 So what we're going to do today is we're going to go through and talk about the logistics of the course, how you're going to get graded, what you have to do to get a decent grade in the class, and then we'll start talking about the statistical mechanics. You haven't found it yet. Here's the URL. What we want to do is just sort of click through some of these links because they contain all the information for the course. That's what I'll do. So, oh, I stole this from some beautiful work. That's been done in the area of molecular dynamics. And we're going to be hopefully talking about molecular dynamics at the end of the course. And if you want to know more about this picture here, which depicts something called a conical intersection. So that's a carrot concept. You can go to this paper right here. That's really all you have to do is if you click on this beautiful picture on the front of our website, it'll take you directly to this paper. You can read more about it. It might not make an enormous amount of sense until we get to the point where we talk about this subject later in the course. Okay. So the very first link on the website is something called announcements. Now, this is where I'm going to be posting announcements that I want to make in the class. I'm really not very good with Facebook, and I'll talk more about that in a second, which is the reason why I post my announcements for this page instead of doing something more intelligent because I know you are all Facebook experts. But what I will do is I will post my announcements here. They will be in inverse chronological order. So the most recent announcement will be at the top and then there will be a list of all the announcements that we made during the course. So you'll have sort of a record. If you miss some, you can just scroll down and find them. And I'll probably post an announcement or two almost every day. So it would be a good idea to just check this bookmark, this link announcements, and check it once a day or so to see if there's anything. Maybe I changed the homework assignment. Maybe there's some information about the quiz that's coming up on Friday. Maybe there's sample midterms. All of that stuff's going to be posted here on this announcement stage. This is the syllabus. We'll go through this in a little bit more detail because this is kind of important. But the first thing I would like to impress upon you is that we don't want to print everything from this website. We don't want to carry around a folder of stuff. All of the links to this course are up. We don't want to print everything out of all the homework assignments. Everything is going to be electronic in this class except for the quizzes and the exams. And virtually everything else will be electronic and that's the way we want to keep it. We want to converge towards having a perfectly paperless course. We're not there yet, but we want to try and get there because, ecologically, it's a lot better. Okay, so please don't print every slide from every lecture. Stick that in a notebook. That's a perfectly useless thing for you to do because these slides are going to be posted on this website until you are old people. Honestly, it's true. If you go back, the very first websites we created, like in 1995, all of that stuff is still on the internet. It never went away. So we don't need to print all this stuff. Let's not do that. Now, we're fortunate that we've got two lecture teaching assistants, Steven Hulsey. Steven, are you here? Steven's right back there. Steven's an expert psychologist. He knows everything about the subjects that we'll be talking about this course. Don't let him tell you anything else. In G. Mark Johns, he was a T.H. who last courted you in 131B. Maybe you know G. Mark. He's back there. These two guys are going to be teaching all the discussions. I'll have more to say about them in just a second. Steven's going to be moderating our Facebook site. Facebook site's going to be important to you, but since I don't know anything about Facebook, Steven's going to be the one to moderate everything that goes on there. So you'll be interacting with Steven through Facebook and seeing them also in discussion. All right, we know what lecture is. We know where my office is. It's in SI2, room 2137. Now, everyone know where the SI2 is. Yes. 2137 on the second floor. And it's in this hallway that's behind a set of doors, the purpose of which is to keep people from randomly walking in to these offices. But you shouldn't be discouraged from coming to find me. Right, this office is right in the front of the building. You can open that set of doors, walk down the hallway, find my office. The doors are virtually always open. But I'm in there and the door is not open. It's because I've got like a grand death on me or something. But most of the time, if you need to talk about something, having to do with the class or the materials, if you have a question about something, you can just come and ask me. We're also going to have office hours that happen sort of right after lecture. There's usually a shady chair in the park right outside this door where we can sit and talk. And so some of you already know what we want to need and some of you will have other classes. But if you don't and you have a question about lecture, what I found is the best time to ask that question is when that's really refreshing your mind. You just heard it. You didn't understand it if you wanted some clarification. All right. So I'm going to try and sit over in that chair and answer my email. And if no one shows up for five or 10 minutes, I'm going to go walk back