Electron Configurations
Knowledge/Understanding:
•	how electron configurations represent the quantum states of all of the electrons in an atom
Skills:
•	write the ground-state electron configuration for any element on the periodic table
•	relate the quantum state to the orbital notation electron configuration
•	predict & explain apparent exceptions to the aufbau principle
The following chart shows the relative amounts of energy that the electrons in each sublevel have.  (Lowest energy is at the bottom, and highest energy is at the top.)

This can be confusing, because the levels overlap.  For example, notice that the 3d sub-level is higher in energy than the 4s sub-level.
This means that the electrons will fill sub-levels in the following order:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...
The following “road map” shows the order in which sub-levels are filled, from lowest to highest energy:

To read this map, start at the top.  The arrow leads you through the sub-levels in order, from lowest to highest energy.  The arrow goes through 1s first, then 2s, then 2p & 3s, then 3p & 4s, then 3d, 4p, & 5s, and so on.
Some people find it easier to just use the periodic table as the “road map”:
As you move through the elements in order by atomic number, you are moving through the sub-levels from lowest to highest energy.
Remember that the “s” sub-levels start with 1s, the “p” sub-levels start with 2p, the “d” sub-levels start with 3d, and the “f” sub-levels start with 4f.  The “gotchas” are:
•	The 3d sub-level is in row 4, right after 4s.
•	The 4f sub-level is in row 6, right after 6s.
Writing Electron Configurations
An element has electrons that correspond with each of the available quantum states, from the beginning of the periodic table (where hydrogen is located) up to where that element is located.
If we were to represent an electron as an arrow, we could represent two electrons in a 1s sub-level like this:  .  The 1s sub-level has one orbital, which is represented by the one blank.  The two electrons are represented as arrows.  Because two electrons sharing an orbital have opposite spins, we represent them with one arrow pointing up and the other arrow pointing down.  The two quantum states associated with these two electrons would be {n = 1; ℓ = 0; mℓ = 0; ms = −½} and {n = 1; ℓ = 0; mℓ = 0; ms = +½}.

We could represent five electrons in a 2p orbital like this:  .  The 2p sub-level has 3 orbitals, represented by the 3 blanks.  Two of those orbitals have two electrons in them, and the third one has only one electron.  The quantum states associated with these five electrons are:
{n = 2; ℓ = 1; mℓ = −1; ms = −½}, {n = 2; ℓ = 1; mℓ = −1; ms = +½},
{n = 2; ℓ = 1; mℓ = 0; ms = −½}, {n = 2; ℓ = 1; mℓ = 0; ms = +½}, and
{n = 2; ℓ = 1; mℓ = +1; ms = −½}.

We could represent all 13 of the electrons in aluminum like this:

This diagram shows the electron configuration of aluminum.
The quantum states represented are:
{n = 1; ℓ = 0; mℓ = 0; ms = −½}, {n = 1; ℓ = 0; mℓ = 0; ms = +½},
{n = 2; ℓ = 0; mℓ = 0; ms = −½}, {n = 2; ℓ = 0; mℓ = 0; ms = +½},
{n = 2; ℓ = 1; mℓ = −1; ms = −½}, {n = 2; ℓ = 1; mℓ = −1; ms = +½},
{n = 2; ℓ = 1; mℓ = 0; ms = −½}, {n = 2; ℓ = 1; mℓ = 0; ms = +½},
{n = 2; ℓ = 1; mℓ = +1; ms = −½}, {n = 2; ℓ = 1; mℓ = +1; ms = +½},
{n = 3; ℓ = 0; mℓ = 0; ms = −½}, {n = 3; ℓ = 0; mℓ = 0; ms = +½}, and
{n = 3; ℓ = 1; mℓ = −1; ms = −½}
electron configuration:  a description of which levels and sub-levels the electrons in an element are occupying.
Notice that we have to show all three of the orbitals (blanks) in the 3p sub-level, even if some of those orbitals don’t have any electrons in them.
ground state:  when all of the electrons in an atom are in the lowest-energy sublevel that has an available “slot”.
Pauli Exclusion Principle:  every electron in an atom has a different quantum state from every other electron.  In plain English, this means that something has to be different about each electron, whether it’s the level, sub-level, which orbital it’s in, or its spin.
aufbau principle:  in the ground state, each electron in an atom will occupy the lowest available energy state.  In plain English, this means that you start with the lowest sub-level (1s) and work your way up until you’ve used up all the electrons.

