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Lecture 04. Wavelengths


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still I cast we talked about how light can be considered a particle and the experience that kind of show us a lot of that that really kind as it humanizes both believe particle duality but there's there's other aspects that shows as much more of a wave than just the photoelectric effect really
does the photoelectric effect is a great job of showing both that once this stuff that were in hot weather data is a little bit more of a job of showing it as a wave in in really distinct ways that we could actually see if we did so In order to stop this experiment effectively I need to give a little bit more background on what we've and is specifically what we've interference it's so we interference as something that you can see and you can see it in ways that upon Dora wherever if you drop a rock into a pond you make waves radiating agency the rippling effect going around and then if you dropped to rocks into the Laker upon something with relatively still water you can see this is weird interference effects in the same thing if you're out and jet skis in the and on a relatively calm day and you can watch the 2 it's kind of each other this is wave interference so this is the kind you can see it in you can see that these interesting patterns that come up that are just on this oranges simple notices positions of the 2 so How is look like when you when you do superimpose the 2 on each other so there's 2 different types of interferences there is constructive and destructive and if you have a whale of a very particular wavelengths of and they're interfering with each other and cooperate on top of each other or exactly you know like profit on each other and if you overlap the red-hot each other they add together if you were to happen exactly opposite each other the best attacking each other now cost you could also do some sort of you know slight also on to the isn't you from waste so I think back to year algebra classes of where it whenever you had those then you may have been forced to go through and you know with these had little .period photograph had added together and if you added the Swede together you had at this point in this point so this is 1 in this was to be add them together to be 3 well this is 0 . 0 and so it adds together the 0 this is a negative 1 a negative to would advocated negative 3 same thing over here is now here only that you have a negative 1 in lots of plus 2 with giving really arbitrary units of so were added negative 1 applies to all that gives you about a plus 1 and so would get back in the woods attacking each of the men enforceable Susan painstaking detail your other professors could do that year but didn't kind understand how it works he decided OK well if there would happen each other they can act if the office each other they're going to subtract and that these are called constructive in destructive interference no this is an important understand when we look at this mess experiment which is called the double Split experiment because patterns of light and patterns of light argument really bright in some places in really dim and others and that's because you get constitute interference making it really bright in destructive interference making a very and so that's how this is going to work on his next experiment now the best way to show you this mess experiment is to have a little video so the
studio does a great job if you want as much as you want and to so I'm going to go through and explain it out he does he does the same thing online with words and such so won't wait for the double Split experiment works is you have this point and you have a place where you can let light through and so this is sort of showing you how the light would go through and light expand out like a wave OK we're start over now the
the only thing that you're going to be able to do is you can make in the exact same thing on the next 1 over so instead of just having 1 point source you can add to point source so you have 1 point source here and that's going to let light in a certain amount now you put another light source in another place or just a hole in 1 of the easiest ways to do this is to actually assimilate source behind the cardboard aboard a reverence for slapped a hole in it now if you put this together what happens is that they interact in you get these interference patterns and when you come over here where ever the light interferes in a constructive way you're gonna get really bright shiny parts wherever it interferes and destructive way you're not you need a very and you can actually see the system of people's standard on freshman physics lab if you at the end of physics and it's really getting a looks exactly like this so this is actually a picture of 1 from 1 of these experiments that was done in it really looks almost identical I using the rightly theirs and things like that you can actually do this at home if In in a slightly different matter if you take a piece of cardboard and canal and become a little slack in the 2 pieces of hair and take down the shine flashlights on you can get the same sort of situation where you can get little interference patterns I used to do in class that honestly to odyssey in big lecture hall so I quit so we'll go home and do that it's it's fun used it to pieces of hair clip it out onto a piece of cardboard and takeover of laser pointer in China and can see interference patterns still now also
get us a little bit more