to my office and have lunch myself. All right. So if you need to find me, that's where I'll be right after lecture. This is the text. I know you all have it because we needed it for 131C. There's our Facebook link. The way we're hoping Facebook works and the way it's worked effectively in the past is that students talk to one another on the Facebook page and offer hints as to how to answer various types of questions and it turns out to be very, very useful. In other words, Stephen doesn't have to answer all the questions although he will stir the pot and answer questions when he can but you can talk to one another about problems, quiz questions and so on and answer each other's questions and in the past things have sort of automatically worked that way. It's a miracle. So hopefully it'll work exactly that same way this quarter. That's what we're hoping for. This is the normal boilerplate that we always have to post. It has to do with dags and drops. You can read it. There will be quizzes almost every Friday. This is coming Friday. I'm going back to the quiz system. If you had 151, we tried to get away from it. That was meant with enormous existence. I got a lot of feedback about homework with 151 and almost all of it was negative. Moving away from that model. In this class, the problem is there really is no electronic homework option for us. In other words, even if we wanted to do electronic homework, there isn't any mechanism for doing it. Paper homework, logistically, is a nightmare and a class that decides to do well. So there will be assigned homework. None of it will be graded. No one will ever know if you do it except that. If you don't do it, the quizzes are going to be focused on trying to find out whether you did it or not. So it'll be helpful for you to do it. All right? We will usually have a quiz for the first 20 minutes of each Friday. Except you'll be able to do all the quizzes with a lot. 200 points out of 600. There will be seven quizzes only. You can choose the top five. In other words, you can drop two quizzes for any reason. If you're going to be done, you don't need to talk to me. You can completely blow a quiz. Or sleep late. I don't know how many. You don't need to worry. You've got two dropped quizzes, not just one. We're going to average those. We're actually going to total those five quizzes to get those 200 points. Each quiz is going to be worth more than the points. Times five is 200 points. All right? Each quiz will be multiple. Yes, that might seem like a giveaway to you. But none of the above will be an option on every question. And the questions, many of them, in fact, most of them are going to be numerical questions where you have to work out a problem, choose the right answer. If the right answer is not there, the answer is none of the above. And none of the above will be an option that we use. Okay? So these quizzes are actually quite difficult. Previous classes have told me it is non-trivial to do well on these quizzes. There will be five quiz questions. And what that means, as I'll explain in just a second, is if you missed one, you've still got an A. If you missed two, you've got a B. If you missed three, you've still got a B. If you missed three, you've got a B. Or you've got a C. So you can afford to miss one. You can't afford to miss more than one. Most of you want an A in this class. Okay? Oh, here's the, I don't know why. Here's our Facebook. Here's Steven's notes. Welcome statement. All right, check out the Facebook page. We have a chance. Okay. In addition to the quizzes, we're going to have two midterm exams this quarter. We have different from previous quarters. One on April 27th, one on May 25th. These are both on Fridays. They're going to both be in class. They're both going to be worth 100 points. They're both going to be completely problem-oriented. And I'll have a lot more to say about this later on. The finals on Tuesday, June 12th. That'll be comprehensive. It's worth 200 points. There are six discussion sections listed here. Here's where they're located. Here's who's going to be teaching them. You can go to one, two, or all six every week. No limit. The way these discussion sections will be structured is that Steven and Jean-Marc are going to prepare a discussion study guide. Many of you are familiar with this concept from the classes that you had with me before. Probably other products. The discussion study guide has three or four problems on it but we consider to be central problems to the material that we're covering or are covering during that week. What will happen to discussion is they will take your questions on any aspect of the course that you have. Ask them any questions that you want. If you run out of questions, we're going to work through this discussion study guide together, maybe in small groups and make sure that we understand how to do these key questions. We're going to pulse these discussion study guides on the lecture page. You'll see where there's a link for those. If you want to look at it before discussion, try these problems out. We'll be able to do that. We're going to pulse them on for this week, later on this morning. We've been working on it this weekend which should be done right about now. Hopefully early in the afternoon, I'll post it if you can look at it. We have a discussion tomorrow. You can be prepared for that. Okay, homework problems will be a sign-on money. Tweaks, blah, blah, blah, blah. I'll show you the homework page in just a second. Your class standard will be continuously upgraded on the Triple E website. Okay, and the way the grades are going to be assigned