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Lecture 21. Bigger Atoms, Hund's Rules and the Aufbau Principle

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today's lecture in can 131 a is going to be about bigger
Adams not just to electrons hands rules which some rules to figure out the most stable state other anatomy when it can have different kinds of electron configurations and the alphabet or building up principle which is the basis for putting Adams on the periodic table on the Periodic Table of course is 1 of the great intellectual triumphs of chemistry is to take all these things that we find in nature and 1st figure out that they're all made up of these Adams and then figure out that the Adams follow patterns and then to figure out what the patterns mean and then to figure out everything else that has followed on and that's the kind of ineligible nature that science has to it once you find out something then that's something else follows from an analog of other stuff is discarded as completely wrong even tho it seemed to be possible before you found out whatever it is that you found out a
close shell which we said could be written as 1 of us are slated determinant in the last lecture can in which you've got an orbital orbitals and their occupied by 2 when electrons half of which you stand up and the other half a spin down otherwise it would satisfy the Pauli principle we can write downs the Hambletonian for a system like this what we have done well we have minus one-half times all these dull square all that is is the kinetic energy we know how to calculate that there is a formula for a it's got are and fly in it and unfortunately for bigger Adams other than helium and hydride and those guys that we've been doing we're going to have to get into the and sigh as well and you can imagine that the equations get more complicated quickly and that we've got to 1 of those because we've got to end electrons in an orbitals and therefore they've all got Connecticut Energy buzzing around we have to keep track of that energy so those terms are in the Hambletonian then we have the potential energy of this big positive charge z which depends on the atomic number of divided by the distance of each electrons From the positive charge where it when we write it like this where were kind of implicitly assuming that the nucleus is a point shot and that's not quite true because the nucleus has a finite volume and if you look very closely at spectral lines on there can be no slight on shifts and various things that have to do With the nuclear volume but for now those are very very very tiny things compared to In fact the accuracy with which we would be able to calculate things with the orbital approximation anyway so we'll ignore them and now we have this giant songs all of all the repulsive parts which every year is a double some from wanted to end and then and I equals J. plus 1 2 2 and just so we don't count things twice we could we could count them twice and divide by 2 and sometimes if you're writing a computer program that might be easier as long as you are actually calculating some terrible integral twice for no reason in which case and in that case you're wasting a lot of times calculated this way and that way which is the same in fact that the computer is not going to correct some Europe algorithm and then divided by 2 look at that and that's pretty easy to understand if I've got 5 electrons I got the repulsion between 1 and 2 1 3 1 and 4 1 5 2 and 3 other 1 account 1 again I don't want count to 1 2 because that doesn't count to and forward to invite and so on and that's all that double some meets this column all up put him in there and now we've got to figure out how we're going to solve this thing with the kinetic energy is the 1st sign the potential energy is the 2nd son and then the sum of all the mutual repulsion terms between the electrons as the 3rd turn the double
we can write about this a little bit needed their fleet I introduce instead of the capital H for the Hambletonian we introduce small wage and we with the electron J and we say Look that's just 1 minus 1 have dealt square J. take the derivative with respect to the coordinates of electron J X J Y G C J or RJD Theodore J. 5 Jr and then minus the over origin that which is the potential if we do that then we can figure the energy of the Adams as a sum of 3 distinct terms now I've out this giant integral which has a lot of integral over R 1 hour to depending how am I to to and then I have also put in and this funny notation the signal 1 the segment to about 2 d segment to when what is that mean well that the the Sigma part has to do with the Spanish we need to take into account the spin as well because all these 2 and electrons have spent and we have to integrate all over the spent part make sure that the spin functions are normalized and keep track of that as well as the spatial part and then we've got the wave function sigh Star which depends on all coordinates of all the electrons in principle the Hambletonian and then sign and that breaks up into 2 times as some of what I'm going to call I said Jay plus a double standard From 2 Michaels 1 and was 1 m of 2 times I J I ge capital J Iger minus capital K i j let's see what that what this means so let's look at
