everybody my name is Iman welcome back to my YouTube channel today we're going to be continuing our lecture on the electronic structure of atoms and we've left off on objective five which is titled the quantum mechanical model of an atom now to begin and motivate this we're going to continue discussing B's model now at first B's model appeared to be very promising the energy levels calculated by bore closely agreed with the values that were obtained from the hydrogen emission Spectrum however when B's model was applied to atoms other than hydrogen it did not work at all and there were some attemp attempts that were made to adapt the model but it was concluded that B's model is fundamentally Incorrect and now you're probably like whoa IM manal girl what are you talking about I thought we liked bore now we're dissing him and yeah maybe a little bit but listen while B's model marked a significant advancement in the understanding of the structure of atoms his mod model ultimately proved to be inadequate to explain the structure and behavior of atoms that had more than one electron now these limitations they were ultimately addressed by the development of quantum mechanics which provided a more comprehensive and broadly applicable framework for understanding Atomic and subatomic systems the wave mechanical model of the atom developed by Schrodinger and Heisenberg among others very much superseded B's model by treating electrons as wavelike entities with probabilistic distributions around the nucleus rather than particles in fixed orbit now the most important difference between B's model and the modern quantum mechanical model is that bore postulated that electrons follow a clearly defined circular path or orbit at a fixed distance from the nucleus where as modern quantum mechanics has shown that this is not the case rather we understand that electrons move rapidly and they're localized within regions of space around the nucleus called orbitals orbitals not orbits an orbital is a region of space around the nucleus that's defined by the probability of finding an electron in that region now quantum mechanics is heavily based in mathematics and we really don't have to worry about the math but it will help us understand where we get our description of atomic orbitals from so I'm just going to briefly work you through the idea all right while we don't need to know any of the math in general chemistry I just want to talk a little bit about where we get Atomic orbitals so in quantum mechanics we have a wave equation a wave equation describes the behavior of electrons and particles then we have wave functions wave functions are the solutions to the wave equation we can get information about allowed energy from this now if we take the absolute square of the wave function this gives us the probability of finding an electron in a location we said quantum mechanics is probabilistic in nature so we can only get a probability of finding an electron but but in the 3D plot of that probability which is the square of the wave function that is going to generate an image of our Atomic orbitals that is where our Atomic orbitals come from now in the current quantum mechanical model we have orbitals because it's impossible to pinpoint exactly where an electron is at any given moment in time and this is best exp expressed by the Heisenberg uncertainty principle it says that it is impossible to simultaneously determine with perfect accuracy the momentum and the position of an electron if we want to assess the position of an electron the electron has to stop and when it does that we remove its momentum if we want to assess its momentum then the electron has to be moving which means it's changing it its position and so this is the expression that demonstrates and expresses the sentiment of the Heisenberg uncertainty principle main takeaway is that it is impossible to simultaneously determine with perfect accuracy the momentum and the position of an electron and that is all that this expression is saying now to better understand the distribution of electrons in an atom quantum numbers were developed these numbers describe the energy the shape and the orientation of an orbital allowing us to predict the electron configuration of an atom and its chemical behavior now modern atomic theory postulates that any electron in an atom can be completely described by the four quantum numbers and to probably to properly understand this concept we're going to have to learn a couple of things in a specific order so here's our workflow guys first we're going to actually need to know about off B's principle poly Exclusion Principle and Hun's rule once we Define those we're going to keep them in the back of our mind and then we're going to talk about the four quantum numbers after we talk about the four quantum numbers then we're going to begin to visualize the differences between shells subshells and orbitals then we're going to connect all those topics together and we'll make the most sense of this information information by talking about electron configuration now all these topics are extremely interrelated so let's just get started let's start talking about these things and then we'll connect them as we go let's start with off bows principle this says that the lowest energy orbital is filled first then we have the poly Exclusion Principle this says that each orbital can accommodate a maximum of two electrons that have opposite spins and then last we have Hun's rule which says one electron is placed in each degenerate orbital first before electrons are paired up so we're going to keep these definitions in the back of our mind and we're going to come back to them a little bit later but what we want to do now is move into our sixth objective and discuss the four quantum numbers principle angular momentum magnetic and spin let's start with the principal quantum number this defines the size and energy level of the orbital where an electron is likely to be found it's denoted as lowercase n and it can take on any positive integer value the larger the value of n the higher the energy level and the larger the orbital within each each shell there is a capacity to hold a certain number of electrons and