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Lecture 26. Final Exam Review


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Title Lecture 26. Final Exam Review
Title of Series Chem 131B: Molecular Structure & Statistical Mechanics
Part Number 26
Number of Parts 26
Author Martin, Rachel
License CC Attribution - ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license.
DOI 10.5446/18934
Publisher University of California Irvine (UCI)
Release Date 2013
Language English

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Subject Area Chemistry
Abstract UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 26. Molecular Structure & Statistical Mechanics -- Final Exam Review. Instructor: Rachel Martin, Ph.D. Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules. Index of Topics: 0:04:15 The Canonical Ensemble 0:08:40 Point Groups: Flow Chart 0:11:27 Group Theory - Molecular Motion 0:16:05 Big Picture: Spectroscopy 0:24:58 Term Symbols 0:30:48 Selection Rules 0:33:41 Electronic Spectroscopy 0:34:54 Nuclear Zeeman Effect 0:38:48 Raising and Lowering Operators 0:40:17 Eigenstates and Eigenvalues 0:41:54 J-Coupling: Product Basis 0:42:59 Statistical Mechanics 0:44:13 Molecular Partition Function
good morning and welcome to our last he can lecture so I know I'm going to miss you guys has been a really great class I've been really happy about you know how much everybody participates in is really excited about the learning the cameraman's that's really cool to a lot of fun so thanks for being such a great class on today were just gonna do a review of what's going to be on the final it is completely cumulative that covers everything that we talked about the cost which is really a lot of stuff so we're just going to go back through and you know I'm not going to anything too much depth but I talk about everything that's going to be on there and if we run out of time in which we might the slides posted and then have a lot of office hours next week I still don't have it posted when I'm going to do it but I'm planning to have you noticed 1 every day Monday through Thursday and possibly more I just spent I can work up the scandal just quick Paul who hasn't a final Monday morning who has the final Monday afternoon Tuesday morning Tuesday afternoon OK looks like Tuesday's a how about Wednesday morning Wednesday afternoon Thursday morning Thursday afternoon attack that's unfortunate that so that's about scandal yeah while I figured you know people mostly taking the same classes so I'm trying to I'm trying to avoid the scandal in the office hours when a lot of people will be able make it OK so looks like Tuesday's a pretty good day from interview extra once and then all still do you know bunch of last-minute stuff Thursday but it's still had a lot of people will have a final 1 is it over the 6 Ouch OK I will see you again have to check the the scandal OK another thing I wanna mentioned before we get started is that of a lot of people sent me e-mails about on the seminars extra credit sheets and exemplary grades and people are getting anxious because I haven't worked on them yet so I was out of town down in the last 3 days and I did not have a lot of Internet access so I could see e-mails on my phone sort when the plane landed in whatever but um you know I've been traveling a lot or was in an 8 hour meeting reviewing grant proposals so I just haven't had a lot of Internet access to upload stuff so I totally get it I know that it's anxiety provoking that you turn in your stuff and you don't know whether you can afford a lot on the issue isn't just behind so when I started doing this extra credit thing with the seminars I didn't know everybody was going to do it and that's also I'm glad you're doing it but it means that you know whatever you give me a piece of paper it turns into a Russian novel when everybody does and I'm just behind so my plans for the weekend is to get caught up on the stuff when I get all the seminar extra credit things done I'm going to post something all posted on the Facebook page and the class website and he also OK I think I have all them done now and at that point if I still didn't get yours then please do send me an e-mail longer look through the stack again but the same thing with these every grades the deadline to asked me about it is tonight at midnight I'm gonna wait until I have all of them and then just do it all at once that'll make sure that it's you know that I'm definitely doing it consistently and also hopefully get it done quickly and again I will post when I think I have them all done and then if I mysterious go ahead and let me know at that time I know it's a it's tough not to know what's going on and I'll try to kind of procedure can alright is did anybody have any more questions about general staff before we start reviewing for the exam OK let's do it
right so as I said this exam is really