in the course, again, if you have 151, you're already familiar with this scheme. You need to get 80% of the course points which in this case is 480 points because there's 600 total course points. All right, you have to get 480 to get some flavor of A I decide where the dividing line is between A and A minus and I do that depending on where there's a break in the distribution. All right, but I guarantee you if you get 80% of the course points you're going to get some flavor of A. If you get between 60 and 80 you're going to get some flavor of B again, I don't draw the lines where it makes sense to draw them but that's a hard cut-off between 60 and A to 60 and 61 that's where the D cut-off is NCs, analogous, and so on. Okay, so in principle everyone in this class can do well and historically everyone in this class the vast majority of the people in the class can do quite well I'll show you in a second. All right, is there any regrading academic that's on the scene? All right, lectures. Here's the lectures that I gave last year. You see how there's an asterisk next to each one of these lectures? So if you want to see what the next lecture is going to be about you can click on this lecture from last year a pretty good idea. Now believe it or not I take each one of these lectures and I try to improve them so there will be a new and improved version of this lecture posted later on today. It won't have a star by it it won't have an asterisk that'll be the new lecture for this quarter. I did make some changes and so but I am lazy enough to tell you that the lecture that I'm going to give you today is closely related to the one I gave last year which I worked really hard on by the way. Okay, here's the discussion study guide for this week it's not actually posted yet but we'll be posted later on today. And in principle there will be a YouTube video of this lecture which is a new experiment that I'm doing the concept very frightening. I'll post that over here if I continue to do this experiment after one or two lectures. Okay, here's where the exams are. Notice that each quiz is listed here's quiz one, week two, here's quiz two, here's quiz three there's no quiz in week four because there's a midterm okay so there's a lot of information on this page remind you where the quizzes are going to be. Here's the homework page here's the homework page homework one is to do all the odd problems in chapter 13 here's the key right? Every problem's worked out click on this and you download a PDF of the key here okay, likewise for the other chapters here's all the homework going to do this course, a thing of beauty results as we get them they will be posted to this website this will end up being a long table there's a lot like this here's last year's table quiz one, quiz two, quiz three here's the key to the quiz here's the grade book in which the quiz grade is tabulated here's the midterm exam key and so on and so forth, every once in a while I post how am I doing in which I work out what your effective course grade is if there's some unusual weighting in this case I don't think there will be in other words you can just look at your course points and if you're 80% or higher if you're doing 68 you know you've got a theme on here's what the histogram of the class is going to end up looking in all likelihood because this is how it looked last year these are all A's see all this red line that's the 80% line I'm going to draw that right through the middle of a big group of students like this because I'm going to promise you that if you get more than 80% of the course points you will get some flavor of A the other side of the coin if you get more than 90% of the course points you're going to get some flavor of B of B plus but I'm going to draw that line right at 80 and I'm going to draw that line right at 60 and then these blue lines I draw see how there's a break in the distribution here boom see how there's a break in the distribution here boom alright I draw the lines between the pluses and the minuses see fair enough you might not like it but you'll know how you're doing except you won't know necessarily if it's a plus or a minus okay you ready so I use PowerPoint you all know that by now I'm trying to get better at PowerPoint so if you have suggestions for me maybe you're really good at PowerPoint you could say you could do this it would be way better you can talk to me you can tell me that I'm not going to be upset I would be happy to receive your criticism these presentations are closer to the website one to ten minutes before or after each lecture usually after take notes so I can look at each slide so not everything that you need to know is written down on these slides I try to keep the slides free of a lot of text and clutter so that they're easier to understand there's a lot of what we need to be knowing for each slide and if I was sitting in your seat and I was taking notes in my notebook I would write the slide number and then anything that you think is important and then the next slide number each slide will have a unique serial number this is slide 19 as it turns out lecture one this is supposed to be one it's a serial number every slide is important if you want to come and talk to me in the park I didn't understand something on slide four 76 I can go right to that you can talk about it that tends to be a useful thing to be able to do many of you know how my system works I will talk to you in lecture write these lectures post all this stuff together Steven and Gianmarca and I are going to write these discussion study guides so you're going to be getting a lot of