welcome to sections 12.10 12.11 12 13 and 12 14. now this is a whole bunch of little sections that are intertwined together so i'm going to try to cover them in one lecture in the last lecture we started talking about the quantum numbers the quantum numbers are the solution to the schrodinger equation the schrojer equation is going to go ahead and describe an orbital that is it is going to describe a wave which is what we are envisioning our electrons to be now the quantum numbers tell us characteristics about that wave or that electron the principal quantum number is going to go ahead and tell us the energy of that electron so in this diagram i have n equals one two and three the things that make up the electronic shells of my atom now in each one of these shells are the subshells the subshells are described by the quantum number l now based on n i can only have certain values of l we usually refer to the subshells in their letter designation so we have s-type orbitals we have p-type orbitals and we have d-like orbitals now each one of these subshells have a certain shape the s orbitals are sphere-like the p orbitals dumbbell the d orbitals the clover now each one of these orbitals are orientated in space a little differently so for s orbitals which are completely symmetric there's only one orientation but for p orbitals there are three orientations and those have different m sub l values for the d orbitals there are five orientations and so there are five unsub l values if we look at this diagram what you'll see is all these p orbitals have the same energy if the orbitals have the same energy we say that they are degenerate now before we move on there's one more quantum number we should describe and that is the m sub s quantum number the idea here is to go ahead and describe a quantum mechanical phenomenon if i were to go ahead and shoot hydrogen atoms through a magnetic field something with a north pole and a south fold what i would see is half the atoms would be deflected up and half the atoms are deflected down this has to do with the one electron in the hydrogen atom it is interacting with the magnetic field we can describe this as the magnetic spin now even though i say the word spin i'm not saying that the electron is spinning like a top that would be angular momentum and there's already a quantum number associated with it this is a purely quantum mechanical effect and does not have a classical newtonian analog what i can say is those electrons that were deflected up had an m sub s value of plus one half for those electrons that were deflected to the bottom i can say it has an m sub value of minus one half now it turns out with four quantum numbers n l m sub l and m sub s i can fully characterize an electron so this is going to tell me how the electron is going to behave inside an atom what you should note is no two electrons in an atom can have the same quantum numbers the reason being is if they have the same quantum numbers you would be describing the same wave i.e the same electron so to get a distinct electron one of the four of these quantum numbers have to be different this is called paulie's exclusion principle so to summarize everything with our quantum numbers n is going to tell you the energy of the orbital l is going to tell you the shape m sub l is going to tell you the orientation of that shape and an m sub s is going to tell you if that electron is spin up or spin down we have restrictions on what n can be and l is going to be dependent on n and the restrictions on m sub l is going to go ahead and be dependent on l once i have all these ideas what i can start doing is writing down the electronic configuration i.e how each electron in my system is behaving what i will say is that i have orbitals in my atoms that is the possible ways that the electron can behave when i fill an orbital what i'm saying is that electron adopts the quantum numbers associated with that orbital and that electron can be found based on those quantum numbers now when i go ahead and put electrons into an atom we will always go ahead and fill or adopt orbitals with the lowest possible energy after those orbitals are filled i can start filling in orbitals at higher energy what i can do is i can go ahead and do a little thought exercise this should be the way that my atom is structured with its orbitals and i can go ahead and do the electronic configuration of hydrogen helium and lithium so let's do the electronic configuration of hydrogen so hydrogen has one electron so i'm going to go ahead and put the electron in the lowest orbital possible so what i'm going to draw is the electron as a half arrow so this electron can be represented by four quantum numbers those four quantum numbers are n l m sub l and m sub s so for this one electron n equals one l equals zero m sub l equals zero and since i drew the arrow pointed up i'm going to put plus one half so what i can say is the electronic configuration of hydrogen has the 1s orbital with one electron in that 1s orbital now let's go ahead and do helium helium has two electrons so the first electron that i could do is going to look exactly like hydrogen and so i'm going to keep it in this blue color now i have to put in the second electron now the second electron i'm going to go ahead and try to put it in that 1s orbital so i can have n equals to 1 l 0 m sub l 0 but i can't put the electron as spin up because i will have the same set of quantum numbers and so remember to have a unique electron i have to have a difference in one of the four quantum numbers so instead what i'm going to do is i'm going to draw that second electron spin down so all my quantum numbers are the same except i'm going to have minus one half for m sub s so my electronic configuration for helium i can write as i have the 1s orbital and there are 2 electrons in that 1s orbital now the next element i can do is i can go ahead and do lithium lithium has 3 electrons now what you guys can see is that the first electron is just like the hydrogen the second electron is just like that helium but now i have a third electron now the third electron what you guys will notice is i can't put it in that 1s orbital because if i try to do it i'll have 1 zero zero i can't have plus one half i can't have minus one half so that means the third electron has to go into n equals two or the second electronic shell so i'm going to put a 2 for my n value now according to this diagram the 2s orbitals and the 2p orbitals are at the same energy level they are degenerate however what experiment shows is that i will always put this third electron in the 2s orbital meaning i go to l equals 0 and m sub l is going to be zero as well i can put a plus one half