some laid out so here is the experiment on dips she had a it is some something else like blocking hearing he cut 1 little hole in it to make sure that the light was coherent and then he shined a light over here so that it came through here at which point it spread out like that now what that has allowed him to have to light sources as well as what they showed in the other video but have a common thread exactly the same way and then at this point now he had this double splat this double slit and it comes through here it comes through and now you have the exact same wave patterns for each slipped by now because they're close to each other they're going to be interacting with each other no if you drop out if you if you then have something over here that protects set of a human eye works just fine and the fact that you could also actually detected with you know something a little bit clear you can see these patterns so where these interfere completely you get this really bright peak and then you get this sort of peaks that get more at a less intense as you go through but you still get these interference patterns so this is how young double slick exterior despite experiment work so again now that we kind of looked at both of these experiments we scene how they have properties involved they cannot play like can act like both the wave and particle in it doesn't exacting fines Callaway particle duality we saw that with the photoelectric effect you actually did see a little bit about fragrance but you definitely solid sort particle like other ways that worked where in the doubles blood experiment will certainly amplified the with like effect you can look at that and say OK it's not acting like a wave after you've seen that in the interference patterns and you can relate that to real life receivables upon you see those interact and is very much the same idea so no this is very true small particles sold out of the way the last time that I have looked they were able to measure the wave-like properties and things up to 16 10 in India which is actually pretty big and hit if you think about it from a thousand grams per mole and you think about so itself so when we say that this is true very small matter that that's about the size that it goes up to now that's just because that's exactly what we can measure so this kind bridges into the idea of World War I was kind of everything that away particle duality in the see the small things but why would an electron have waived particle duality but I don't know why can't I act like a wave that's what the released in in not quite so I'm colloquial terms so she talked with particle duality from light in various inside well that's true of matter too and that's true of larger matter to some extent but will see why doesn't quite work so I would always has as well wavelength is equal to each Planck's constant over pay the so depending on how much visiting I'm merely not know that is that's momentum otherwise known as end-times times the is a finances into trouble again because most of the equation editors like to make it the kind of like that which looks too much like a new but that is indeed what is velocity so he is about equal to Andy we're asking the to send 1 more time that it's 0 quite important to make sure you notice of India also this this is more just sort of a general problems problem-solving saying that you're going to run into a lot of your allotted time is going to be given kinetic energy and asked me if I in ossified literally wave like well you can do that by finding velocity from the kinetic energy and plugging them into here so this takes the way particle duality and says OK well that's great we have from light why Canada matter had to come in and give us an equation that we can actually use for so quick reminder there on your equation for kinetic best way to go through reducing the burly waving is to do some problems on it so far the first one I say let's find the Brawley wavelength of elect so something small on it and see what I give you the kinetic energy system giving the kinetic energy we can just directly fill in the the burly wavelength because of the Bali with it is a over and the so we need to find the Soeharto if I did well we know that Connecticut Energy if you called one-half and the square elect someone we go through we do this we sulfur velocity just 2 times the kinetic energy this month divided by the Mass take the square root so we can fill in from the problem now we get to the mass media will I don't know the massive electron local users of homework had problems you can look it up on an exam in that would just be given to you on the table so we get this and we get a velocity now can a careful of here was the man doesn't come up here or only other example actually will continue homework you Conoco about exams and I will massive election and or proton or neutron or anything like that I'm going to have to give you that if I ask you for the wavelength of nitrogen atoms do I have to give the last while no it's on the periodic table right you have so if you you think about maintenance or are you just going to go through and still in the massive it's an EU Justin Adam where going go fell in 14 well dancing grams per mole and if you look at this unity we have Jules and we need to get meters per 2nd so we remember what a jewel is equal to Ray Jewel Millside sidebar here enjoys equal to kilograms meters squared or 2nd squared so we can have something that just we can programs for so you have to go through in you would have to convert anything from the periodic table into kilograms CEO make issued a note that and you it's because it comes up in people tend to mess up that if you're looking for an on the role wavelength and how you're going to be tempted to film that grants from all from the periodic table you can't do that you