these 3 terms while the iPod is just the energy of each single electron ignore the other the part is the what we did when we take the integral of so I I R 1 seige too then the repulsive terms so I I R 1 side Jr to that we've seen before and then take a it is an integral that's a new 1 it's the inability so I star are 1 sigh J star are too so on I are too there the 1 so I J R 1 so that the indices the swap In the 2nd part the
other so that the guy is the single electron kinetic and potential energy j I J is the cool mineral that we've encountered before and Jerry is called the exchange integral k i j is a new player in the game it has no plan no analog in classical mechanics
and here's why have have rented out here on the bottom of slide 523 it has if we want to interpret things charge of clouds interacting and we can't do it because we've got so I start of R 1 which is the coordinator of the 1st electrons and that's going on to the site of art to which is the 2nd electron and likewise we've got side star Jay of art too then the report 1 over R 1 2 and then sigh J of R 1 but I think you can see why it's called the exchange and because he swapped the indices on the other side the With a larger Adams that the self-consistent field method stills will still works but there is this exchange contributions on which the Vladimir Fox saw and that's why it's called the hot tree Fok method and keep in mind but there is a kind of a shorthand here but by using 2 Jr and that is that 1 K I 10 k or J. if both the indices of the same then it doesn't matter that they were swapped so K 1 1 as J 1 1 and K 2 to J 2 2 and so on and that lets you write it in a tricky way with 2 minus the other 1 because when they're the same as you get the right answer and therefore here set up self-consistent field equation becomes this new equations rather than just the Hambletonian like we had before with the effective potential we've got this new player in the game and that they have which is a function of our 1 on Sunday the trial functions sigh of our 1 is equal to epsilon J psi Jr of 1 and this operator as our little Hambletonian age which as the kinetic and potential energy of the electron and then has this some of these terms which are the cool long 2 Jr to capital J have subject of our 1 and hatch and the reason we water right this is operators because and we want to operate on the way function with them we don't want to just leave things as integral girls than we've come already operated and done the integral so let's look at what these operators are the Coolum
operator when the Coolum operator With subscript J. operates on some way functions site a year returns site K times the integral of seige integrated out over the other coordinator and the exchange operators similar when the exchange operator operates on a function it returns the function and it integrates over its own index so if I have a case of J on site care I returned sidekick times the integral of seige With the repulsive turned on and off with the exchange term rather on site care and that then lets us set up all of our equations and in fact it's nice to set them up like these because you can set them up as matrices and then you can use and very very powerful linear algebra techniques to solve for the energies and to minimize on the energy as before however I and it just gets worse in fact these and the little energies epsilon Jr Our not if we summed them up they're not the energy of the atom so we have to be careful when we do this kind of thing that we keep track of the algebra appropriately we can't just blindly summed things up and expect to get the energy of the and we have to look at what it actually comes to and what the energy the atom actually comes to him and make adjustments to get the thing right it
turns out that so I don't want to solve the but I do want to point out that optimized orbitals are available online and you can go look the here's an example I've taken here on slide 526 of a screenshot From this time website that CCL . net which talks about what they call Ruth hot tree flock ground state atomic wave functions and what I've given here is is what they have for helium which is written the total energy is minus 2 . 8 6 1 6 etc. and I think you know now that that's in hard tree and they gave up some coefficients here they give 1 s and they give to columns they have 1 . 4 5 9 5 and 1 . 3 4 7 9 and they did 3 years and then they give to us and then they give another to ask question is what is this so the are the accepted Haji flocked orbitals the
question is then who was and Clemens reason was at the University of Chicago in the 1950's and that was around the time that full-fledged but future and slow computers were being developed for their work a number of just absolutely visionaries like Alan Turing and Jon Bon anointment and others who I were so good with math they worked out that you could make a machine that only used the images and that such a machine could simulate any other kind of machine which isn't very interesting idea of course now we we recognize that as a computer but before you then a computer it's not at all clear that such a thing could exist even and here's a quote them from Popular Mechanics in March 1949 and this is this is a cautionary tale on how hard it is to predict the future here's what they said while a calculator on the the act is equipped with 18 thousand vacuum tubes and weighs 30 tons computers in the future may have only 1 thousand 2 and where only 1 and a half times and just imagine what happens in the next 65 years Ruth and championed the use of Slater orbitals remember I have