information from me you're going to be seeing me for almost three hours a week then you're going to see one of these two guides or more if you go to more than one discussion they're going to be teaching the discussions hopefully they will tell you the same stuff I'm telling you a different way tell you it in a way that makes more sense to them kind of said it really makes sense to me but here's another way to explain the same thing that makes a lot more sense that's the whole reason why we have these guys teaching the discussions they're going to put a different spin on the same material that tends to be very helpful for you then you're going to do the homework and that's the most important part of this process in terms of actually learning the material doing problems yourself find out you guys all know that's the key to doing well in a class like this and so hopefully it's made it easy for you to do the homework we've posted solutions the way to do the homework is not to look at the solutions and then go and do the homework is to attempt the homework work really hard on it and you can't get it then go with the solutions you understand all that right okay so quiz Friday we're going to get started with this craziness right so hopefully not too much longer than that and we'll take it right at the beginning of class so it's important that you be here right at the beginning of class there'll be a stack of scantrons in the back there somewhere pick up a scantron when you come in please take just one even though we're going to quiz this all quarter I would really appreciate it if you didn't take 10 scantrons because these scantrons are expensive for us and if that starts to happen we're going to have to do something dumb you don't want the scantrons yourself at the bookstore I mean we don't want to do that we want to bring just the right number of scantrons for the class each week right so please take just one alright now I said I didn't know what the name of the class is and then it has to be true but let me tell you what's going to be it because that'll be it at the beginning of week one we've got 10 weeks we're going to start off by talking about statistical mechanics and thermodynamics so first of all let me just back up and say in 131A you learned about quantum mechanics and quantum professor concepts in 131B you learned about spectroscopy from professor Martin in 131C in principle we have to cover all the rest of physical chemistry now I'm sure you agree with me that this is a foolish way to organize a three class sequence that we understand now and we're going to reorganize this class in future years but this corner we're going to cover everything else in this 131C curriculum what that means is it won't be an in-depth study of all of these revealing subjects it won't be, it can't be because we don't have time to do it but I'm going to try and convey to you what I consider to be some of the most important concepts I hope you'll agree there's cool stuff in this class because I think there really is okay so I know you started to do chapter 13 with professor Martin but we're going to go back from the beginning of the subject because this is a super confusing subject the statistical mechanics we're going to stop by talking about that if you read chapter 13 at the end of the last quarter great, if you have it please read it now this is confusing stuff and as I indicated the quiz on Friday to be on the stuff started in the first half of chapter 13 here's where the midterm is going to be notice that the midterm is not aligned so if I stop right here I may try to push this block back to the left but in the past I have been successful in doing that it's hard to shorten the subject this happens to be a very important subject a lot of courses have this whole 10 weeks dealing with this subject that would be the appropriate way to teach this subject because you can't do that at school then we're going to talk about chemical kinetics again this is a whole class we're going to condense it down to just a few weeks we're going to hit the high points try to convince some of the main themes chemical kinetics and finally, underlying chemical kinetics is this subject called reaction dynamics I'm not sure if we even got to this last year alright this subject tries to take up a whole 10 weeks I would try and find room for this because it's important to understand what it's about at least a few concepts here's where the midterms the dates of these midterms are selected based on my travel schedule because I want to be here for as many lectures as possible so on days when there's a midterm I'm not going to be here those two guys are going to give the midterm exam I don't think that'll present problems for anybody but in terms of me being here that's absolutely the best way to do this any questions on anything having to do with logistics of the course can it be similar to the homework problems in a quiz? yes they will will the quiz questions be similar to the homework problems? yes they will what I will do is I will post a sample quiz tomorrow or later on today so you can look at what quizzes look like what quiz questions look like I want you to be calibrated on that so those will be on the announcements page of our site hopefully later on this afternoon if not tomorrow any other questions? so what is statistical mechanics who invented it why did we need it and how do we start thinking about this subject quantum mechanics was discovered in 1924 this is a timeline from 1800 there's 1900 there's 3000 here's when quantum mechanics was discovered in a period of time starting in 1924 and