have to convert 2 kilograms and not just killing 11 years meaning divide by Thousand year Reich kilograms per mole isn't what you're looking for here looking for a kg per adult so you have to convert from grams per mole kg per atom or molecule depending on which are so make sure you make noted that you know biomass of continuing on them so now we have a velocity and we can fill that in notice is searching by units for planes constant around it's just so I can watch other units Council when you get and you end but that variances now I did a few people who ask well can I just take this equation and filet into here and find it all at once that is perfectly fine go for it probably is how I would do it harridan problem but I think probably the presented here so prefer this way where you do it out separately so whichever way you prefer you can do it but it doesn't really make too much difference in the way so if you prefer to sell this equation into here you are welcome to it said that the equation for an electron now if we move on a little bit that's real small right militants mounted can definitely still OK it's this pretty tiny considering you know it's electron sold ,comma particle all but what's to say we can't do this where is not so must do it must calculate liberally with links for something
bigger something we can see in real life because I'm telling you that electron-hole whaling which by that same token have wailing I should have a whaling my water bottles to have a way of life so why don't we see that why can't we why can't we look at that and see something there while the easiest way to figure out why we can say it is told in a calculator so we'll do that so I give you the massive baseball and I give you an approximate meters per 2nd obviously this is gonna change alive I for a baseball or if on something this pitcher throws a baseball so the same rules apply for any felony here again just for the sake of watching the units going to just fill in on May thinks Constantine a slightly different way so we got there we do the exact same thing we did before and a little easier this time because they give you all the values our right and we get back Societe who face what does have a way now why don't we see well you know what a baseball looks like grant you know a decent-sized you can see that size thing now look at wavelengths where to negative 34 senators that's not something we can see that's not something that we would calculate it's not something that we would you know we will look back in so short meaning by this definition macroscopic matter does have a wavelength but it's so tiny that it doesn't matter and if we look at this equation again this is the masses enumerated the editing the denominator so the bigger the the mass gets what's going to happen to the wavelengths this gets bigger and bigger and bigger it makes this whole thing smaller and smaller and smaller so that they can something gets smaller than its wavelength gets so you're making something larger you're making his wavelength smaller in proportionally in the just not mattering anymore when you had electron we had a wavelength of this just a very very tiny now we have a we link the vests for something as relatively large and so the whaling is just starting out so that's what I meant when I said the largest thing was that I had has sort of show that would enable the measure way particle duality in it's that that point where are measurements are really good enough and it doesn't really make any difference anymore something like an electronic neutron indefinitely matters for limited baseball not so much so now we had to move on to something ,comma Heisenberg Uncertainty Principle so what kind immigrants and she principles set eyes on 1 level is that it's impossible to simultaneously Knowles both the momentum in the position so would it with absolute certainty so it puts a limit on how well we were able to know that it says that if you take the uncertainty in act knows that's not act since certainty and acts the part that we don't know about where the position so annoying rolling crude terms you maybe if I take a gas and I say you know I'm still reading meters away from that door I'm not very good with destinations so my help act might be meter Media and measure it now and I say Well you know my uncertainty and measure it is really close and I'm actually 3 . 5 meters away they can say OK well I'm I'm pretty sure that within plus or minus 4 centimeters because my measuring isn't very good use cheap measuring now media measure in a stand-alone places calipers and really careful and I know it within a millimeter worry that's what uncertainty would be it's how well you know where something it's this comes into play much more a is this is really more popular with small things the electrons protons and aspect that's really want I think about momentum is going to be the same way now assuming that keeping in mind the momentum and mass times velocity and a lot of times you'll just see this as an the because you assume you know what the mass of the particle is used to make him look that up in a way that and that's pretty perfect so what happens if you're momentum in uncertainty decreases let's see you using ruling really good equipment because dealers and this is greater than or equal to meaning that it's got be greater than that that's the lower limit but it might be more and maybe that year uncertainty involved are huge because you are using married equipment but according to this even the best equipment in the world which arguably there may be some people who who had published things saying that they may have broken will will see how that works on but according to