to maybe go back a couple of lectures but I said that we wanted but also were easy to integrate right so we want to know that tastes good and we're going to be doing a lot of orbitals and therefore we want to have a canned formula for the entire derivative and it just turns out for the radio parts it's much easier to use and the Slater orbitals even know they are orthogonal because they're just much easier to integrate and so in this database than when they refer to 1 s and so forth they are not referring to the hydrogen type orbitals they're referring to the Slater orbitals S & L and the I I gave you which have different radio parts than the hydrogen and when and using these and computers they can systematically improved the energy of multi electron Adams it's very very hard once you get things in the exponent to minimize if you just have a fixed but if you have a linear combination of things with 6 bonds that's OK that is on his yacht monkeying with the exponents but what you put Zeta up there anyone and minimize and find a minimum of these Co ,comma much of this and how much of that plus these guys can shift around like shifting sand dunes as well that it is much trickier and you need some numerical methods to actually find find the minimum so you may be able to calculate the undergoes analytically but he's still there need to find the minimum of of the energy which is as you saw when we just had a couple of Zetas there was a man as you can imagine what it gets like and so we don't try to do that than by writing out a giant formula staring at it you do it numerically it's much quicker you just calculated and then you minimize it by moving to a lower value the
orbitals then that you extract if you look at those columns are the Slater orbitals and therefore the atomic orbital and helium then sigh of are explicitly I've written it out here it's 1 . 3 4 7 9 0 0 times the Slater 1 as type bauble which is coincidentally is exactly the same as the hydrogen 1 with a value of Zadar in the exponent of 1 . 4 5 9 5 and then there's a small correction -minus so you can see these numbers tell you about how much of this other stuff is in there that's the major won 1 . 3 -minus .period old 1 6 1 3 times as 3 years that has a different value bar with a big value of Zeta 5 . 3 2 and then about a 10th of an ass to us with 2 . 6 and then minus about 1 . 2 7 of 8 with a 1 . 7 5 and this stand becomes the approximation Florida ah ah helium atoms and you can look up some of the other atoms on the website and that's very interesting reading would be interesting to most people of course because of this he don't know what anything means of course nothing's interesting book is an interesting nothing but if you know about what these things mean and you've tried to calculate them yourself or is puzzled about what these orbitals actually look like In these complicated Adams and then it is interesting because now you've got these functions and with mathematical or some other programs you can plop them you can look at them you can square the newcomer contours of and you can learn an awful lot the energy that we get out of this function for helium with these 4 terms is pretty good it's limited more by the orbital approximation the fact that we are not allowing electron correlation in this approach then it is by the number and choices of the functions so we can't necessarily improve the energy by just adding more and more Slater functions because we've made us we've made a fatal flaw in the beginning in that we've averaged out all the other electrons well that's because we're chemists and we like to think in terms of orbitals all just note that the simple to symmetric some but I initially suggested earlier but had 1 electron bound and the other 1 lose plus 1 electron the other electron bounded 1 loose but that did better even for helium than this much more complicated looking thing but that's not the product of 1 electron orbitals and so that's that's a different kind of thing and I would not necessarily be able to write down something so clever for a barrier for example where is this will be a systematic way to get something reasonable for them
now if every time we wanted to figure out what kind of configuration of UN Adams out of all possible once there might be is the most stable if we had actually go through and solve all these equations it would be pretty slow going that's for sure but luckily we do not because there some rules and like all rules they're made to be broken away but most of the time they're quite good especially for a ground state Adams they're quite good and I don't even know of any ground state and the doesn't follow these rules which are called Collins rules and they tell us of which of the possibilities were the electrons could be in which orbitals which was the lowest energy that's very important to know what the law ground stated the Adams is going to be before the talk orbitals we wanna know the configuration of the ad for example honda's rules predicts that if we have a nitrogen element of acting by itself that the 3 key electrons are going to be distributed 1 for each of the 2 P orbitals one's going to be PX I was going to be in PY or ones going and was going to be in PC or we could think of was going to be an M sub belt plus 1 0 on minus 1 same thing in the end ,comma but they're going to be in these 3 orbitals they're not going to be jammed together with 2 and 1 orbital and then 1 in the other or some other combinations and furthermore Huns rules is going to predict the following that if these 3 electrons are in the sleepy orbitals for nitrogen but their bomb magnets are all going to be a lot the organ of the the stand up or spend down if we don't have an external magnetic field there is no difference but there is a difference between having them all aligned and then and then having 1 difference then the others that could be different and Huns rules predicts that the electron bar magnets will all line each other when they're unpaired electrons let's go through these rules so here