that is given by the equation 2 N squared this will make a little more sense later then we have our angular momentum quantum number denoted by L and this defines the shape of the orbital and it can take on any integer value from 0o to n minus1 each value of L corresponds to a specific subshell dictating the shape of the orbital when l equals 0 we're talking about a subshell that's going to be called s when L equals 1 this gives us the P subshell when L equals 2 this is the D subshell and when L equals 3 that gives us the F subshell next we have the magnetic quantum number ml this defines the orientation of the orbital in space and it can take on Integer values anywhere between minus L to positive L including zero this quantum number arises due to the orientation of orbitals within a magnetic field then last but certainly not least we have the spin quantum number denoted Ms and this only has two possible values plus 1/2 or minus 1/2 and this reflects the two possible orientation of an electron spin we're not going to get into electron spin because that is a very complicated topic and we don't need to know that all we need to know is that there's two possible values for the spin quantum number plus 1/2 and minus one2 now we're going to take our first pause here all right we've defined some terms offb poly hund and now we've gone over quantum numbers what's the connection here the connection is that the arrangement of electrons Within These orbitals is governed by the fundamental principles we covered now this next topic is really going to help us frame these ideas together even better that topic is what are shells subshells and orbitals let's first start with shells shells are the primary energy levels of an atom and they're defined by the principal quantum number n this figure here shows two such shells we have the innermost shell Nal 1 which is the closest to the nucleus and it has the lowest energy and then we also have the next Shell Nal 2 which is at a higher energy level and farther from the nucleus each shell can hold a larger number of electrons as n increases accommod accommodating them within subshells and orbitals that exist at that energy level that helps help us transition into subshells now subshells are categorized by the angular momentum quantum number L and they specify the shape of the space where electrons are likely to be found so for our shell n = 1 if n equal 1 L can only have one pos possible value and that's zero because remember L is equal to 0 all the way up to n minus1 but for n - 1 the only possible value here is going to be zero now L equal 0 refers to the S subshell now if you look at the Nal 2 shell when n equal 2 L can be zero or one where zero refers to our s subshell and one refers to our p subshell and we see both of those subshells here all right our s 2s and our 2p sub shells next we have orbitals orbitals are the individual regions within a subshell where electrons are most likely to be found all right and it's actually kind of shown here by the different shapes of the p subshell in the Nal 2 shell each orbital can hold up to two electrons with opposite spins so let's go back to the start if we have an nals 1 shell we only have one kind of subshell that's the S subshell the S subshell is just circular it's spherical indicating an equal probability of finding an electron at any point around the nucleus all right the 1 s orbital then can fit just two electrons of opposite spin then we have our Nal 2 shell which has S and P subshells the two the the s subshell all right it can hold it's also spherical it can only hold two electrons of opposite spin so in the 2s orbital we have two electrons then we have our p subshell and again like we said there are three orbitals in the P subshell we have 2 PX 2py 2pz this refers to the different orientations in Space the 2p orbitals are dumbbell-shaped and they're oriented along the x y and Z axis showing that electrons at this energy level have a higher probability of being found in certain directions relative to the nucleus and each of these P orbitals PX py pz can fit two electrons in opposite directions with that here's our second pause let's go back to the page with our quantum numbers and start working through some examples and start visualizing things a little bit better so we're going to erase so we can make some space and then let's talk through these quantum numbers again and do an example or examples all right so our principal quantum number again this describes the energy level of an electron and the size of the orbital the larger the value of n the higher the energy level and the larger the orbital size and it can take on any positive integer value then our angular momentum quantum number describes the shape and the number of subshells within a given principal energy level or shell it has important implications for chemical bonding and bond angles and for any given value of n the range of possible values for L is 0 to n minus1 the subshells remember are designated by the letters SP PDF for L values 0 1 2 3 respectively then we have our quantum number our magnetic quantum number this describes the orientation of an orbital in threedimensional space and the possible values of ml are the integers between minus L and positive L including zero now the number of orbitals in a subshell is going to actually be equal to 2 L + 1 all right then last we have our spin quantum number this describes the spin of an electron in an orbital and they can have values of plus 1/2 or minus 1/2 now whenever two electrons are in the same orbital they have to have opposite spins all right so that's an important thing to remember now let's go through different shells all right let's pretend that n is equal to 1 if n is equal to 1 then L can only be zero and if L is equal to zero we're referencing the S subshell all right the S subshell here then ml is anywhere from minus L to plus L but we just have zero here so for ML this is also going to be equal to zero and that makes sense because what does ML tell us what does magnetic quantum number tells us it tells us the orbital orientation but we know that when L equals z we have the S subshell this is a spherical subshell there's really only one