this you can and if this happens so let's say best instruments you right at that Heisenberg Uncertainty Principle limit if you're momentum uncertainty decreases well what it means for your position well it's insane junior momentum decreases if you measure that better and better and better that means that you're uncertainty in Europe position will increase so every time you move from 1 you lose the other so you can prove that you can know where that particles that with a little bit more certainty but you're not going to know its momentum very well you can get better and better better knowing its momentum but not notes position very well so what happens here uncertainty and position it decreases while the new position the other 1 is going to increase so always is back and forth you decrease 1 you increase the other new decrees that when you increase the other up to this problem is based off the uncommonly toehold in really bad chemistry joke so that the the joke goes that Heisenberg is driving along and he's pulled lower by a police officer in the police officer comes up to him and he says the new Miss indeed you know how fast you're going in looks the police officers as not they'll exactly where I am so the joke there being that you only know 1 or the other so I want to try to prove whether or not we can use the system beyond driving to work arguably probably too pullover cannot argue with the cop on the the the thing that while he knows where I am so can know how fast I was going to obviously there there there's enough some sort of quantum system here that he can't write you take it and I don't think I would suggest this argument anyway the let's see if it's actually valid let's see the holdup he so we're starting from this equation on the slide which is to say that fact times Delta p palestinian greater then a for the Eagles so that now cost it's gotten equal to that so let's rewrite is a little bit differently so that we have velocity that 1 was summarized with my car and I know exactly how much waste since this is a little about the number of calculations OK so I tell
you that I feel I think move officer should be Elementary ,comma is by about half a meter and I know the math McCarty 13 100 kilograms so we need to sell Delta so we can see whether I can argue myself I take it so so must 1st offer Delta the and then fill in everything that we need so if we do this we adults I don't think he has to be less than are greater too according to the quantum mechanics the OK so now can argues the cooperation to get no right is made all the here's tiny so Correa quantum mechanics the she knows where and how fast was going pines 10 negative 38 meters for a 2nd I promise you I was speeding by more than that so this is a quantum mechanics 1 it is an issue here on some this year silly example but it does show how you would go over and do it for any other particles you would just have a different so same rules apply here Hassani kg right so grams per mole is going to cut it needed change kilograms per annum of if I give you the amassing GM you need to be treated as 2 kilograms so same rules apply here for I'm aces subatomic particle but it's in a lot more fun to try to calculate the sweat so this is not a good way to get out of the ticket when you get pulled over even if you're payment if you're particular police officer does have a strong background in quantum mechanics but I it's annexing Oregon and talk about that and is it seems to me that refreshment favorite topic in the streets so wave functions energy levels and particle in box so this certain sets up this next big section of this chapter we started talk all the history and the basics to get us to the point where we can start building up a molecule we can start building up a hydrogen atom and move on to multiply electrons as parliament convened the diatonic and at that point will kind of just give some steps and just have molecules so what we function is this into represented by the side which is another Greek letter and it's described the movement of a particle compared so it just a symbol for mathematical functions so I will show you those functions in a little bit whenever Arlington have to work with them I'm going to give you the solutions economic the picture that they'd they'd they pull out of that you need to know what general way in which these work that I need to know that it described the movement of a particle you need to know that it is a function that you can actually grass that they they've solved these functions and making people demand of impeded thinking back then and that's what gives us a word different particles are going to have different wave functions solar particle and a 1 as a and 1 as orbital isn't gonna have the same way function as a particle to us were lost to keyword word oral doses now we have something called squared or the probability density now but this is this is going to give us the probability of finding a particle in a particular region so if we say we want friend particles from here to here what is the probability that it's going to be there and that's what the probability density what we can gain from it now given the end mind if we function or side is a mathematical function what square will set functions square so that's why it's called sigh squared so technically the probability density is the probability of finding a particle divided by the volume of Celestia sort a technical thing make the numbers work that I wanted ad here but we don't worry about that too much so let's go through in and talk this out with like a super super simple example of not something I would actually be a wave function of play it gives us a little bit more of a clear way in which held the bigger functions the show you work so this is more understanding purposes and being able to replicate it is sold what they can sample were size and number I do this to make it simple right helping a simpler function in a number so we're gonna say that sciences . 