Huns rules the 3 rules and they're meant to be applied in order and only in the case that the rule doesn't adjudicate what happens to you go to the next rule the 1st rule is the state with the largest value of the which is the total spin multiplicity to ask plus 1 remember we've got as is 1 one-half and we add them up and we can add them up couple them together to get the the overall spending and the multiplicity is to ask plus 1 those of the number of US sub states that you can have for a certain value of s just like you could have 3 substitutes for L equals 1 and a half only 1 sub-state for L equals 0 then the state with the highest multiplicity or the biggest value of vessel is the most stable and stability decreases with decreasing 5 4 on her electrons in a deep in and 4 d orbitals this will be although amount will be the most stable and to open 2 down will be worse than 3 up and wonder for example if you have to possibilities With the same multiplicity the same value the guests then the state with the largest value of the orbital angular momentum Big L so bold the spend 1st aligned the bar magnets then get I'm going around together is going to be the most stable and finally if you have states that have the same value and the best then if this if the sub shell is less than half full for example if you have 1 or 2 electrons in in in the P shell then the state with the smallest value of J is the most stable and if the sub shows more than half filled than the state with the largest value of chip is the most at 1st these rules seem to be completely arbitrary but we can give some rationale for them and that makes some physical sense of course you don't invent the rules before you know the answer where we get the rules from looking at how things turn out right so Honda knew the answer before proposing the rules the
other rules apply to excited state Adams too but not quite as well but they do for example allow us to predict the ordering of terms in atomic spectroscopy we have energy levels there the best way to keep track of them is with the term why because cut to best plus 1 we wanna know that to know where the energy is it's got we wanna know that to know what the energy is a Schedule and that's the final arbiter and so if we've got the term symbol for the state we know what we've got and that Wikinews Sun's rules to predict that 2 P 3 halves for example is higher in energy to 1 at which we saw with sodium giving them of 589 Douglas but what's the physical basis if there is any for these rules and we have to be a little bit careful because you might be rationalizing something that seems reasonable but I unless you've done a calculation of some time to show that it is true you have to be a bit careful well we can sort of understand why the total spinach should be maximized but let's look at the case of 2 spends in something like helium now the 2 stations cannot be parallel if they're in the same and helium so I have to be an excited state but less but 1 electron in an excited orbitals so that it can have the same spent state and then let's compare this 1 to that 1 and let's see if there's any argument that we could make I'm so let's look at 1 as to West state for example and what's the reason why parallel spends could be lower in this state why you might
argue that well maybe it's a magnetic energy so the bar magnets lining up because of the 3rd their Barmak that might be an argument that's not the argument that usually given the argument that usually given is that if the standard part is symmetric that means because of the Polly principle but the space part is antisymmetric because of these 2 1 swap another change sign then that means the space part has to be antisymmetric and I and vice-versa therefore I am we could have 2 combinations here we can plus and miners and 1 of them is 1 S R 1 2 S R 2 plus 2 S R 1 1 S R 2 and the other 1 is minus the question is do the spatial parts have any difference and the answer is suppose a spatial parts antisymmetric so it's 1 S 1 to Assad to minors 2 S R 1 1 start to what happens to that functions it R 1 and R 2 become the same what is it mean 1 R 1 and R to become the same it means the electrons are getting very close together well sorta like magic 1 R 1 equals are too sigh vanishes that means that this antisymmetric the spatial wave function automatically causes the electrons to avoid each other in some sense because the way because of its very structure it doesn't allow the electrons to be at the same point in space without banishing them memories of probability of that is very low and that means that the electron electron repulsion that could occur if they got close like that is gone if they're antisymmetric there's no such thing restriction and they couldn't principal get quite close and we would expect them to have a big electrostatic repulsion that's the conventional argument but that may or may not be true however there there have been some more detailed calculations which indicates that there may be other effects like that penetration and shielding that might be it's players in the game here but for now I will accept that at least this is this is kind the stock argument is this antisymmetric spatial part and therefore the electrons pair only if they have if they have to be in the same orbital they pay if they do not have to be in the same orbital than their book either both affable style