orientation for a s orbital anyway AKA one orbital all right it's just a sphere and then Ms refers to spin and that can be either plus2 or min-2 now if we're in the N equals 1 shell all right our subshell can only be the S subshell and there's only one orientation for that subshell and in that orbital all right that one s orbital we can house two electrons and they have to have opposite spins one with a plus one2 value one with a minus one2 value okay that was simple and easy for the Nal 1 let's continue let's do Nal 2 and make sure that we really understand this okay n equal 2 when that's the case L can be zero or it can be one zero refers to the sub subshell one refers to the P subshell then our values for ML they can be anywhere from minus L to positive L which means they could be minus1 0 and positive 1 now we just discussed that for an S orbital there is only one orientation all right cuz it's spherical and that means that we can house in this s orbital just two electrons of opposite spin but for our P orbitals our P orbitals can have three different orientations X Y and Z and this minus one 0 and + one refers to the three orbitals we can fill in the P subshell each of these orbitals houses one electron uh two electrons of opposite spins wonderful all right and then Ms again +2 min-2 those are the possible values okay let's get just a little bit more complicated all right just a little bit more complicated n equals 3 if n equals 3 then L can be 0 1 and 2 zero is for the sub subshell one is for the p subshell and two is for the D subshell now for our values of ml it can be anywhere from minus L to positive l so we can have values of min-2 -1 0 + 1 and + 2 now again we have to use our logic here right so for our s subshell it's spherical there's only one orientation and this orbital can hold two electrons we just talked about our p orbital it has three POS possible orientations and each orbital can fit two electrons all right so we have these three orbitals that house two electrons each our D orbitals are a little more complicated our D orbitals can have five different orientations each orbital can house two electrons that is where those ml values of -2 -1 0 + one + 2 come into play in describing the D orbital and the possible orientations for the D subshell there are five orientations or in other words five orbitals in short we have our four quantum numbers all right and our principal quantum number gives us information about our shells and energy levels our angular momentum quantum number tells us information about our subshells and their shapes and then our magnetic quantum number tells us about the orbitals and the electron probability regions now when we get into electron configuration which is the next step here all right we're going to use these quantum numbers to predict an atom's electron configuration which is going to tell us the number of electrons in each orbital and the number of veence electrons and in our discussion of electron configuration what's really going to be important is our reference back to the three principles we talked about off B's principle poly Exclusion Principle and Hun's rule for a given atom or ion the pattern by which subshells are filled as well as the number of electrons within each principal energy level and subshell are designated by its electron configuration electron configurations use spectroscopic notation where the first number denotes the principle energy level the letter designates the subshell and then the subscript gives us the number of electrons in that subshell now to write out the atoms electron configuration we need to know the order in which subshells are filled electrons they fill from lower to higher energy subshells according to off bous principle and each subshell will fill completely before electrons begin to enter the next one now here we see a list of the ordering from lower to higher energy subshells we have 1 s then 2 s then 2 p 3 S followed by 3 p then 4S then 3D then 4p 5S 4D 5p 6s 4f 5D 6p 7s so on and so forth now this is a lot too memorize but an easier way to approach electron configuration is through simply reading the periodic table so what I'm going to do is I'm going to scroll down here all right and we saw an image earlier about which blocks refer to which subshell so this right here is our s shell here is where our P subshells here are our D subshells and these refer to our F subshells I'm going to go back to it just to show it to you again all right right here our s block P block d block and F block and if we just remember that then we can read electron configuration just by looking at our periodic table if we're interested in an element that is like right here then what we can do to write its electron configuration is read the periodic table like a sentence we go through one s and we fill both of those so 1 S2 cuz there's two of them then the next thing we fill is the 2s subshell and we fill both of them here so 2s2 all right and remember in an S subshell you can only fit in two electrons then we make it to the P block all right and here we pass through 1 2 3 4 5 six elements and that is the most electrons that you can fit in a p subshell so we write 2 P6 then this is followed by the 3s subshell 3 S2 and then we make it to this element right here this mystery element all right and that is the P block the 3 p all right but we're only filling in two of these so 3 P2 and just like that we can read off of the periodic table the electron configuration so this is the electron configuration for this unknown element right here now keeping that in mind let's just go over some tips and tricks to keep in mind to write an electron configuration first you want to start with the element and then add electrons one by one following the subshell order that's indicated by that periodic table remember use the offb principle to determine the subshell filling order 1 S 2 S 2 p then 3s then 3 p then 4S then 3D and so on and so forth make sure to apply the poly Exclusion Principle to ensure that each orbital gets at most two electrons with opposite spins and then follow Hun's rule by filling all orbitals in a subshell singly before pairing electrons in one orbital now with that let's