4 4 7 years interest so a yearbook walks you through this sort idea to but I wanted to go over it again so we grasp this function . 4 4 centimeters inverse we did so what's midsize square going the walls . 4 4 times . 4 4 to we I mean really simple examples these wave functions as something would actually calculate but it gets the point across so this would describe the movement of the particle this would describe the the probability of finding any particular place so the wave function and that this a sort of nomenclature however suggests the wave function is equal to . 4 4 centimeters killed in their interest the probability density is equal to . 2 centimeters so if I wanted to know what is the probability of a particle being within 0 3 centimeters Q I say 1 is the probability of me finding this particular particle between 0 and 3 centimetres cube lowered between here and the 3 centimeters out from the circle while the probability of that you just multiply this together at it's effectively taking an integral but it's a simple integral because of the box is just there is 3 times by the 2 so are Y axis times by the x axis of the box and that would give us a probability density no this is a very simple example with a very simple function when we do this with bigger functions were going to get much more complicated probability densities and of different shapes and things of that sort but this is how they do it they just do it with a computer instead of by hand so let's look at some things about that so some questions for you size of function so at any point can we determine its fine meaning positive A-minus does have to houses that have negative candy bowl it was just a function right so shares function accidental last 1 was always have that we agree that was sort of a simple example the function it's just a function so it can rebuild it doesn't matter the find doesn't matter so if I show you a graph like the 1 in the other slide like that and I say Well which 1 the wave function you would know that it's the 1 can negative this 1 now In the modify square as they wall the square that function right it's just taken function
squaring so if you square something can never be negative to that were in the realm of real numbers will now that's not always the path so if that always found if I were to give you a grand like this 1 and I say I have both the probability and the probable error have the wave function and sigh squared graft you could pick out which ones which you could this 1 negative so it's gonna be signed this one's always positive so that will be sent squared the next thing to talk about them is no so notes occur when sizing over 0 now it's size is equal to 0 what ending about I squared that was going to mean a squared also equals 0 8 0 and 0 is most certainly 0 so where at the outset wave function called the 0 signs the sites where it is equal to 0 as well now think about what square is that it's a probability density so it's where you're likely to find something so at no-load what's the likelihood that the particle will be there is sigh square 0 it's going to be there but because of the size 0 that news sites where it has to be 0 inside squares probability density so the probability of finding a particle someplace 0 it's not going to be there so we functions have and minus 1 notes that may not mean a lot to you right now but when we start talking about energy levels that mean a little more achieved so if we have a wave function at a particular level for particle a box it's going to have in mind is 1 notes so here we don't really have a known but technically this is asymptotic so it just approaches 0 never quite hits and you talk about nodes just being in the satire like right here so this is absent probably going to 0 it's not a node this is an odd however soon now showing equation to worry really getting colleges to things so what showed Ingush equation does it allows us to take the wave function and come up with an energy level now we talk to energy levels already right with talk with the Baum model without my having an Eagles wide angles to win any equals 3 and only did oversimplification of energy levels but it does work to help you can think about some assuring the equation gives us way to actually go through and find his energy levels no you don't have to worry about this equation show much of I put it there mostly because you but does and it's going to have seen once if you go on in physical chemistry you'll see a lot of but the Wade that this works the way that this equation works as H is common operated and what that means is that you're taking something and you're doing something this function and operator operates on a function sold for those of you who have had some calculus which is most of you that means that for instance if you take a derivative of something if you take the derivative of signed it the derivative of coastline that is taking the derivative of an operator immediate something simpler maybe it's just too so if you take whatever function having you add to investor operator of it just means you're doing something to that functions so this happens to be the H the operator this is what happens this happens to be what we call the Hambletonian and this is the Hambletonian for effect now if you care is a lot those for info Services things this is the double derivative right so that would mean you take the wave function take