cumulative and before we get into the all the material I want to just talk about the canonical ensemble little that so we got about this far in talking about the the connections between the canonical ensemble and just the Standard partition function that we've looked at but we didn't quite get 2 to finish up and then in between we had example data which by the way I heard John Marks a lecture debut was also so that's great I'm not surprised but I'm glad it worked really well OK so we have and we learned about the canonical distribution and the canonical partition function so this is for a canonical ensemble which remember is a collection of Little individual ensembles they're all at the same temperature and the thing we like to use this for Florence Ky feature is the fact that the canonical partition function is more general than our normal partition function and that's because it doesn't assume that all the particles are independent and so on that is really useful when we want use for studying condensed phases so liquids and solids or even gasses that that don't behave ideally so it's a lot more general and it can be used for more things and you know obviously were about a time this quarter but so we're not going to do too much with this but I want to make sure that we cover it to set you up for next course so next quarter with Dr. Gerber you're going to do a lot of working with the canonical ensemble statistical mechanics and get into the thermodynamic properties so the last thing that we need to talk about is the fact that you can get the ball properties of the system from the partition function so the average energy of 1 of our little member ensembles is it's given by you we've got here it's it's just the average energy for around for individual ones and we can write that down in terms of the relative populations which again we're aware that was and what would be really nice is to have this in terms of just a few because that it's a lot more useful and so we can substitute using the derivative of 2 with respect to Baidoa remember Bader is 1 of a treaty and we know that that equals deal debater and so the result we get is for distinguishable molecules being Q is curlicue to the end so distinguishable molecules could be it could be some young molecules that are in a crystal lattice so that they occupy a particular position all the time so it could be that they're all the same but they're in a particular point in space history can distinguish them that way it could mean that they're all the same that they're they're not all the same type of molecule so you might have a solution of say ethanol in water so they're moving around at some of the molecules are distinguishable because they're different molecules and in that case Q is little cute Indiana over and factorial and so this is stuff that I basically just want you to hold in your mind for next court for when you work on thermodynamics with Dr. Herbert it would have been ideal if we had time to get to it last lecture but we didn't quite so that is why organizational statistical mechanics and with that let's move on to the review for the final OK so what do you need to know
so the 1st thing is being able to assign molecules to point this is really important because there are lots of types of problems where you have to assign stuff to the right .period group in order to get the right answer and you know that that will be the key to the whole thing there might be year maybe 1 problem that's not worth very much that says you just to sign something to appoint group but most of what's going to be going on is just having use this information to learn something about bonding or molecular motion or you know whether certain kinds of orbitals can overlap or whether certain kinds of wave functions can overlap and this is something that you definitely need to review their far if you had trouble with that or even if you didn't have trouble with that news haven't looked at it all while it's important scalp and so remember things like you know we talked about different objects and how they transform the under the operations in a point group and so clear I bring up this Osiel to example again that we saw before in class where depending on whether the phase of the orbitals is In phase out of phase they have different behavior with respect to the operations and so you get different matrices for those operations this is something that you definitely need to be able to do and hopefully you see a little bit more why it's important now that we've talked about the rotation statistics of things like molecules that have found fermions verses bows arms you might have been transforming differently under this rotation operation so this is something that you should definitely be able to do so without win that with a basis said that's described in words should be able to figure out a few hundred drive and write down appropriate matrices for these operations and so again depending on whether the rules are out of favor in phase in this case you get differences another thing it's important to point out is that in this particular case we talked about the basis that being the P orbitals so you treat them separately we've also seen other examples where the basis said is of molecular orbital consisting of a linear combination of those Puel's that's a little bit of a subtle difference but you definitely have to pay attention to it so far if our basis that is the linear combination the orbitals then you treat it as just 1 thing then you know how you count what what happens with the operations is a little different so keep that in mind we also need to do things like looking at the molecular motion in determining which vibrational modes are on ROM inactive so remember the general procedure for doing this we have you know some molecule learn about it there in ROM active vibrational modes the 1st thing you do is set up the basis which is going to be x y and z unit vectors on each Adam mistakes that I saw people make them the 1st coupling exams including you know not putting a basis set on the central adamant just doing me Our ones that's so you make sure you don't make that mistake again that the