for my m sub s and so i can draw the third electron and so my electronic configuration is going to be 1s2 for the first two electrons and then 2s1 for that third electron but let's go ahead and talk about why the 2s is preferred over the 2p the idea behind this has to do with this phenomenon called shielding so what we can talk about with shielding is first what's called the z effective what we have at the center of our atom is our nucleus it's going to have a positive charge and so let's say that positive charge is z now what an electron feels is what's going to be called z effective and so if i look at inner electrons well there's nothing blocking that inner electron from the nucleus so the inner electrons the z effective or what it feels is equivalent to z however if i start looking at outer electrons what you guys will notice is that these electrons right here are blocked by these inner electrons these inner electrons are going to start pushing the outer electrons away what that means is that these inner electrons are shielding those outer electrons and so what happens is the z effective for an outer electron is less than the z or the real charge of the nucleus the z effective for those outer electrons is going to be z minus the amount of shielding those inner electrons are going to cause now if we look at the probability distribution of a 2p and a 2s electron what you guys will see is the 2s electron approaches the nucleus very closely that means there's a good probability of the 2s electrons getting really close to the nucleus meaning it can shield the 2p electrons now the 1s is going to go ahead and shield both the 2p and the 2s but because of this probability for the 2s to get really close we say it can penetrate so in general the 2s orbital is going to be lower in energy than the 2p orbital because it approaches the nucleus more and is shielded less now this progression happens throughout all the orbitals an s orbital is going to be lower in energy than a p orbital which is lower than energy than a d orbital which is lower in energy than an f orbital so what i get is a rearrangement of the orbital diagram for my atom what you guys will see is the 2s is lower than the 2p and remember i always feel lowest to highest and so that's why when we looked at our lithium picture that that third electron preferred to go to the 2s rather than the 2p now this brings about a complication what you guys will see is right around here we start jumbling where our orbitals are for example what you guys will notice is that the 4s is lower in energy than the 3d what that means is is the 4s orbital is filled before the 3d because it is lower in energy now there's a couple of ways that you can memorize how to fill out this chart one way is to do this diagram right here and the way to do this diagram is you write down your n values 1 2 3 4 5 6 and then you go all the way down you write all the orbitals available in each one of these shells so for n equals one there's only an s orbital for n equals two s and p for n equals three s p and d now once you go ahead and fill out all these lines you can go ahead you start from the right hand corner and work your way diagonally down so you fill the 1s and after you fill the 1s you fill the 2s the 2p to the 3s the 3p to the 4s to the 3d to the 4p to the 5s and so forth now if you're more mathematically inclined you guys can use a formula the way that you figure out which orbital is lower is you can use the simple formula and plus l whatever has a lower value is going to be filled first so if you're trying to figure out which is the lowest energy the 3p the 3d or the 4s you can go ahead and use this mathematical formula so in the first one i have 3 plus 1 which gives me four for the second one i have three plus two which gives me five this is going to be four plus zero or four so what i can see here is 5 is the highest number so it is the highest energy next what i see is that i have a tie between 4s and 3p if it has the same n plus l to break the tie we are always going to put the lower end lower in energy so in this case the 4s is going to be in the middle and the lowest energy is going to be the 3p and so this is the order you're going to fill the 3p first then the 4s then the 3d orbitals the last way that you can do it is you can just simply memorize the order in which the diagram is laid out do whatever is most comfortable for you but let's go ahead and practice doing more electronic configurations let's do beryllium boron and carbon so i can draw my energy diagram out and let's go ahead and start with beryllium so beryllium has four electrons so one two the third one is going to be just like lithium and goes in the 2s orbital and then the fourth electron i'm going to go ahead and pair it up in that 2s orbital what you guys will notice is every orbital is going to get two electrons so the electronic configuration for beryllium is going to be 1s2 2s2 because it has two electrons in the 1s orbital and 2 electrons in the 2s orbital next let's do boron boron has 5 electrons so i'm going to start from the bottom 1 2 3 4 and now i've run out of space in the 2s orbital so the next lowest orbital is the 2p so i'm going to go ahead and put an electron in the 2p orbital so its electronic configuration 1s2 2s2 2p1 all right let's do carbon 6 electrons so one two three four five just like boron and now i have to put the sixth electron now i have a choice i can go ahead and pair it up like this or i can put this next electron into an empty orbital now what we see experimentally is that this is the configuration we see we see that the electrons are going to go ahead and spread out in degenerate orbitals and this is what hund's rule is going to describe when you have orbitals that are at the same energy what we can do is we can go ahead and fill up every degenerate orbital first before we pair it up now this should make sense to you guys remember these orbitals right here are describing the location of where those electrons are and so if i pair them up that means those electrons are much closer together and remember electrons are negatively charged they want to go ahead and spread out as much as possible before they go into the same location that's why they will go ahead and adopt orbitals in different orientations to spread themselves out further so to summarize electronic configuration first you guys are going to follow what's called the aufbau principle that means fill the lowest energy orbitals first remember that each orbital gets only two electrons because of paulie's exclusion principle and finally hund's rule tells you that if you have degenerate orbitals meaning they're at the same energy you are going to spread