the double derivative of it you multiply it by that this is just a number right in the equation but this part is just a number it's each bar which is a chore to pie just constant squared to and which is just a constant so you have that and then taking the double derivative so again you don't need to worry about this too much assessor Fourier involved parties do need to worry about is knowing that this is ensuring equation that this means you have to do something to the wave function and then you get your energy so 1 of the easiest ways to think about how this would work is if you take the double derivative of the signer co-signed if you take the double derivative of sign you end up back back with signed now I has a negative 1 in front this would be like this you you get the same equation back but you have some number in from to double derivative assigned would give you a negative sign In you'd get the negative 1 back if you don't have any calculus is a little bit harder to come up with a way as to work out so we will discover leave it at that but you have to know you have operator it operates on a function and you get an energy level that sort of the condensed version of what I want you to know for this class so there we were in use is we can use this to find the way function and iii now for this class were just beneath the results that we are going to go through do this we're going to calculate the these word against them say OK here the energy levels through the result but so what you start with a system called particle now this got started with because the little with employers something like a hydrogen and hydrogen atom hazardous three-dimensional space but apart econoboxes simpler so way that this works is you have a box giving out of the box and the electron can go through the box and it's in the middle after me inside the box and it's going back and forth into the world of work not quite the way 1 awarded but it's in the box so can the real life where you can think about this since it's hard to picture an electron beam the localized a box is if I took a stranger in a stretcher from room to room and mutilated departs stringing plucked it and you have this going back and forth so we'll go home still someone's good hard look at the of the strings what happens utility the way kind of oscillating back and forth now you're allowed certain wavelengths this is relatively easy to do something like a jump rope right you can take a jumper from very slowly go like that you can get this pattern or you can speed up we speeded up you can get a sort of pattern like this and fast you go the more times you can get it softly in 1 mentally you're more able to do anymore but that's not the issue with the empirical about system so that you can kind of think about this work and but now you'll notice only certainly links are allowed seems sure go use the jumper right you're allowed those certain link for you get this the certain willing for you get best but not in between and when you try to meet has switched from going the slowly away to a little bit faster there's weird .period created this is it's not a awaiting it's not designed awaited the transition .period so it kind works there too now here take deferring the equation and entire all its soul that he in that use each each cycle the size of this year's tables the site and told you that we're going to just fall for EU I'm just going to tell you what it is but it will hear the results so this is this describes the difference equations that can really at this electronic box and this is our solution suffering because this is our energy now I don't want this equation bother you there's a lot of things that the number and good deal and that's just
1 2 3 4 is thinking about your jump rope that seal which level of energy about how hard you have to you move your arm to get that now each place constantly 90 different will be talk about 8 and if the European generate hopefully noted and that the mass does whatever particle were talking about In an hour the link of the box so that's not a big deal that's just a number that we're going decide on for any particular system it's just from here to here but so what we can do is we can I use this term modeled on a particle in the box for example where were given a wavelength of electron a fine the way Lincoln electron of a theoretical Adam given an approximate diameter if we say that the diameter is about 100 people meters in we can find the wavelength of the theoretical and the so and changes example around a little bit from what was on the slides so there's a lot of on the worksheets and as they were going to go ahead and reinstall for this so actually I just decided to stick around about that we decided to step back and do that at a later time once we know little more about the way I mechanics work on making only a little easier to understand and In the meantime let's not take go to the next step so the particle boxes nice model at the kind of let us take a moment when if you actually go through and do the quantum mechanics it's a little easier to work with and something like a hydrogen at the equation the simpler so that was kind of why was developed but now we also have hydrogen atoms and we can actually go through we can find the equation for that now I talk to different ways of thinking of all of this with the hydrogen atoms the Ribery equation and I don't through injury with the astronomer equation as well now the results of these are exactly the same so what you're defined as regardless of which way we do it you're going to have the same incident enhancing equations so you can sort of take the easier of the equations when you're trying to solve for