transition that you see in the spectrum is maybe 0 to 3, 0 to 4, 0 to 5, and so on.2826
The relative intensities of each of those lines is going to depend on the probability density at that particular position.2833
Let us go ahead and do example and see if we can make sense.2844
The following data table lists the observed frequencies of the first 3 vibronic transitions of hydrogen gas2850
to a certain excited electronic state.2857
We see a line at 121 to 76 inverse cm for the 0 to 0 transition.2863
We see a line at 123 to 70 for the 0 to 1 transition.2869
And we see 124 to 438 for the 0 to 2 transition.2874
In this case, we do see 3 lines.2878
We do not know what the relative intensities are.2879
At this point, that is a separate problem, I do not know.2882
We see the 0 to 0, 0 to 1, 0 to 5 vibronic transitions.2885
These are the frequencies that we see, that we observe on the lines on the spectrum.2889
Use this data to find the values of the spectroscopic parameters, ν sub E upper and X sub E ν for the upper excited state.2894
We are going from 0 to 0, 0 to 1, 0 to 2.2907
We want you to use this information, these 3 lines on this electronic spectrum to actually2910
find spectroscopic parameters for the upper electronic state, and this is how we do it.2917
Let me see our equation.2926
Let me go ahead and do this in red, I think.2928
I’m getting really tired of writing here.2935
I apologize if my writing is sloppier.2937
Our equation for the observed frequencies, the vibronic transitions is ν observed is equal to ν 00 +2940
ν sub E upper × R – X sub E upper ν sub E upper × R × R + 1.2955
Let us go ahead and take R = 0, 1, 2.2968
When R is equal to 0, it represents the 0 to 0 transition.2971
In other words, just the ν sub 00.2975
Let us go ahead and do the 0 to 0 transition.2979
The 0 to 0 transition, let me actually write down each one so we have everything.2981
When R is equal to 0 that represents the 0 to 0 vibronic transition.2989
Our ν observed is going to equal ν sub 00 +, if R is 0 this term is 0.2996
If R is 0, this term is 0. 0 + 0, we end up with ν observed = ν sub 00 that is equal to 120,176.3005
This one of the equations that we want.3025
We will call it equation 1.3028
Let us go ahead and deal with the R = 1 case.3032
This represents the transition from 0 to 1.3035
In this particular case, ν observed is equal to ν 00 +,3038
We are putting 1 now, R into the equation.3046
+ ν sub E × 1 - X sub E upper ν sub E upper × 1 × 1 + 1.3051
We end up with ν observed = ν 00 + ν sub E upper -2 X sub E upper ν sub E upper.3066
This one was equal to 122,370 inverse cm.3084
This is our second equation that we have.3090
Let us go ahead and find the R = 2.3096
This represents the transition from the 0 to 2 vibronic line.3100
Here we have ν observed = ν 00.3107
Ν sub E upper × 2 – X sub E upper ν sub E upper × 2 × 2 + 1.3116
The equation that we get is ν 00 + 2 × ν sub E upper -6 × X sub E ν sub E.3133
Upper upper ~ ~, and that one, the table said is 124,438 inverse cm.3147
In order to solve this, I have 3 equations and a couple unknowns.3158
I'm going to go ahead and take equation number 2.3162
This is this one right here, it is going to be equation number 3.3168
I’m going to take the equation 2 - equation 1.3173
When I take equation 2 - equation 1, I end up with the following.3180
I end up with ν sub E upper -2 X sub E upper ν sub E upper is equal to 2194 inverse cm.3190
We will call this one equation A.3207
When I take equation 3 - equation 1, I end up with 2 ν sub E upper -6 X sub E ν sub E both upper, both ~, and I end up with 4262.3210
This one is going to be my equation B.3242
I’m going to solve equation A and equation B simultaneously.3247
I'm not going to keep writing out these X sub E and ν sub E stuff.3252
I’m just going to call it S and T.3258
I’m going to let S equal to this ν sub E upper and I’m going to let T = this X sub E upper ν sub E upper.3261
Remember that is a single a parameter taken together.3273
What I end up with is the following equation.3278
I get S -2 T = 2194 and I get 2S - 6T = 4262.3280
2S - 4T multiply the top by 2, I get 4388.3295
I will not do this for you but what the hell.3303
-6 T = 4262.3306
I subtract and I end up with 2T = 126.3312
T = 63.3318
I get S - 2 × 63 is equal to 2194.3325
I want to make sure my numbers are right here.3343
I get S is equal to 2320.3345
There we go, we said that S was equal to ν sub E, that is equal to 2320 inverse cm.3351
This is ν sub E upper.3360
That is what we are doing. We are finding the parameters for the upper state and T is equal to X sub E upper ~ ν sub E upper ~.3363
It is a single parameter, that is equal to 263 inverse cm.3374
There you go.3382
We finished this problem, I thought you guys might like to see what a particular table of parameters of states actually looks like,3385
if you happen to be interested.3395
If not, not a big deal.3397
If so, this is what it looks like.3398
This is from the NIST website, the National Institute of Standards and Technology.3403
They have a bunch of databases, a bunch of spectroscopic databases, all kinds of things.3409
You should check it out.3416
If you want to see for yourself, basically what you are going to do is you are going to go to,3418
web book.NIST.gov/chemistry.3428
Under general search, click formula or however you want to search.3444
I generally just click formula.3456
Enter molecule in the box on line 1.3462
Check off the box that says constants of diatomic molecules and click search.3478
After that, you are going to scroll down to give you some information and they will give you this very long table.3502
I have only taken a section of this table and they will go all the way down.3510
Scroll down until you see the table and we are interested in the ground state, it is at the bottom of the table.3515
This is the bottom of the table photograph that I actually took.3538
The ground state is going to be represented by something like this.3548
You are going to see an X, you are going to see this singlet sigma +,3551
Do not worry about the term symbol for the electronic state,3558
I will be explaining what those mean in subsequent lessons but you want to look for this X and3561
you want to see this 0 here for the P sub E.3566
It is the ground state electronic energy, we set that equal to 0.3572
Notice, the first column, this is for the NIST website, this table is ω E.3579
For our purposes, this is our ν sub E.3585
Ν sub E, ω E, in this particular table you will also see it with an ω.3589
That is 29946.3594
This O sub E X sub E, this is the X sub E ν sub E.3598
That is that for the ground state.3605
Do not worry about that, here the B sub E that is the rotational constant.3609
There is the α sub E, that was the constant that had to do with the vibration rotation interaction.3614
Here is the dissociate energy.3623
Do not worry about that, do not worry about that.3626
Here is the R sub E, the equilibrium bond length.3630
This is the transition as represented.3633
And here is the ν sub 00.3636
Very important, that was the difference between energies of the ground vibrational state in lower electronic state3640
and the ground vibrational state of the upper electronic state.3646
That is what those columns mean.3650
For the states are concerned, here is the ground state, you might jump up to let us say that excited electronic state.3653
You have a whole different set of parameters for each electronic state, for each potential energy curve.3665
I hope that helps.3678
This is not something that you need, most of the information is going to be provided for you in your problems.3680
You have tables in your books but I figured if you want to see, you can go ahead and see for yourself.3684
Thank you so much for joining us here at www.educator.com.3689
We will see you next time, bye.3692
0 answers
Post by Van Anh Do on December 14, 2015
Can an electron transition from v''=0 to v'=0 of E0 to E1? Thank you.