in this video we're going to talk about quantum numbers there's four of them that you need to know and basically the quantum numbers tell you the address of an electron inside an atom every electron has a unique set of four quantum numbers based on the pauli exclusion principle the first one is n n is the principal quantum number and n is an integer 1 2 3 4 and so forth and can be zero the principal quantum number describes the energy level of an electron inside an atom so looking at the picture on the right we basically have a boy's model of the atom and we can see that the first shell represents the first energy level the second circle is the second energy level where n is two and the third circle is the third energy level and the string and so that's the first number you need to be familiar with the principal quantum number now the next quantum number that you need to be familiar with is the angular momentum quantum number this number is indicated by the symbol l and it describes the shape of the sub level within an energy level now we have four different sub levels that you're going to see on a regular basis the first one is the s sublevel which is basically a sphere the second one is the p sub level and then we have the d sub level and the f sub level now what you need to know is that for the s sublevel l is always a zero for p l is one for d the angle momentum quantum number is two and for f l is always three now let's talk about the relationship between n and l l is less than or equal to n minus one and l and n are both integers so let's talk about what this means when n is one l can only have one value that's n minus one or one minus one which is zero now when n is two according to this equation here l has to be less than or equal to n minus one or two minus one which is one so that means l could be zero or one and this expression will be true now what about when n is string when n is three the maximum that l can be is three minus one or two so l can be zero one or two when n is four l could be 0 1 2 or 3. now let's think about what this means so remember when l is 0 what sublevel do we have when l is 0 this corresponds to s now when n is 2 l could be 0 or 1 which means that we can have the s or the p sub level when n is 3 l could be 2 so we can have the s p or d sublevel and when n is 4 we can have the s p d or f sub levels now notice that there's no one p sub level this does not exist the first energy level doesn't have the p sub level and let's say if you were to write the electron configuration for an element you'll know that there is no 2d sublevel you have 2s and 2p but not 2d in the third level you could have 3s 3p 3d but not 3f so 3f is not possible now you could have 4f that's possible now here's a question for you let's say we have an electron in the 3d sublevel based on that information what is the n value and the l value that corresponds to an electron in the 3d sublevel n is basically the number that you see here so n is 3 now for the d sub level l is what value so if you recall for the s sublevel l is always zero for the p sublevel l is one for the d sublevel l is 2 and for the f sub level l is always 3. so for the 3d sublevel n is 3 and l is going to be 2. so let me give you another example what if we have an electron in the 4f sublevel what's n and what's l as we can see n is the number in front of f so n is 4 and f always corresponds to an l value of three so for an electron in the four f sub level n is for ls3 now let's move on to the third quantum number which is the magnetic quantum number represented by the symbol m sub l this number describes the orbital within a sublevel an orbital is basically a region in space in which the probability of finding an electron is very high in an orbital an electron can have an upspin or a downspin and so every orbital can hold a maximum of two electrons but now let's talk about the relationship between l and m sub l so as we said before l is the angular momentum quantum number m sub l is the magnetic quantum number so when l is zero we have the s sublevel and ml can only be zero when l is one we have the p sublevel and the p sub level has three orbitals the first one has the ml value negative one the second one is zero and the third one has an ml value of one when l is two we have the d sublevel and there are five d orbitals negative two negative 1 0 1 and 2. when l is 3 we have the f sublevel which has 7 orbitals negative 3 negative 2 negative 1 0 1 2 and 3. so what you need to know is this ml is between negative l and l so let's say if l is 4 that means ml will be an integer between negative four and four so it could be negative four negative three negative two negative one zero one two three four so this expression shows the relationship between ml and l so let's say if we have the 1s sublevel s only has one orbital and for s l is 0 and ml which is this number will also be zero now let's say if we're focused on the 2p sublevel p has three orbitals now for 2p we know that n is 2 and for p l is always 1. because l is 1 ml could be negative 1 0 or 1. and so as you can see the ml values they correspond to the specific orbitals within a sub-level now let's say if we have the 3d sublevel where n is 3 and l is 2. now the d sub sublevel has five orbitals which means that it can hold a maximum of ten electrons because you can put two electrons per orbital since l is true ml could be anywhere from negative two to two and so each ml value corresponds to a specific orbital in the sub level lastly let's go over four f where n is four and l is 3. the f sublevel has 7 orbitals where ml can vary between negative 3 and positive 3. so hopefully this helps you to see the relationship between l and m l which gives you these numbers now the last quantum number that we need to talk about is something known as the electron spin the symbol that corresponds to this is m sub s now the electron spin could be one of two values positive or negative one half now recall that an electron in within an orbital can either be going up or down so if it's going up the spin is positive one-half and if the arrow is going down the electron spin is negative one-half so that's the last quantum number that you need to be familiar with now let's say if we have the 3d eight electron what are the four quantum numbers that correspond to the 3da electron what would you say well we know that n has to be 3 based on this number and for the d sublevel l is always 2. now we know that d has five orbitals and so the ml values will range from negative two to two now we need to find the location of the eight electron the location will tell us the ml value and also the ms value now ms will always be either positive or negative a half which i'll explain shortly so let's start with parallel spins facing upward so this is 3d1 3d2 3d3 3d4 35 3d6 7 8. so the 3d8 electron it landed in this orbital where ml was 0. now we have a down arrow which means the electron spin is negative one-half but now you might be wondering okay what if we started with down arrows as opposed to arrows facing upward so this won't affect your ml value but it will affect your ms value so this is one two three four five six seven eight in this case the eighth electron is still in the same orbital but this time it has an upward spin of positive one half so this can vary this can always be either plus or minus one half depending on how you draw it but these three numbers will be consistent ns3 ls2 and ml0 so that's basically it for this video for those of you who like it feel free to subscribe if you haven't done so already and don't forget to click on that notification bell in addition for those of you who want a more deeper review of quantum numbers with more examples and practice problems including those with electro configuration i'm going to post a few links in the description section of this video and when you get a chance feel free to take a look at that so you're going to have uh other resources on this topic thanks again for watching