issue is were interested in the despite the relative displacements of all of the Arabs and so we have to include all of them and so of course getting the molecule into the right .period group is an important part of this I you need to be able to set up in the 1st and then look at this and determined whether you can use the short cover not to just get the character I'm probably not mean enough to give you 1 where you can't in the context of the molecular vibration problem maybe in some other contexts I might but in this case it's probably too long and then In our right to be able to write down your reducible representation representing the molecular motion and reduce To get the modes and so then we should have some 9 remind elements in the basis because we have 3 unit vectors and that's going to be 3 times the number of atoms and molecules so that's a good waited to check yourself you should get 9 symmetry species and the final answer then and then what we have to do is go through and take out the translations and rotations because those are something that we don't see in vibrational spectroscopy but their accounting for some of those cemetery species and so you just by looking at the character table and finding the cemetery species that correspond to x y and and then X or Y and in the vibrational modes are whatever's left over so here's another note about this so in this case we only have symmetry species that belonged to a and B type representations that means they're not degenerate when you have things like E which is doubly degenerate and tea which is strictly degenerate if you have say at T something cemetery species and x y and z all belong to it that that takes out 1 that takes out the tea 1 time from your representation of what's left so you have no 318 reusable representation and then you see that he x y and z you have to tear left for the vibrations that does not make sense of it's not clear asked me about it that's something that some people got a little bit confused on last time like if you have a you haven't you representation and you're removing X and Y that only removes 1 E from whatever you have left not to because they are doubly degenerate OK yes you did on defender wasn't questions are right column OK so what's left of the vibrations and you figure out whether they're IRR of active by looking at the character table and you see whether there is a component of the if if it belongs to the same cemetery species as a component of the dipole moment that being ex-wife and if it doesn't active and if it's wrong and active that means it belongs to the same cemetery species as a component of the polarize ability so something like X Y y z exported maize Square squared something like that and of course so much the cemetery species can be both on either on 1 idea so I think we've done plenty
of examples of using class and they've showed up on the other exams so just make sure you go back and review and you know if you made mistakes be sure that you understand how to do it OK so that's what we have to say about group theory we also need to talk about different kinds of spectroscopy see you should know sort of the big picture of spectroscopy What are you measuring when we talk about different kinds of spectroscopy and we've talked about quite a few so we have electronic spectroscopy we've got vibrational spectroscopy I R in Roman we also have a rotational spectroscopy which could either be in direct rotational spectroscopy or occasional Roman and you need to know how those mechanisms for these things are different from each other and you haven't how how your physically measuring a signal and we also talked about in March is different from all of these and you should also know the relative energies that are involved so which was so if you only have enough energy to excite rotational states you should know that everything vibrational using the ground state but the opposite is true right if you're exciting vibrational states then you get the rotational excitation is along with that OK again he should be able to look at the Roman spectrum and you know what's different about it then the absorption spectrum and again there are 2 kinds of Roman spectroscopy rotational and vibrational if it's not mentioned which kind it is minutes vibrational that's the 1 that's most commonly used but rotational Roman spectroscopy does come up as well OK so once you have these either by racial or rotational spectra we should be able to analyze them and so remember that if you have this one's entire spectrum if you have the IRA spectrum you should be able to make some of the correspondence between that spectrum and the energy level diagrams to remember that the peaks in the spectrum correspond to transitions between the levels can you not the not the levels themselves so given 1 of these things like the particularly the potential energy diagram for the spectrum you should be able to draw the other 1 and say you know which which levels correspond to I'm also you should be able to explain certain general features of the spectrum you should know about this election rules both the gross and specific selection rules for all the kinds of spectroscopy that we've talked about this is just another picture of what these things look like so remember Specter sometimes plotted like this with the peaks going down there sometimes bordered with the keeps going up it doesn't matter that gives you the same information OK so given these kinds of spectra we should be able to calculate different things from