Quantum Numbers, Atomic Orbitals, and Electron Configurations

0:00 professor Dave here, let's learn about quantum numbers now that we understand that electrons are both particles and waves we are ready to learn about how electrons are arranged in an atom. the location and energy of every electron in an atom is determined by a set of 4 quantum numbers that describe different atomic orbitals. an orbital is a region of probability where an electron can be found. there are s, d, p, and f orbitals with different shapes and they look like this remember these shapes are not electrons, just regions in space where electrons can be and each one can hold up to two electrons. the more electrons an atom has the more of these orbitals it will need to accommodate them all. the first quantum number is the principal quantum number n, which can have any positive integer value. we saw this when we learned about the Bohr model, it represents the energy level of the electron. each orbital will have an n value and the larger the value of n the further away from the nucleus it is. the

1:07 next quantum number is the angular momentum quantum number l, this can have any value from 0 to n minus one. for example if an electron has an n value of three it can have an L value of either zero, one, or two because two is 3-1. the L value describes the shape of the orbital. when l equal 0 we are describing s orbitals which are spherical, just one of these per energy level. when l equals one we are describing P orbitals which are lobes that extend outwards on three axes. there are three of these per energy level. when l=2 we are describing d orbitals which are weird looking, five of these per energy level. and when l equals three we get f orbitals, which are even weirder looking, 7 per energy level. next we have the magnetic quantum number m sub l. this could have a value of anywhere from negative L to L so if L is 2 m sub l can be -2, -1 1, 0, 1 or 2. this quantum number determines

2:08 how many orbitals there are of a type per energy level and therefore describes a specific orbital amongst a particular set. when l is zero m sub l must also be 0 and that's why there's only one s orbital per energy level. when l is one m sub l can have three values which is why there are three P orbital energy level. an L value of two gives us five values for m sub l and five d orbitals, and an L value of three gives us the seven f orbitals the last quantum number is an easy one, it's the spin quantum number m sub s. this one will be either one half or negative one-half no matter what. so every electron in an atom has a unique set of quantum numbers, no two electrons in an atom can have precisely the same four quantum numbers as stated by the Pauli exclusion principle. this is because any orbital can only hold up to two electrons and even the two electrons in the same exact orbital will have

3:09 opposite spin values. so let's try to describe different sets of quantum numbers and what they mean. when n equals 1, l must be zero and m sub l must also be 0, that means we are describing the 1s orbital. it can accommodate two electrons which will have spins of half and negative one-half respectively this is the lowest energy orbital so any atom on the periodic table will fill this orbital first. the electrons in hydrogen and helium occupy this orbital since they have only one and two electrons respectively. when n=2 l can be zero which would give us the 2s orbital or l can be 1 meaning m sub l could be -1, 0 or 1 giving us the 2p orbitals. the outermost electrons in the second row of the periodic table will occupy these orbitals when n equals 3, l could be zero, giving us the 3s orbital, l can be a giving us the 3p orbitals or l can be 2, giving us the 3d orbitals. a large atom will have to

4:14 use all of these orbitals and more to house all of its electrons. the Aufbau principle tells us the order in which an atom will fill up its orbitals this is determined by their relative energies. orbitals that are further away from the nucleus have higher potential energy so it'll be 1s first, then 2s then 2p, 3s, 3p and so forth. we can use this to determine the electron configuration of any atom. for example a neutral chlorine atom has 17 electrons. looking at the orbitals, each of which can hold two electrons, let's fill them up starting at the lowest energy and then climb upwards. the 1s orbital gets two electrons, one spin up the other spin down, then the 2s then the 2p's, then the 3s and the last five will go in these 3p orbitals Hund's rule says that for electrons of the same energy you put one electron in each orbital first before doubling them up, so one two three four and five gives us a

5:16 total of 17 electrons for chlorine. that means chlorine has an electron configuration of one 1s2 2s2 2p6 3s2 3p5. the numbers before the letters are the n value for the orbital, the numbers after the letters tell you how many electrons sit in each type of orbital if you want a quicker way to determine electron configurations just know which areas of the periodic table correspond to which types of orbitals. this area is called the s block this is the p block here's the d block and then the f block when we are determining the electron configuration for an atom of a given element the easiest way to do it is just travel left to right and up to down on the table until you get to the element, since each element has one more electrons in the last. looking at chlorine again the top row is just the 1s orbital, that's full so 1s2. going to the second row where n

6:13 equals two we fill the 2s orbital which holds two electrons, hence two elements, the 2p orbitals which hold six so we pass six elements, then the next row down we fill the 3s orbital and lastly we get to the 3p's and count 1, 2, 3, 4, 5. 3p5. a common abbreviation is to use the noble gas from the row above and list it in brackets. this would be read as neon core and it implies the ground state electron configuration of neon. then you just list the valence electrons of the element or the ones that correspond to the row it is in. we can use orbital diagrams to visually depict how the orbitals are filled and they look like this. don't forget Hund's rule. fill each set halfway before doubling up. for a quick definition, atoms with unpaired electrons in their orbital diagrams are called paramagnetic and are attracted by a magnetic field. atoms with all of their electrons paired are diamagnetic and are

7:11 not affected by a magnetic field. so to summarize, n tells us the energy level L tells us what type of orbital, m sub l tells us which specific orbital amongst a set, and m sub s tells us the spin. each electron in an atom has a unique set of quantum numbers and an atom will fill up orbitals with electrons according to the Aufbau principle until all of its electrons have a place to stay this is a tricky concept, if you feel confused try watching one more time from the top, otherwise let's check comprehension

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