actual number so of in my opinion adding the Ribery equations Polydor work with now this both these we're all used to describe the hydrogen atom but the differences in how they were were discovered Marburg did experimental she looked at a whole bunch of spectra coming in and said notice patterns in notice that we numbers work together and came up with an equation that described it and had a constant in there that calling the ride the confidence band had all of the energy levels and everything now what Schroeder dead is she said well under staff from you know that we function and I'm going to put the Hambletonian in the south of the energy and then that's going to give me all the energy levels so 1 was done experimentally 1 was done theoretically but either way you do it you get the exact same results so riders was on 1st and ensuring there's agreed which is always great and signs as we what you want someone to do experimentally and someone or someone to do it on the radically and habitue results agree because I'm in that your theory is relatively sound if your Serie doesn't agree with experiment area experiment doesn't with theory you're obviously not understanding from something so this does show that you know they both kind had it right so this is going to be true for the hydrogen like Adams and widening by hydrogen like Adams is a 1 electron systems so if you take some sort of out you take away all but 1 of its electrons you can use this solution set to do it when 1 little change now I understand backwards from reality and start was because I think having the theory based 1st and then working into the experimental is is a little bit easier to understand so when strongly here and this is going to walk through the exact same thing that we did the protocol on the box so now remember I thought I was just going to be the result of this is the results when you come out this is the energy level now is the is equal to that the atomic number so the is 1 of those numbers those letters that is is kind of universal in chemistry and see what I recognize that as the pollen number each planks consonant with Tucker R. Anderson it will leave introspection and in the energy level so now what are is this this is whole series of the equation this whole series of constants nearly are a big deal they're all just constantly can look up it just gets a little tedious to write them all and so have a ton of Constance here and this the squared age over and square so really it each is a constant you right so you're really does have the squared or and squared turned the whole winter so keep that in mind when we go to derided the equation is really just the squared over in squared times a whole bunch of constants now let's look at the war model the animal murder so remember we have nucleus will all positive charges and we have our air that rings electrons going around the outside now this arose because they knew well that we had a proton film nucleus end had the electrons going around them now the interesting thing here is that if you look at the laws of physics it says that the electron should spiral into the nuclear that it should be going around and around and around into just spiraling in everything slides and together nope after plane discovered quantification employing said Hamed these particles are admitting all different sorts of of wavelength and the very particular wavelengths and not not in between Boris said all doubts because the energy levels are going be quantized that you can have this energy and can this energy being can have an energy in between the 2 no this particular model is only gonna work for 1 electron systems it does turn out that the quantized just a a slightly different way than what were thought now the energy difference is given by negative R H z squared over and swear and that's what my bird went through inside so before we talk about exactly what Ryburn said I think this kind worth noting staring ball analogy for quantification energy levels the idea here is always that if you sent a ball down on you this energy level or this energy level at this energy level it can be at any stair step energy level never intervened between it can transfer between the energy levels it can go from here to here but it cannot be like a hold in the middle somewhere in needs to be on 1 of these particular levels so that sort of how you I think of these as you can be here you can be here you can never be in between OK snow moving on all
right Birch said Weinberg looked at all the sources spectral wouldn't talk about an imminent inside Well this is what I think the energy levels are at I think that is that some constant that I'm a Colorado company combining right Bergantzel I like the way that sounds times the squared over and squared no keep in mind what it we have assuring equation we had a whole bunch of random constants that all had numbers associated with them times the squared Over and square so the 2 on any difference the only difference is that when board that it she just knew it was a number he just knew because experimentally this had to be number and he called it 1 constant were strutting her because he did it theoretically was able to say Well I know constants are I know that there is the old it's all of these combined together if you multiply all of those together it comes out to constant contact with the same number and so that's how these 2 are related I think that the 0 and work with because we only have to worry about 1 constant as opposed to those like 5 or 6 different kinds so that the energy level don't frenzies topic number so that's the worst don't always know title 1 electron systems but because we can have our towns z can