For more information, please see full course syllabus of Physical Chemistry

For more information, please see full course syllabus of Physical Chemistry

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### Electronic Transitions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- 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 of*1227

*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 chemistry*1268

*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 clear*1280

*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 equal*1372

*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 lower*1395

*- 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 and*1657

*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 symbolism*1776

*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 case*2098

*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 fast*2193

*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 and*2274

*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 state*2295

*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 electron*2543

*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 density*2629

*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 hit*2719

*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 gas*2850

*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 actually*2910

*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 and*3561

*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 state*3640

*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.