him so for a simple molecule we should be able to get a bond length from this and so yeah the things that you need to know included the spacing between the lines for the different rotational states is to be sports for me if you take it across the the middle where there's no peak the center because the J. equals 0 Jaipal 0 transitions Forbidden City that's me and so based on the occasional constant you should be able to get the bond lengths using these equations said that we've used before you should also be able to estimate the force constant which is something that we did on the last exam and for the force constant you just need the fundamental frequency of the whole thing which of course is the point in the center where there would be a line of the J-PAL's era J-PAL's era opposition were allowed and I also want to point out that these things could be in all kinds of crazy units that could be a wave numbers the frequency your energy or you know some some combinations of of these things and no matter what it is you should be able to convert back and forth in use all these things it's it it's an important skill because when you read the literature of you'll actually see these things written down in different ways and it's important to be able to convert among them fluently it would be nice if everything were consistent and in units that make sense but alas it's not like that OK so From this is from the practice exams there questions like why isn't there a peak in the middle again that's because these slight but the specific selection rule for rotational transitions that JRC has people of Delta Jay has equal parts of minus 1 yeah ends didn't mean energy for the new equals era new equals 1 transition it is just you read off the at the point in the center of the spectrum where is the line missing you know or if you had a molecule that can keep their because it hasn't heard electron safe and that would be where that is other questions include here is a molecule perfect rigid rotor and how do you tell so again this was last exam if the spacings aura really exactly equivalent then you can say the same behaves as a perfect rigid rotor and if they're not if it's stretched on 1 side and switched on the other than you know that you have some centripetal distortion and it's not a perfect bridge over so what that means that is as the molecule rotates really really quickly then it starts to stretch out and if it doesn't behave as an ideal case so in these particular set of examples I would say that C to actually looks like a pretty good rigid the spacings are quite even an end to all really doesn't question in the car will be intensities yeah that's a good point as to whether the same on on both sides but the intensities mostly come from the Boltzmann distribution of the population ever in public that a little bit yes all along if if you
send its here she was a perfect the year in this therefore this 1 mean can be it can be hard to to tell but for this 1 and that it does look like the line spacings really even and particularly you know maybe a better question would be compare them which 1 is about rigid and then you know that it's clearly 0 2 OK so Back to the question of the line intensities if we say the structure were collected at room temperature and then we lower the temperature to 10 Calvin how would they change how they look different and and in that case we would seem
more intensity in the lower transitions and also the distribution would sharpen up because we're filling she were States they're just your state's available at lower energy and so we also seeing this picture before here's the How the population's look different at low temperature verses at high temperature so noticed that the scales on these are different and it's a little bit harder see when it goes from here 10 to 100 gigahertz on the top and 0 2000 on the bottom so that's just showing you that at higher temperature there are many many many more states that can be populated than at low temperature and also we see in a cellar temperature we see everything piling up in just a few states so that's something that you should be able to explain and you know be able to to sketch what it looks like qualitatively and so that's that's most to the effect that accounts for the distribution of the levels the attack and we've already talked about Roman spectroscopy OK so
we went through that pretty fast but there's a lot of information in there about vibrational rotational spectroscopy is not something to spend his time reviewing looking the exams from this quarter make sure you know how problems that were there you also look at the practice exams From a couple years ago that I that I posted and make sure that you know how to do those problems and then we get to electronic spectroscopy so make sure that you know how to write term symbols so here the rules for term symbols for Adams again probably not going to have a question directly but terms symbols for Adams because I know that you covered last quarter what were mode that were going to be concerned about is the term symbols for diatonic molecules but of course you have to understand how did the ones for Adams inaudible to do that it's uh it's also important to remember Funds rules in determining which of these states are lower energy so a lot of times for particular electron configuration the electron configuration itself will be ambiguous you can get different arrangements of electrons for the same what kind configuration which is of course quite medium-term symbols in