Well lets say you have a Hydrogen atom. It only has 1 electron - so the principal quantum number must be 1 - OK so far?
Actually that is too easy - let me take Samarium -element number 62 - makes it more interesting don't you think? We will fill by the Aufbau principle and note the Pauli exclusion principle that no two electrons can have the same set of quantum numbers because they cant occupy the same space. So Samarium must be 1s2 ,2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6 (that takes us to Krypton by the way) then it would go 5s2, 4d10, 5p6 (up to Xenon) 6s2 4f6 (Lanthanum would have been interesting by the way having 5d1 but lets not go there)
OK so what does this mean. Well the principle quantum number is 6 - and the azimuthal quantum numbers (I am sorry I know you could use orbital angular momentum quantum number, but my first professor taught me azimuthal) must be 0 up to 5 - So s =0, p=1, d=2, f=3 (g and h are possible in theory )
I just realized I should have chosen Europium as that would be f7 - and that would give us what is called "Maximum spin multiplicity" - the electrons in these orbitals would all align parallel. I liken it to a train (there you are mods back on topic of trains) - person one fills an empty seat but person 2 would not sit next to that person but fill another empty seat. This is energetically favorable.
Now this post has got too long so I will continue with magnetic and spin quantum numbers in a later post. Notice I use orbital - the region of maximum probability of finding an electron - not the old Bohr model of orbit.
By the way if you integrate over all areas of space then the probability of finding the electron must be 1 !! The electron has to be somewhere!
Now of course you might say to yourself - well this guy could have just googled all this and cut and pasted or similar - but you are welcome to continue this in private email
Graham A. Howarth, BSc (Hons), MSc(distinction); DIC, C.Chem, FRSC, FTSC, C.Sci, MICorr, MIM - now that is just me being a total showoff.