what about rule to well this is even more Wally in my opinion and quite qualitative and the idea is that if the value of big Ellis high that means the value of little else for the electrons is all adding up we can in some sense imagine then that the electrons removing the same way around so if they're moving in the same way around the ad then they're avoiding each other if they're moving in the opposite way so that El-Asira or a lower value of the summer going 1 way summer gone the other way so that the total is not the maximum then they can crack they can crash into each other and get closer and that means that the energy could be higher on average because the crashes push up the potential energy and therefore we want a high values L To avoid these crashes and push up the energy now if you added I don't think you wanna believe that too literally but anyway it's a it's a qualitative argument that gives you a feeling for wider repulsive forces may be may be lowered the justification for Rule 3 it is even more subtle and that harks back to remember what we talked about was sodium while I was there the splitting because we argued that we haven't and unpaired electron In the orbital up there and it's In the gut non-zero elephants in a peace deal that means that in some senses going around something imagine the nucleus from the perspective of the electron going around the other way and that looked like a current loop and that created a magnetic field that acted on the magnetic moment of the electron and the electron could even be aligned with or against the magnetic field and we call that the spin orbit coupling interaction that we introduced won't talked about atomic spectroscopy if we look at the state with the lowest value of Jr it's lowered by the spin the coupling and therefore for everything else is equal then we look for the small magnetic effect the spin-off the couplings if the load shall is less than half full it's going to be lowered if the shell is more than half full and I remember when we were working out the terms I said if you can do flaring you don't put 5 p electrons and then drive yourself mad you put in 1 hole in and get the configurations for 1 whole but since you're putting in a hole that reverses the the algebra on Jan and so when the shells more than half fill you work with holes and then the roles were reversed and therefore you should go with the highest value of chip rather than the lowest value too on the way to do it always is look at the term symbol that the configuration of electrons gives rise to certain terms the terms are what you want to know because that the term symbol is going to tell you what ground state of the you've actually got let
stand predicts stability here on on Prop practice problems 27 let's consider an excited state beryllium atoms 1 S to 2 S 1 3 S 1 you see how I go back to the orbitals right away don't even consider actually the real thing and the across state carbon 1 S 2 2 S 2 2 P 2 analysts predict the most stable state for each of these Adam well With 2 s electrons L must be 0 and that's :colon as state but that's not the best of the spin that's the essence the state of L is equal to 0 so it's big and there are 2 possibilities for that state there's the triplet state Triplett S 1 because if 2 hours plus 1 has 3 than jails to be 1 and then there is the same with state 1 S 0 or single address 0 the term with the highest multiplicity Is the triplet term triplet as 1 and so that 1 is the most stable that's what we predicted with earlier and that physically means that the electron are aligned where is
carbon we have to to figure out the terms that can arise with the Peace square configuration and the terms that can arise are 1 at a trip on a single s not Triplett P not Triple P 1 Triplett P-2 and security now we look at all these well according to Hands rule number 1 the triplet states are lower in energy well it has to be 1 of the Triple states the value of L is the same in all of them because they're all P we don't have to worry about different kinds of we don't have a triple a D or a triplet ass to worry about and so therefore we have to go all the way To the 3rd rule and the shelves lesson have failed because there's too the electrons and there can be 6 p electrons in In the show and therefore that got the the most stable configuration of the the most stable term Triplett P 0 beat because that has the lowest value of J 100 knew the answers before he proposed the rules and the rules are generalizations they work best to predict the ground state and not not for necessarily for excited states we can