I know this is one thing that you understand extremely well after studying it for 20 weeks these are the pioneers of quantum mechanics Eisenberg, Schrodinger de Broglie Durrack, not shown here what does quantum mechanics tell us? among other things it tells us that if we assume the potential for the electron we're going to generate energy levels as soon as you confine the electron you force discrete energies, allowed energies to be produced and quantum mechanics allows us to calculate what those eigenvalues are also to figure out where the electron is we can calculate the complex conjugate of the electron spatial distribution depending on what that confining potential looks like so quantum mechanics taught us that there are discrete quantized energy levels in atoms and molecules we didn't know that for sure before quantum mechanics came along and in fact all of the time before 1924 this would have been considered to be an extremely controversial issue in fact when were atoms discovered? anybody know? proposed by a man named Dalton hi there might have been a great deal yeah so Dalton was the guy we actually said atoms got to exist based on all of this experimental data that we've got, the one thing that explained all of this experimental data is 1806 okay, did Dalton discover molecules? my name is Amogadro proposed molecules Dalton guy later on in the 1800s right about here did everyone just hear about atoms and molecules and buy into this concept? not at all the existence of atoms and molecules was controversial during this whole period of time here right up until Einstein observed Brownian in 1906 right about here alright everybody know what Brownian motion is? you know how many people have looked through an optical microscope at a bacteria you know all that thing wiggles around when you're looking at it it's jiggling that's Brownian motion what it is is it's collisions of atoms and molecules with the bacteria that object is small enough so that those collisions are not isotropic in terms of the perimeter of the bacteria there's more water hitting it in one direction and then more water hitting it in another direction so it jiggles based on this influence of these collisions and when that was observed by a physicist named Brown of course Einstein correctly interpreted his observation he said what's happening is atoms and molecules are colliding in a catastrophic way with this tiny microscopic object and that's the source of these fluctuations and that was the only explanation that made any sense so right up until 1906 this subject was discussed in scientific meetings there were the so-called positivists who believed in the existence of atoms and molecules this was considered a controversial issue for almost 100 years that's pretty amazing what's really amazing is that in the middle of this controversy all of these guys together figured out statistical mechanics and thermodynamics and as you'll see knowing that discrete states exist is absolutely essential to really putting this construct of statistical mechanics together if you don't have states it's hard to think about statistical mechanics which has something to do with the occupation of these states the statistics of that it's astonishing atoms are discovered here molecules are proposed somewhere around here and here there's just this vitriolic discourse that's going on in the middle of this these guys put together thermodynamics and statistical mechanics really quite extraordinary these are the guys mainly responsible for the statistical mechanics part Maxwell, Boltzmann, Gibbs those are names that you probably know already here's Maxwell this guy was a genius Stocksman maybe one of the less important things that he did was contribute to the Maxwell-Holtzmann distribution he actually derived Maxwell's equations which are unbelievably important he invented three-color photography it turns out in a spare time theory of compound color he did the first three-color separation to generate a photographic image and here it is this is a ribbon a Scottish tartan it turns out appropriate because he's Scottish he told the photographer how to do this three filters, three photographs all three of them black and white RGB red, green, blue filters put them together to generate a color rendering Maxwell did that guy was full on genius Boltzmann can take first character volatile grown to depression eventually hung himself when he was 62 years old because he got so depressed at one point in time depression is a terrible disease Maxwell-Holtzmann distribution pretty essential for thermodynamics and statistical mechanics S equals K log W how many people have seen that equation on the side of the license plate Professor Gavias is Prius that's his Prius with it K log W nobody in his car in this is his grave in Vienna S equals K log value make sure you're wondering that was his idea Willard Gibbs one of the first great American chemists this guy is an Austrian this guy is a Scotsman it's nice to have an American make an appearance we don't hear about any Americans in quantum mechanics it's all Germans the Brawley French guy Gibbs entered Yale when he was 15 years old stayed there got his PhD you're sorry got the first PhD in chemical engineering in the United States go ahead on here something like 1863 stayed there as an unsalary professor of mathematical physics just worked there this was not uncommon at that period of time if you hadn't published papers you could still get appointed as a professor or you had to work your butt off teach classes, do research but you got paid nothing this was not uncommon in the U.S. and