the 1st place there are a lot more specific than just the electronic figuration and so you should be able to to use this to figure out which 1 is the ground state and then the part that you're actually going to have to do is figuring this out for diatonic molecules and so this will be pretty similar to what we did last exam you get some sunlight ,comma molecule you have to draw the molecular orbital diagram and figure out the properties of these electrons and CDR how many alike .period configurations you can get and of a particular well how many other arrangements you can get out of a particular electron configuration and then right on the terms symbol so then make sure that they you know that you know how to do the example from last exam I think the TVA's did a really excellent job of this in the review session last time so look over your notes from them and also remember things like the even odd rule and you know how to determine whether a particular transitions are allowed or not by symmetry and so for electronic spectroscopy there are going to be too considerations for transitions so 1 is just further transitions allowed a not by cemetery not something that you get by looking at the cemetery of the wave function you have to take into account the about GNU and if it's a signature terms plus and minus and then the other thing that we have to remember is on Frank factors so you should know how to write down in expression for the Franklin factor between pairs of states again you're probably not going to need to evaluate that because you don't have time to do hard roles during the time of the exam and honestly you're not going to have a lot of extra time to do much of anything because it's going to be long but just like that the midterms event it won't be twice as long as you have twice as much time so that's so that's a little bit better but you know just I wanted take this point to say make sure that you read the directions really carefully because there will be things where I'm trying to save the time by giving you an intermediate step a single do this part of it just make sure you read them really carefully and if you're confused about it ask I mean I do stay here for the examiner around answer questions and you have to have something that is information you certainly know all to say sorry ready to know that there's no harm in asking the question well you kind and you know the format so I've already given you to practice midterms and then we just have to be Stepanek of questions from you know that the quiz kind of services that may give you a bunch of practice homework problems so I think I know you do pretty much know what the formats can be liking you know sort of how I ask questions so I'm not going to give you suffer practice final but I do think have a lot of practice from the so yeah I read the directions very carefully and ask if you don't understand and the other thing is when you get the exam you know take a deep breath and read the whole thing and make sure that you do the easiest problems 1st because what's easier what's hot is a matter of opinion some people understand some concepts more readily than others and so I want everybody to do their very best so to make sure that you do the ones that you think you can do really quickly 1st and then go back to work on the things were maybe you need more time because I don't want people to get into a situation where you spend all your time on something that's really hard and then you find that you know there was an easy 1 that you could have done quickly so just just some general exam strategy OK
so we definitely need to know about selection rules and this this slide on selection rules is really general was could be for just about anything so it's hands on the island this election rules depend on a transition dipole and so there are different ways to to look at but sometimes you can just do it by inspection basically like if you have say the harmonic oscillator wave functions and you can just look at whether there even and odd and remember that the transition dipole the ear of the dipole moment operator is always on unity the grows wires eh and then if you can't just do it by looking at it and say OK there even alive then you need to do it by looking at the character table and so in that case you need to find cemetery species in each function and then multiply the characters for all 3 of those together and then you'll get some reducible representation in general sometimes you're lucky to get something that looks like a reducible and irreducible representation the Guardian the character table and you can look at it but sometimes get something that's a reducible representation and then what need do with that reduce or representation and see if there's a component of a 1 in it or you know if it's not call they 1 in that .period group whatever the cemetery species is that has ones under every operation so again that's the 1 that's invariant all transformations and so what what what we wanna see there is that if you have things that that actually overlap an hour coupled by that dipole moment operator and overlap no matter how you move the thing around in space so we just have to make sure that there is a component of the cemetery pieces its invariant all transformations in order to say whether that exists on questions that's right that means that it has a component that invariant all transformations in the integral does not vanish and you get an answer another mistake that I've seen people make with on the previous