build up then the periodic table by adding electrons to orbitals which we very root loosely associated with the solutions for the hydrogen atoms we sort of think of them as having similar shapes but really what we ought to do is go website and look at the shapes at least for the I'm self-consistent field orbitals because then we'd have a much better feel and then we see that they change as the goes so 1 has becomes difference and that while 1 has become much different but some of them do become different as you add more electrons and get more repulsion the real situation of course for any of these multi electron Adams is much more complex than this but at least this is a good start the periodic table itself can help us decide which orbital were gonna fill next because of the problem is the ordering gets jumbled by all the electron electron repulsion we can't solve for the hydrogen atom where there's no electron electron repulsion and then expect that all our solutions are going to be the same in the same relative even ordering of energies 1 we've got 18 electrons orbiting around and all these repulsive terms and all these effective charge distributions what we have to do is is go through and see what happens and the periodic tables the best way to do that because the Periodic Table by looking at the atomic number and where it comes out you know exactly which orbital got failed because things that have the same outer electron configuration have very similar properties and that's why we put them into columns and that's why we recognize that there were patterns in the 1st place the most dominant
effect as you go up the periodic table is that s electrons are lower energy than P or D P is lower than the arrest and so on the US electrons as we saw when we did those radial distribution functions can be found very near the nucleus if you have a big Adam like seeing honors cesium or something like that than those electrons way out there those 5 essence 6 0 s electrons can spend some time quite near the nucleus and then they see that it is not at all like a hydrogen atom where you have the charge and all the other electrons canceling about so to speak and just 1 charge it's much different than that the U.S. can sample that the P has no there so it cannot sample it very much but the DEA has a crisscross at least there so the sampling is very small and efforts even more notes at the nuclear and therefore it hardly ever sees the nucleus why should it isn't an electron and so it has a high angular momentum and it's out there and orbiting around doesn't know much about the nucleus it's far away like Pluto for example then the ground state of the potassium atoms is closed shell are gone he put the closure of the manner of a rare gas in square brackets to indicate well that's those 18 electrons take care of and then I'm for this 1 you know Oregon is about 3 P 6 instead of going 3 D 1 you go for this 1 we know that because we know that potassium is under sodium on the periodic table which is under lithium and follows a S 1 and they have very similar chemistry very similar properties soft silvery Altschuler reactive metals and they didn't have anything To deal with something like boron on over or which being 3 P 1 but Skandia mn has totally different chemistry which has 381 the
order the occupation of the orders of the orbital stand in these multi electron systems as we got Periodic table keep in mind this is as we filled if we take a light Adam and we look high up in its energy and is 5 above 4 D or not for a lighter Adam those energy levels to unoccupied on the ordering may be different but this is the ordering if organist as we go 1 as obvious to us to 3 S 3 P 1st jumble for 3 then for then inside 6 5 finally 6 and so we get the success we get to cesium before we get too for that but do that far but heart and that's it really has to do not with the penetration shielding and the electron electron repulsion the systems that have a lot of that and they're just they're just different and we have to have to look at them differently in hydrogen we don't have any of these issues foreign Affairs very very very similar energy to Forest there's always small sense but basically they're degenerate and they're both well below successes no confusing that but by the time you get to cesium where you actually want feel success is below 4 now there's a
cautionary note the order of the orbitals is not always predictable without a detailed calculations and sometimes even the idea that you know which orbitals are occupied is a little bit slot remember this is quantum mechanics so if there is a choice the Adams picked both choices at once and you have to always be prepared so that if you have nearby energy level With the same term symbol as 1 of your looking at then the use and can enter actor OK like neighbors that both play loud music they don't like each other and they tend to move apart and the same thing happens you have to have some of the same kind of term symbol you have a different kind of terms symbol that it's like you're on a shift work and I'm playing loud music at nite but but Europe work and so you don't care and then I'm working in the day when you're doing it so we don't interact at all but there are some systems for example and this was worked out in the 30's even that they in magnesium on the excited state 3 3 D but the trip would do higher In energy then the single at the and that violates hums rule number 1 that's for an excited state Adam and I said that it works best for ground state but nevertheless is kind of interesting to say Well why why did that fall apart from magnesium it's not like it's really heavy atoms or something where you could argue that there is some other effect may be coming in and the reason why it happens is that there's another of another state nearby that's too 3 P electrons rather than 3 S 3 D it's 2 3 please and alone also gives rise to a single at the state and so Peronists and with the state's here the triplet D was supposed to be lower these guys hate each other so they pull apart and this sends being pushed lower so as usual there's some some subtle effects that go on and sometimes it can be a little bit harder to predict every little detail that's what makes the periodic table sort of interesting as the they're all these countervailing trends survived predicting which politicians gonna vote on which they and they're going to get elected again and so on and so forth same thing here there's repulsion there's there's there's that and then there are these fine effect OK this slight