Germany at this time but eventually he worked out of thermodynamics during this period of time when he was unpaid and Johns Hopkins offered him a $3,000 a year salary so then Yale countered with a $2,000 a year salary and he took the job stayed at Yale and his family was there he loved New Haven at that period of time if you've ever been to New Haven let's just say it was a nice town in those years he died in 1903 so this guy was one of the first great American chemists and he's buried in the famous Grove Street Cemetery if you're ever in New Haven, Connecticut Yale for some reason maybe you go to grad school there this is a beautiful cemetery in hundreds you can go in there, you can find these two in fact Grove Street Cemetery is one of the few cemeteries that has a great website you can put anybody's name in here just buried there it'll show you there are gravestones pretty cool okay why do we need to discuss thermodynamics we've got thermodynamics we can calculate things about bulk amounts of molecules so we can look up in any CRC handbook why do we need statistical mechanics what does that bring to the table here's a Wikipedia a piece of a Wikipedia page on ammonia standard enthalpy change of fusion standard enthalpy of formation heat capacity standard enthalpy change of formation standard molar entropy we can use these numbers and use them and that's what thermodynamics is all about is how to parameterize the physical behavior of substances the problem is is it makes no connection to the attributes of molecules in other words, I can look at this number here heat capacity but there's no way for me to calculate this number starting with the molecular properties, for example, methane CH4 I know what the structure of methane is I know what the bond distances are I know everything about that molecule measures spectroscopic properties but I can't calculate anything having to do with the thermodynamics of that molecule from thermodynamics thermodynamics doesn't give us the tools to do that statistical mechanics builds that bridge it allows us to go from the properties of ammonia to the bond angles, bond distances number of atoms, number of normal modes it allows us to calculate these numbers from these molecular attributes that's the key and I think you'll agree that's an amazingly important thing to be able to do we can take the molecule we can learn about its structure and then when we're done learning about the structure we can calculate the thermodynamic parameters from that that's really, really important this is one of the first papers where that was done for ammonia back in 1939 by these two guys and here's the equation that we're going to be familiarizing ourselves with later and the important thing in this equation is a parameter called Q this is something called the partition function it is this central construct statistical mechanics Q is the key if we can understand Q it's linked between molecules and their structure and thermodynamic variables we're going to be getting to that we want to really get to the point where we understand Q in some detail now I use to teach this stuff I use a really great book by a guy named Leonard Nash can you see how thin this book is it is a thing of beauty it is perfectly concise easy to understand and it explains this really esoteric subject in a clear, understandable way how many of you hope to have a career in science or engineering I hope by now that's a lot of you you appreciate the fact that you can't find all the information that you need on what you need it's not this some of it's wrong there's a few key books that you ought to have in your library and this is one of them particularly because it costs like $4 it's down here on my list of all time greatest hits buy all of these use the course don't buy any new books but these are all irreplaceable books that you will use throughout your life every time you open some subject you're reading something in science magazine that you don't understand in the area of biochemistry you open up this book right here it's in there you know what I'm talking about so this is one of these gems there's no replacement as far as I'm concerned for this book it is special in terms of how clear it makes this explanation of statistical mechanics okay now we're not going to finish this lecture but let me just tell you let's get started I think you guys recognize this is a Morse potential these are the bound vibrational states of this molecule here's the harmonic approximation to that potential I'm not telling you anything that you don't know everybody knows about vibrational spectroscopy in this room am I right now we can approximate this green guy here with this ladder right here right this is the B equals zero state that's the ground vibrational energy level one two three four okay and so we can talk now about the three dimensional array of molecules here this is my sharp form notation for a molecule let's just forget about the zero point energy for now there's an energy level there's another one they're evenly spaced in energy and there's three molecules here A, B, and C that's what that denotes okay now if this is such that three molecules has zero energy our energy level diagram looks like this if it has zero energy then all three of these guys have to be zero and we're going to be collecting now the zero point energy let's just call B equals zero to zero for energy in this system everyone agree that's the only molecular configuration that's going to add up to zero energy for molecules A, B, and C if there's no way for any of these other energy levels to be occupied otherwise