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# Quantum numbers

## Video transcript

in the Bohr model of the hydrogen atom the one electron of hydrogen is in orbit around the nucleus at a certain distance R so in the Bohr model the electron is in orbit in the quantum mechanics version of the hydrogen atom we don't know exactly where the electron is but we can say with high probability that the electron is in an orbital and an orbital is the region of space where the electron is most likely to be found so for hydrogen imagine a sphere so a three-dimensional volume fear around the nucleus and somewhere in that region of space somewhere in that sphere we're most likely to find the one electron of hydrogen and so we have these two competing visions right so the Bohr the Bohr model is classical mechanics right the electron orbits the nucleus like the planets around the Sun but quantum mechanics says we don't know exactly where that electron is and the Bohr model turns out to be it turns out to be incorrect and quantum mechanics has proven to be the best way to explain to explain electrons in orbitals and we can explain we can describe those electrons in orbitals using the four quantum numbers and so let's look at the first quantum number here so this is called the principal quantum number and the principal quantum number is symbolized by n so n is a positive integer so n could be equal to 1 2 3 and so on it indicates the main energy level occupied by the electron so this tells us this tells us the main energy level and you might hear this referred to as a shell sometimes so we could say what kind of shell the electron is in as n increases the average distance of the electron from the nucleus increases and therefore so does the energy so for example if this was this was our nucleus right here and let's talk about n is equal to 1 so for n is equal to 1 let's say the average distance from nucleus is right about here let's compare that with n is equal to 2 as equal to 2 means a higher energy level so on average the electron is further away from the nucleus and has a higher energy associated with it so that's the idea of the of the principal quantum number you're thinking about energy levels or shells and you're also thinking about average distance from the nucleus alright our second quantum number is called the angular momentum quantum number so the angular momentum quantum quantum number is symbolized by L and L indicates the shape of the orbital so this will tell us this will tell us the shape of the orbital values for L are dependent on n so the values for L go from zero all the way up to n minus 1 so it could be 0 1 2 or however numbers how are values that are are up to up to n minus 1 for example let's talk about the first main energy level or the first shell so n is equal to 1 there's only one possible value you could get for the angular momentum quantum number L and minus 1 is equal to 0 is equal to 0 so that's the only possible value the only allowed value of L when L is equal to 0 we call this an S orbital so this is referring to an S orbital and the shape of an S orbital is a sphere so we've already talked about that with with the hydrogen atom so just imagine this as being a sphere right so a three-dimensional volume here so the angular momentum quantum number L since L is equal to 0 that corresponds to an S orbital so we know that we're talking about an S orbital here which is shaped like a sphere so the electron what is is is most likely to be found somewhere in that sphere let's do the next shell so n is equal to 2 so if n is equal to 2 what are the allowed values for L so L goes 0 1 and so on all the way up to n minus 1 so L is equal to 0 and then n minus 1 it would be equal to 1 so we have 2 possible values for L L could be equal to 0 and L could be equal to 1 notice notice that the number of allowed values for L right is equal to n so for example if n is equal to 1 we have 1 allowed value if n is equal to 2 we have 2 allowed values all right we've already talked about what L is equal to 0 what that means right so L is equal to 0 means an s-orbital shaped like a sphere but now in the second main energy level right or the second shell we have another value for L so L is equal to 1 and when L is equal to 1 we're talking about AP orbital so L is equal to 1 means a p orbital and the shape of a p-orbital is a little bit strange so I'll attempt to sketch it in here so you might hear several different terms for this so imagine this is a volume right this is a three-dimensional region in here so you could call these dumbbell shaped or bowtie whatever makes the most sense to you but this is this is the this is the orbital this is the region of space or the electron is most likely to be found if it's found in AP orbital here sometimes you'll you'll call the you'll hear these called sub shells alright so if n is equal to 2 if we call this if we call this a shell right if we call this a shell then we would call these sub shells okay so these are sub shells here and again we're talking about orbitals L is equal to 0 s and S orbital L is equal to 1 is AP orbital let's look at the next quantum number so let's get some more space down here so this is the magnetic quantum number symbolized by M sub L here so M sub L indicates the orientation of an orbital around the nucleus so this tells us this tells us the orientation of that orbital and the values for M L depend on L so ml so ml is equal to ne integral value that goes from negative L to positive L all right so that sounds a little bit confusing let's go ahead and do let's go ahead and do the example of L is equal to zero all right so L is equal to zero up here so let's go ahead and write that down here if L is equal to zero what are the allowed values for ML there's only one all right there's only one the only possible value we could have here is zero so when L is equal to zero when L is equal to zero let me use a different color here so if L is equal to zero we know we're talking about an s-orbital right when L is equal to zero we're talking about an S orbital which is shaped like a sphere and if you think about that we have only one allowed value for the magnetic quantum number that tells us the orientation so there's only one orientation for that orbital around the nucleus and that makes sense because a sphere has only one possible orientation so if you if you think about this as being as being um an XYZ axis excuse me and if this is a sphere there's only one way to orient that sphere and space and so and so that's the idea of the magnetic quantum number all right let's do let's do the same thing for L is equal to one alright so let's look at that now so if we're for considering L is equal to one let me use a different color here so L is equal to one let's write that down here if L is equal to one what are the allowed values for the magnetic quantum number so ml is equal to this goes from negative L to positive L so any integral value from negative L to positive L well negative L would be negative one so let's go and write this in here so we could have negative one zero and positive one so we have three possible values all right so when L is equal to one we have three possible values for the magnetic quantum number so so one two and three the magnetic quantum number tells us the orientations right so the the possible orientations of the orbital orbitals around the nucleus here so we have three values for the magnetic quantum number that means we get three different orientations and we already said that when L is equal to one we're talking about AP orbital and a p orbital is shaped like a dumbbell here so we have three possible orientations for the four up for a dumbbell shape alright so if we went ahead and put some mark these axes here let's just say this is x axis y axis and and the z axis here so we could put a dumbbell we can put a dumbbell on the x axis like that so again imagine this as being a volume this would be a P or but we call this a px orbital right it's a p orbital and it's on the x axis here so we have two more orientations right so we could put again if this is X this is y and this is Z we could put a dumbbell alright we could put a dumbbell here on the y axis so there's our second possible orientation and then finally if this is X this is y and this is Z of course we could put a dumbbell on the z axis like that so this would be a P Z orbital so we could write we could write a P Z orbital here and then this one right here would be a P Y orbital so we have three we have three orbitals we have three P orbitals here all right so one for each axis alright let's let's go to the last quantum number so the last quantum number is the spin quantum number so the spin quantum number is M sub s here and so when it says spin I'm gonna put this in in quotations like this this seems to imply that an electron is spinning on an axis so that's not really what's happening but let me just go ahead and draw that in here so I could have an electron let me draw two different two different versions here so I could have I could have an electron spin like a top if you will this way or I could have an electron spin around that axis going this way and again this is not actually what's happening in reality the electrons don't really spin on an axis like a top but it does help me to think about the fact that we have two possible values for the spin quantum number so you could spin one way so you could say we could say the spin quantum number is equal to positive 1/2 so usually you hear that called spin up so spin up and we'll symbolize this with an arrow going up in later videos here and then and then the other possible value for the spin quantum number so the spin quantum number is equal to a negative 1/2 so you usually hear that referred to as spin down and you could put an arrow going down so again electrons electrons aren't really aren't really spinning in a physical sense like this but again - if you think about two possible ways for an electron to spin then you get these these two different these two possible spin quantum quantum numbers so positive 1/2 or negative 1/2 so those are the four quantum numbers and we're going to use those to again think about electrons in orbitals