change we can have a human 1 possibility to plus new things of that sort that were calculating so this is not the right constant turned out to be although there are some other versions of the Ribar consummate you'll see although a lot of times you'll see it written in terms of courts and you'll see the Ribery equation there and talk about an imminent rented a as 1 land on the way I'm doing on the slides are of the way that I found the least amount of people do make mistakes on actually doing the problem I would suggest doing it this way your homework suggest doing it a different way of the remember what your particular books says it and then there's like 4 or 5 different ways do all these problems I think this is the best way to not make mistakes a year at that level so the is again here atomic number try that we hold on it so what is the energy difference so I care a lot about these transitions how much energy it takes to go from this level to this level how much energy we get back if instead now drops down to this level and we were not able to calculate all of these you can do this with both for Ingres and Ribery's equation but again showing there is is a little bit complicated because of all these different on Constance where Wiberg only has are so it's a little bit easier work with so we're going to go through organ work with Ryder so if we define the difference in energy levels the difference that it takes for an electron to go from here to here or from here to here and so on it's a different so it's always final minus initial so the were kind of and deride this as sort of a lasting of the so for a given energy level it's going to be defined by this this is just from the last line so we know that we can find the difference and energy by taking the final in subtracting the initial that's just a definition change now we we also know that we can to find both states we can define the initial only the final so all we did was rewrite this equation 2 times one-time calling it arbitrarily initial and one-time quality a final now we can fill these ends To which soaring the final intelligent and take initial and fileted so changes equal finalize initial so we sell everything and so again taking the energy levels filling it and so were trying to find the difference in energy between 2 different levels now we have all H which doesn't change in the which is an ever-changing array because it's not switching Adams is just switching within 1 arm so we can just factor those out of the equation and set them aside for the sake of algebra so when we do that we did this where we take and we had ah age the squared you can back in the the squared out to some obsolete and some books won't on you end up with this equation now it's something that gets talked about a lot of students have issues with is the fact that this is where in 2 different ways depending on where you happen to find it sometimes you have a negative sign and sometimes you don't so the difference here is that here you have a 4 the final minus initial a new factor about the negative here you basically put the negative inside but when you did that you ended up with an initial minus final it doesn't really matter which when you use on the final I'm going to be 1 of them so just use that 1 but when you're doing your homework be careful if you're doing this soft memory not seen massive this up the 1 with the negative his final minus initialed the 1 without the negatives initial minus-5 if not that 1 of them was wrong 1 on the right is just different ways of writing the exact same thing so keep that in mind so next time will go through and will do some examples using less and learning and do a lot of talking about sign convention because the signs for all of these are really important and honestly while most commonly missing the entire if you mess up the siren have problems again going naturalism before there's different versions of this equation see with 1 Overland of sapling does that on some books do that I think it's easier to do it this way and I'll show you why when we go to worry about signed conventions and we do some examples you have to be really careful about which direction these transitions are going all
Mandelson is going to be a largely positive or negative and you never run into problems if you must that up if you mess up whether the Delta is positive or negative and so will talk about all that next time all this thank mentioned examples things of that sort and and really kind of finish up the hydrogen atoms on next time
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Formal Metadata

Title Lecture 04. Wavelengths
Title of Series Chem 1A: General Chemistry
Part Number 4
Number of Parts 23
Author Brindley, Amanda
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 10.5446/18969
Publisher University of California Irvine (UCI)
Release Date 2013
Language English

Content Metadata

Subject Area Chemistry
Abstract Chem 1A is the first quarter of General Chemistry and covers the following topics: atomic structure; general properties of the elements; covalent, ionic, and metallic bonding; intermolecular forces; mass relationships. Index of Topics: 0:00:24 Wave Interference 0:03:22 Double Split Experiment: Young 0:07:25 Wave or Particle? 0:08:58 DeBroglie Wavelength 0:18:54 Heisenberg Uncertainty Principle 0:26:09 Wavefunctions, Energy Levels, and Particle in a Box 0:32:05 Nodes 0:33:38 Shrodinger Equation 0:36:57 Particle in a Box 0:41:20 A Hydrogen Atom 0:44:00 We'll Start with Shrodinger 0:45:24 Bohr Model of the Atom 0:46:39 Stair and Ball Analogy 0:47:12 Bohr Model Energy Levels 0:50:07 Rydberg Equation: Derivation

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