the system will not have zero energy now let's consider the case where we've got three quanta of energy distributed over three molecules alright how can we do that? well we could put all three quanta into one molecule put it in A, put it in C put it in B that's one way to distribute these three quanta of energy to one molecule put all the energy into one molecule there's three ways to do that another way to do it would be to put two quanta of energy into one molecule one into another zero into the other and it turns out that there's one two, three, four, five six different ways to do that if you work it out and here they are that's two quanta into one one quanta into the other and zero into the other six different ways to do that and finally you could put one quanta in each of the three molecules and there's really only one way to do that I think you can see intuitively okay so there's one two, three, four, five, six, seven, eight, nine, ten ways to put three quanta of energy into three molecules everyone agree? so we're going to refer to each one of these these guys that guy, that guy these are microstates that's what we're going to call them there's one over there here's one down here alright there's ten of these guys ten microstates now there's ten microstates but there's only three configurations of microstates three configurations it's easy to see that these ten microstates exist let me just press my finger see this does this look confusing and cryptic? now it's easy to understand that's the number of quanta in v equals zero that's the number of molecules in v equals zero two two here, these are all the same configurations so that's two, that has to be two and that also has to be two that's the number of molecules in quantum state one zero zero zero quantum state two zero zero zero quantum state three one one one alright so this guy is two zero zero one, boom that's his configuration you with me? look at this guy one one one one one, so that's a one one one one that's a one right there and one one one one that's a one right there and then zero that guy describes the configuration of all of these okay, so we've got this shorthand notation that we can use for the configuration this guy is zero three zero zero boom okay okay now, we need to count the number of microstates associated with each configuration is there a formula that we can use in other words, are we going to have to go through the exercise of making these diagrams where we've got oligodra as a number of molecules that could be tedious we need a formula can we derive a formula that allows us to figure out something about these microstates starting with the first two quantum make-up we're going to okay, so let's look at this guy let's say I want to put a two quantum two uh I want to occupy b equals two I can put it in there or I can put it into b or I can put it into c in other words, there's three ways that I can put that first quantum that first b equals two into these three molecules we can go to molecules a, b or c then if I choose a, there's only two places left over where I can put that's one quantum of energy then the second one quantum either of the reading of two molecules and finally, zero is going to have to go right there into molecule b that's the last parcel of energy so this system has three quantum energy alright and the number of ways to generate this is three three different places to put that first quantum times two and then the second quantum times one, only one remaining place to put that last quantum three times two times one is three factorial equals six boom that correctly predicts the number of micro states in this configuration three factorial now let's try the same thought process with configuration one whether it's b equals three starting with the three quantum energy rc if I choose a here then the next two are going to be zero so the next two are going to be zeroes we can put the first zero here or here it's got to go remaining two so we start here we can put the two zeroes here we can start with b, we can put the two zeroes here the difference is that there are two verbally distinguishable ways to put these two guys in the molecule I can put three quantum into a and then I can put this guy into c and that guy into b or I can do it the other way around I can put b in first and then c after putting a three quantum energies into a alright so we have to adjust the number of quantum states here by a factor of two factorial it turns out because there are two distinguishable ways to insert these two guys or these two guys that one going first and that one going second or vice versa alright, when we make that adjustment we're going to have three factorial divided by two factorial or three possible microstates configuration three that's this guy where we have all three of these guys in quantum state one starting with the first finger making one of the three models the second we're going to be reading two third we're going to be reading three but there are three verbally distinguishable ways so it's three factorial divided by three factorial or one in boom there is only one state so this is our equation the number of microstates w that's n factorial states occupied in zero number of molecules that have zero one, number of that have one, number of that have two so take this random example apply those numbers in to our equation and you get 168 microstates for this guy I think you have to agree it would be messy to work that out now let's come back, we're going to do this again on Wednesday so if you didn't get any of that because I went fast, don't worry let's do it again