them out before pairing them up you want to maximize the number of unpaired electrons in your system you can use whatever you guys want to draw your energy diagram either this way to generate the picture memorize the picture or use the formula n plus l to figure out what's the lowest in energy so why don't we go ahead and try a quiz question out tell me what the electronic configuration of chloride is so this is an anion i want to negatively charge chlorine all right gentle people chlorine has 17 electrons but if i make the chloride ion i have 18 electrons so let's go ahead and fill 18 electrons into my energy diagram so i'm going to start with alpha's principle and start from the bottom i'm going to use paulie's exclusion principle and only put two electrons in each orbital so i got my first four when i get to the 2p i'm going to follow hund's rule first i'm going to spread them out and then after i spread them out i'm going to go ahead and pair them up so i've got 10 electrons 11 12 13 14 15 16 17 and 18 electrons so what i can say is that i've got 1 1s squared 2s squared 2p with 6 electrons 3s with 2 electrons and finally my 3p is fully filled with six electrons and so this should have been choice d for your all let's go ahead and take a look at some electronic configurations because what you'll notice is that a lot of these electronic configurations become very tedious to write so what you'll notice is the noble gas right here neon and if i were to do its electronic configuration 1s2 2s2 to p6 or if i want to draw in the box diagram format you can see it like so what you will notice is that neon has all its shells filled the 1s is completely filled and the 2 is going to be completely filled as well if i go ahead and look at sodium i can say it's 1s2 2s2 2p6 3s1 what i can see is n equals 1 and n equals 2 they are filled but then i don't fill my highest shell so what i can do is i can use a shortcut i will see that every noble gas is going to have its shell full if the noble gases go ahead and represent a full shell and then the outer shells of all the other elements are unfilled what i can do is i can describe the inner electrons in terms of a noble gas what i mean by that is if i look at the inner electrons of sodium i can see it exactly matches that of neon and i can split up my electrons into two categories the electrons that are on the outside which are going to be called the valence electrons for anything that's not a noble gap my valence shell is not going to be filled the inner electrons are going to be core electron the core electrons are going to be in shells which are completely filled and so what i can do is i can describe my core electrons in terms of a noble gas so instead of writing sodium like this i can say that sodium has a neon core and then on the outside it has one electron in the 3s orbital and when i say it has a neon core i'm saying this is the inside configuration you guys can test yourself with calcium calcium what you will note is the core electrons are the same as argon the noble gas that immediately precedes it calcium has two more electrons than argon and those two electrons go into the four s orbitals so this is the electronic configuration of calcium we can continue our discussion on these electronic configuration by looking at the transition metals the element after calcium is scandinavia sc what you guys will see is its core is filled and is similar to argon this element has three more electrons than argon so that means it has an argon core the first two electrons are going to go into the 4s orbital and then the third electron is going to go into the next highest orbital which is 3d so its electronic configuration is argon 3d1 4s2 sometimes you will see that they switch places with the 4s and the 3d and so they might write it as argon 4s2 3d1 either one should be fine now what you guys will notice is we can continue this progression down the transition metals filling up 10 electrons once we get to zinc now what you will see is that this matches the periodic table the periodic table we told you was based on reactivity that reactivity is actually based on the electronic configuration and so in reality the periodic table is a range based on electronic configuration you have n equals one and there's only the s orbitals so only two elements are up on the top you have n equals two and then you have the s orbitals which can only accommodate two electrons and then the p orbitals which can accommodate six electrons so that's why the second row in the periodic table is two elements followed by six elements on the other side same thing happens with n equals three two and six then once you start getting to the fourth row you start to introduce the d orbitals and what you'll notice is that i can put 10 electrons and the d orbitals and that's why you have 10 transition metals going across you'll also note that those elements the lanthanides and the actinides on the bottom there are 14 across and that's because there are 14 f electrons so if you look at the periodic table you can determine the electronic configuration just figure out which row you're at this is going to be your s block so that means your valence electrons are going to be in an s orbital this is the p block that means your valence electrons are going to be in the p orbital the d block with the valence electrons in the d orbitals now just be careful the d orbitals are offset by 1 meaning 3d starts in row number 4. the same can be said with our f orbitals our f orbitals they start to come here so they are on the sixth row and so they are offset by two now i should note there are two exceptions to the rule that always appear on standardized tests and that is chromium and copper so chromium appears here on the periodic table so if you were to do its electronic configuration you would say that it has an argon core 1 2 so four s two one two three and four so three d four that's normally how you would do most transition metals it turns out that chromium is an exception instead of being this configuration here it turns out it's more stable if one of these s electrons gets promoted and so what happens is that chromium becomes argon core 4s1 3d5 this is called the half build stability and so chromium is one of these elements that does this exception and you're just gonna have to memorize that it does the other exception is copper if copper were following the rules it would be argon core 4s2 3d9 but it turns out it does the same thing and promotes one electron to get that s orbital half filled so its true configuration is argon core 4s1 3d10 so these are the only two exceptions that i want you to note welcome 1a i hope that made sense and remember to stay safe