exams is that that doesn't mean that the overlap is 1 so you can't tell whether it's 0 really easily From this treatment but you don't know what the value is so all you can say is it's not 0 so enough people put its equal to 1 things you got some partial credit but Be careful that you know if you don't actually know what the value is just from the cemetery treatment it could be really tiny it could be 1 you don't know don't you have to do something you have to do some more sophisticated computational able to get that OK so continuing with electronic spectroscopy we looked at birds former plots and how these compared to the the potentials associated with the electronic spectroscopy we've seen a couple different examples of this there was an example on the practice exam that I gave you exam the at the actual test was maybe a little bit harder because it was it was a weird example where the thing had a break in the slope so we again just make sure you read the directions and and look at what the questions actually asking and know your equations for how this plot pertains to the potential energy diagram of the molecule OK so that's what we have done with electronic spectroscopy you need to know how to write your term symbols and be able to figure out which transitions are allowed you need to figure out the franc Condon factors and also be able to use some of these plots to find out some properties of molecules we also talked about animal and that's a little bit different from these other types of spectroscopy bite what you need to know about it is kind of similar so they're both sort of theoretical things like that of the need to understand about it and then also in a practical sense of being able to look at the Spectrum and learn something about molecules a look at the molecules and figure out what spectrum is gonna look like so the important things snow here is how the same effect works we have our nuclear stands there in all kinds of different states if there's no magnetic field they're all equivalent in energy if we put the magnetic field on that generously is broken and we've got a couple of states for spend 1 half we can have plus or minus a half that corresponds to stand up a stand down and in the spin one-half case these states have nicknames even column Alpha and Beta if it's not been 1 half then you have to use their full names you have to write a cat that has yeah for for instance 1st 1 did have 0 1 0 sorry 1 1 1 0 1 minus 1 and you can do this for any kind of nucleus it's just that we have to remember that whatever its whatever the value of ideas you go from "quotation mark A-minus applied it to minus in in increments of 1 so here that is
written down a 3rd the component of the angular momentum goes from "quotation mark A-minus in increments of 1 and there are a few stand operators that we learn how to use In the context of Panama and we talked about how you can use these things to to generate pulse sequences and foot the spends we're not going to get into you and I can expect you to know too much about but as far as as far as how you use it at this point is why did introduce you to it but we do need to know how to use a couple of these spin operators that we've talked about so 1 is eyes so when we make these sounds these states that we're looking at Nzimande basis or the items states of survives and so you should know that when you operate eyes on state you get it's Ellabell you back that's the biden value and then the Eigen state is that same cat so for Spain one-half case if you operate Zia and offer you get one-half elsewhere and if you operate data you get minus 1 have but again be equation that the top here is the general definition of icy and you should be able to apply that any I value for your skin and you should also be able to write a matrix representation of something like crazy in the Zaman basis and so you do that by generating each of the matrix elements and so the important thing is to know here is 1st of all how to operate IV the states and you do these things from right to left so you operate eyes on the cat 1st and then you take the overlap integral whatever's left and these things make up north normal basis so if the states are the same the values 1 if the different it's 0 and so you should you should be able to use that to generator matrix representation for something like I see it we also learned how to use the raising and lowering operators so here this is just written down for the spin one-half case so if you operate plus on Alpha you can't you can't resell Fennimore 0 if you operate I plus beta you get Alpha I would recommends checking out your on your exam look at the general definition of erasing lorry operators so we mostly talked about this in the spin one-half case by year examiners through the general definition of them and you should check that out make sure that you know how to use it and so again we can write down the matrix representations of these things because we know how to operate the operators on the states and then we can take b overlapping roles of the state of the states with each other and so you should know how to write down these matrix representation and when you do this on the exam you should definitely sure your work if you don't wanna right out all the matrix elements at least write out a couple of them so that show you know how to do it so if you just write the answer I'm going to assume that you put on your cheat sheet murder down and you will get full credit you get some credit but you have to show some