X

Hund’s Rule:  electrons don’t pair up in orbital until they have to.  (This is kind of like siblings not wanting to share a room if there’s an empty room available.)  For example, the electron configuration for nitrogen would be:

Wrong:  
Right:  

If you don’t need to draw every electron, you can use a shorter form, in which you just write the level and sub-level, and use a superscript for the number of electrons in the sub-level.
For example,  would become 1s2, and  would become 2p6.
The electron configuration for aluminum would go from the orbital notation version:

to the “standard” version:
1s2 2s2 2p6 3s2 3p1
The shorter version can still get tediously long for elements with a lot of electrons.  For example, the electron configuration for gold (Au) is:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d9

To shorten this even more, you’re allowed to use the element in the last column of a row as an abbreviation for all of the electrons through the end of that row.
In our example, gold (Au) is in the 6th row of the periodic table:
This means we’re allowed to start from xenon (Xe) at the end of the previous (5th) row, and add on the parts that come after Xe.  This gives us:
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6  6s2 4f14 5 d9

	Noble gas configuration: 	[Xe] 6s2 4f14 5d9
This notation is called the noble gas configuration, because the elements in the last column are called the noble gases.

Apparent Exceptions to the Aufbau Principle
Atoms are the most stable when their electrons are the most evenly distributed within the atom’s energy levels and sub-levels.  This means that elements with completely filled principal (numbered) energy levels are the most stable.  
•	The “noble gases” (the last column of the periodic table) already have all of their principal energy levels completely filled with electrons.  This makes them very stable, because they do not need to react with other atoms to get their electrons into a more stable configuration.  This is why noble gases almost never react with anything.
•	Other elements gain, lose, or share electrons (in chemical reactions) in order to end up with electron configurations that are like the nearest noble gas on the periodic table.
Atoms with p, d, and f sub-levels that are exactly half full are more stable than atoms with slightly more or fewer electrons in their p, d, and f sub-levels.  This makes those atoms slightly more stable (and therefore less reactive) than other atoms.  For example, nitrogen ([He] 2s2 2p3), which has an exactly half-filled 2p sub-level, is chemically less reactive than oxygen ([He] 2s2 2p4).  Manganese ([Ar] 4s2 3d5), which has an exactly half-full 3d sub-level, is chemically less reactive than iron ([Ar] 4s2 3d6).
In fact, elements with a d or f sub-level that is one electron away from being half full will “borrow” one electron from the nearest s sub-level, because the half-filled d or f sub-level is more stable than the full s sub-level.

For example, chromium“borrows” one of its 4s electrons to make its 3d sub-level exactly half full.  This means that instead of having predicted electron configuration of [Ar] 4s2 3d4, it actually has the electron configuration [Ar] 4s1 3d5.  This happens because a half-filled 4s sub-level plus a half-filled 3d sub-level is more stable than a completely filled 4s sub-level plus a 3d sub-level with 4 electrons in it.
Similarly, copper “borrows” one of its 4s electrons to make its 3d sub-level completely full.  This means that instead of having predicted electron configuration of [Ar] 4s2 3d9, it actually has the electron configuration [Ar] 4s1 3d10.  Again, this happens because a half-filled 4s sub-level plus a completely filled 3d sub-level is more stable than a completely filled 4s sub-level plus a 3d sub-level with 9 electrons in it.