do a couple of example problems to make sense of that workflow okay so this first problem says which will F fill first the 5D subshell or the 6s subshell so we can easily look at our ordering here or we can also just work through it mentally so we can look at our 5D that's right here all right and then our 6s is right here all right 6s comes before we make it to 5D all right so 6s subshell has lower energy and it will fill first now we can also work through it like this so for the 5D orbital our n is going to be equal to five and L is going to be equal to two because that's what refers to the D subshell now what we can do here is we can add the principal quantum number and we can add the angular momentum quantum number together n plus L and this gives us a value of seven okay keep that in mind we're going to talk about this little trick right here then we can do that for 6s the N here is equal to 6 and this is the s subshell so L is going to be equal to zero let's add up the principal quantum number and the angular momentum quantum number this gives us a value of six all right six is less than seven so this is a lower energy shell and it will be filled up first so the 6s subshell has lower energy and it will fill first so this is a quick trick that you can do to figure that out if you forget the ordering figure out the quantum number the angular momentum quantum number sum them up and the one with a smaller value is going to fill first because it is lower energy okay let's do some more problems this one is really fun this says what is the electron configuration for nitrogen and then according to Hun's rule what is the orbital diagram okay so let's find where nitrogen is nitrogen is right here all right I'm going to point to it in Black and we're going to write the electron configuration for nitrogen we're just going to read it off of the periodic table all right we start off with 1 s one and two we fill up the 1 s orbital with the maximum two electrons then we make it through the 2s part and we fill both electrons in that orbital as well now we've made it to the P block the 2p block and we make it through 1 2 three elements before we get to nitrogen so this is going to be 2 P3 that is the electron configuration for nitrogen wonderful now what we want to do is we want to draw the orbital diagram for nitrogen according to Hun's rule so what we need here is we need to remember that nitrogen has atomic number of seven and its electron configuration we just figured out is 1 S2 2 S2 2 P3 according to Hun's rule the two s orbitals are filled completely so if we draw a 1 S2 orbital this has both electrons in it and if we draw the 2 S2 orbital this has also both electrons in it now we can draw the two p orbital this has three orbitals Each of which can have two electrons this is where we have to really remember Hun's rule which says that you that you will fill each orbital with one electron before you double up all right so this is our 2p orbital we have three electrons that we need to fit in here we're going to put them in each separate orbital we will not draw them like this this breaks Hun's rule we have to draw each electron as a single electron in each orbital before we pair up any electrons so this is the electron configuration for nitrogen and this is how we would draw the orbital diagram for nitrogen following Hun's Rule now there's one more thing I want to talk about before we end the chapter in the realm of electron configurations there are a few exceptions to the predicted order of filling orbitals particularly within the transition metals here these exceptions arise because of subtle differences subtle energy differences between orbitals which can lead to more stable Arrangements when orbitals are either half filled or fully filled now there are two keep key exceptions that we should know chromium and copper so for chromium we can write the electron configuration as so 1 S2 2 S2 2 P6 3 S2 3 P6 4 S2 and 3 D4 3 D4 because chromium is is right here all right so 1 S2 2 S2 3 P6 3 S2 3 P6 4 S2 and then 3 D4 now also by the way sometimes notations can be simplified since this is so long so sometimes what people will do will they will write the electron configuration in a simple way they take the most recent noble gas that you would pass before you get to your element of Interest here that would be our Aron and then they would write argon in Brackets and then they would just write the following electron configuration after argon which would be 4s2 3 D4 now here for chromium according to the rules established this would be the electron configuration however actually moving one electron from the 4S subshell to the 3D subshell will allow the 3D subshell to be half filled so if one electron moved from here to here and we would have 4s1 3d5 this would actually result in a half-filled orbital remember D orbitals have five the D shell has five orbitals five orientations and if you had five electrons to fit into these orbitals you would simply put one in each based off of Hun's Rule and having this half-filled shell is extremely desirable so much so that the actual electron can configuration for chromium is 4 S1 3d5 instead of what you would assume following the convention we talked about all right so chromium is an exception another exception here that we want to talk about is copper so copper is right here if we were to write the electron configuration for copper keeping our easy not notation we can write argon and this is going to be 4s2 3 D9 so close to having a full D subshell and actually this would not be the correct electron configuration you would have one electron that moves over here to satisfy a full shell so it's going to be 4s1 3d10 all right and that's because it's just more energetically favorable to have a full Dell than it would be to have an S shell here so these are the two exceptions to keep in mind copper and chromium there are more but for General chemistry these are the main ones that we should commit to memory with that we've completed everything that we wanted to for this chapter please let me know if you have any questions comments or concerns other than that good luck happy studying and have a beautiful beautiful day future doctors