worker explain your rationale to get b UK IXI why can also be written in terms of the raising and lowering operators this is something that you should know about the actual or duration of high you get this we didn't homework and it's important it's probably too long do on example but we should know what these are OK so now we get to what the spectra actually looks like and so that's something that you know you have a lot of experience here from organic chemistry to build on and the rules are the same as far as with the specter of look-alike inured you know a lot about our Yuri did know a lot of it before starting his class and the differences now you know how it works so why a why the specter look like so this is something that you should be able to do you have a molecule we should be able to generate its and more spectrum L you know that should be true for any kind of nuclear that we want to talk about the same principles apply so whether it's Proton see 13 you have 31 P you anything like this you should be able to generate with the specter and look like the same as last time I'll give you a chemical shift table so you just have to figure out what functional group as well and things in the right general places I'm not really worried about people memorizing the chemical shifts of other things if you either become a synthetic chemistry never marched across the western you really need to work with us all the time you'll definitely remember it then but for now I just need to be able to use the table you should also be able to generate of the coupling patents for J couplings and you should be able to explain where these come from in a physical sense
and you know you should be able to dry specter different kinds of of molecules basically putting everything in the right general location and figuring out the J. coupling Fatah and you know again you should know what those things look like with and without the coupling of various nuclei and then the last thing we talked about is statistical mechanics and so we don't have time to review all of that because there were also time and also we just went over it but the important
thing is that you should be able to do now is is how to set up your partition function for an ensemble of molecules you should be able to think about the most probable configurations of various states so in for instance you should you should know that you don't pile everything into the ground state necessarily because it doesn't have it often doesn't have any generously whereas higher states do have multiple ways to get the same configuration you should be comfortable with how these configurations are written down and with Boltzmann distributions and how we get the relative populations of the States Israel kind good things straight down a cheat sheet we should know how to find the relative populations of 2 states or the population of a particular state relative to the whole ensemble and you should also be able to write patrician functions for various things so here's a general case of a partition function and also how you write that down high rate the relative populations in terms of that and you should be able to do this we talked about some specific examples in class so we talked about rotational states a lot so you probably want to know how to do that we've also talked about vibrational states a bit so that's a good thing you know we also talked about the end of case of this so that's another 1 where it would be good to know that the specifics about that 1 there also these questions where you're given the you're given a description of the system in words and you have to write an energy level diagram and write the partition function and so here's a case where people seem to get confused about this a lot where are you people look at this and say well I don't know the value of Jay and generous used to J. plus 1 so how do I do that I remember that's for the case of a rotational spectrum and so you should know that the pigeons that it the generous Eva rotational levels to J. Foss 1 that's an important thing now but don't try to apply it to other cases so in the In the case of the the vibrational partition function if we just have a harmonic oscillator which were going to Frank and we talked about in this class those states are all on generators have here parabolic potential and you have all the states so those are not degenerate for electronic states it's more complicated you don't know what it is but for this tournament general system where he told you that generous in the problem and so that's a year said don't get don't get hung up there on you know wanting to use these other rules that you know for different systems if it just says the 2 generous state 1 of Act is accidents for state to its wide but this directly write that down and use it it doesn't it doesn't matter where it comes from in that case but you should know how to write these partition functions in a general cents versus like this that's described in words and you should know how that changes with respect to temperatures so if you make the temperature really low really high you should know how that affects the relative populations and how it affects the partition function and I
think goes we're about done and that's what's going to be on the final so thanks again for a really great class I really do think thank you is also a place I look forward to seeing you in the office hours next week ,comma around a little bit in the presence of the class
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