I've called Vision no not atomic fission as a nuclear power but I suppose we began no we do a metal experiment we do a thought experiment we spent a lot of time on helium and was state helium unless break the nucleus of apart slowly In the system Majid so we've got to electrons that and now we're going to break this alpha particle this helium nucleus apart into 2 due Deuteronomy 1 proton and 1 neutron each of the neutron we don't care about changes that reduced but the question is what would happen if we did that experiment and With the resulting things but has to positive charges and 2 electrons we know helium stable but suppose we "quotation mark apart what it wouldn't be energetically stable compared to 2 do the honors deuterium atoms which is just a heavy hydrogen atoms it's just like a hydrogen atom with an extra neutron in in the nucleus which as far as we're concerned just changes the reduced mass and nothing else In other words if we imagine mentally columnists helium nucleus apart I would it hold together even though that things aren't held together by the strong force in other words with the electrons hold it together or would there be chemical bonds between these 2 positively charged particles while clearly
won the 2 nuclear fire close but they're not in contact once they're in contact their held together by the strong force which we don't write a potential for and we don't ever treat excitation in the nucleus and explicitly but let's just say that 1 there close enough there how like super glue so you know there to positively charged particles they still hold together and they're very stable and they're not going to come apart but once we mentally pull them apart so they don't the strong force it's like a big wrestler but he's got a limited reach if he can grab ahold of you look out you're never going to get away but if he can't reach you then you're saying and once the particles get far enough apart there is no strong force but there certainly is electrostatic repulsion and they hate each other because they both have positive charges and so they push apart like crazy and if we mentally pull them way up or then they have nothing to do with each other than the to add the wave functions of the electrons have died off they don't even know the other ones there so that was just have the same manages to Adams that's not going to be more stable now but so initially is very bad if they're too close and then something happens and then it's 0 of their way apart the question is could there be a sweet spot where the nuclei of far apart then they aren't repelling each other in and destroying just moving apart but the electrons can overlap and share an orbital with each other and then create a stable configuration and if so what does that well look H to a stable hydrogen is probably going to be the economy of the future for our transportation 1 day so we know for sure H 2 does exist and D 2 heavy hydrogen would exist and even age class H 2 plus exists it's very important in astrophysics for example to look out and see that there is a 2 plus way out there on so we know they exist what we're gonna find out in the next series of lectures there's the exist
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Enhancer

Metadaten

Formale Metadaten

Titel Lecture 21. Bigger Atoms, Hund's Rules and the Aufbau Principle
Alternativer Titel Lecture 21. Quantum Principles: Bigger Atoms, Hund's Rules and the Aufbau Principle
Serientitel Chemistry 131A: Quantum Principles
Teil 21
Anzahl der Teile 28
Autor Shaka, Athan J.
Lizenz CC-Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben.
DOI 10.5446/18900
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2014
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Chemie
Abstract UCI Chem 131A Quantum Principles (Winter 2014) Instructor: A.J. Shaka, Ph.D Description: This course provides an introduction to quantum mechanics and principles of quantum chemistry with applications to nuclear motions and the electronic structure of the hydrogen atom. It also examines the Schrödinger equation and study how it describes the behavior of very light particles, the quantum description of rotating and vibrating molecules is compared to the classical description, and the quantum description of the electronic structure of atoms is studied. Index of Topics: 0:01:22 Closed Shell Atoms 0:05:12 The Energy of an Atom 0:08:47 Fock's Contribution 0:13:40 Optimzed Orbitals are Online 0:22:17 The Most Stable Atom 0:24:45 Hund's Rules 0:36:08 Predicting Stability 0:39:02 The Aufbau Principle 0:43:29 The Periodic Table 0:48:17 "Fission!" 0:50:09 Chemical Bonds

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