Electron Configurations
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The distributions of electrons among the orbitals of an atom is the atom's electronic structure or electron configuration.
Basically, the distributions can be laid out in this fashion (read from the bottom up):
O O O O O 6d
O O O O O O O 5f
O 7s
O O O 6p
O O O O O 5d
O O O O O O O 4f
O 6s
O O O 5p
O O O O O 4d
O 5s
O O O 4p
O O O O O 3d
O 4s
O O O 3p
O 3s
O O O 2p
O 2s
O 1s
The bottom energy level is 1--it has the lowest energy level.
Each "O" represents an orbital.
You can see that there is 1 orbital for a s subshell.
There are 3 orbitals for a p subshell, 5 for a d, and 7 for a f.
Each orbital can hold 2 electrons.
Therefore, the s subshell can hold 2 electrons, the p can hold 6, the d 10, and the f 14.
And thus, the first energy level can hold 2 electrons (1s -- 2), the second energy level can hold 8 electrons (2s2p -- 2 + 6), the third energy level can hold 18 electrons (3s3p3d -- 2 + 6 + 10), and the forth energy level can hold 32 (4s4p4d4f -- 2 + 6 + 10 + 14).
In a neutral atom, the number of electrons equals the number of protons of the atom.
When the electrons fill the orbitals, they occupy the lowest energy orbitals that are available.
For example, hydrogen is atomic number 1 (has 1 proton).
The one electron that it has occupies the lowest orbital, which is 1s.
To write it's electron configuration, it would be 1s1.
In an orbital diagram, it would simply be a circle with one up arrow in it, which represents the 1s orbital:
H
Likewise, helium has 2 protons and its electron configuration would be 1s2.
It's orbital diagram would by a circle with one up arrow and one down arrow.
He
An the same with lithium (1s22s1) and beryllium (1s22s2)
Li
Be
Now things get trickier with higher orbitals.
For example, Boron has an electron configuration of 1s22s22p1 and the orbital diagram looks like this:
B


Now one might think that carbon, with an electron configuration of 1s22s22p2 would have an orbital diagram of this:
C


But that is incorrect.
It acutally has one of this:
C


The rule for doing this is that when electrons are placed in a set of orbitals of equal energy, they are spread out to give as few paired electrons as possible.
For carbon, that means that the two p electrons are in separate orbitals.
Using that rule, we can complete the orbital diagrams for the rest of the elements of the second period.
N 1s22s22p3


O 1s22s22p4


F 1s22s22p5


Ne 1s22s22p6


The Periodic Table
The Periodic Table of the Elements is constructed and arranged so that similar chemical properties were arranged in verticle collumns called groups.
Because chemical properties are based on electronic structure (electron configurations) we can use the table to predict electron configurations for elements.
The way that the table is structured also shows how to predict electron orbitals.
On the left is a block of 2 columns, then on the right is a block of 6 columns.
In the center is a block of 10 columns, and on the bottom there is a block of 14 columns.
These numbers, 2, 6, 10, and 14, are the numbers of electrons that can occupy the s, p, d, and f subshells.
Chemical properties of an elements are basically how different elements bond to each other to form compounds.
The valence shell or the outer shell (the shell with the highest energy level) is the one mainly responsible for how an element reacts to form compounds.
The core electrons are the rest of the electrons, and they are buried deep within the atom and usually do not play a role in chemical reactions.
Elements with similar properties should have similar valence shell electron configurations.
Going down one column of the periodic table, one can see that the valence shell electron configurations are similar.
For example (valence shell in bold):
Li 1s22s1
Na 1s22s22p63s1
K 1s22s22p63s23p64s1
Rb 1s22s22p63s23p63d104s24p64d105s1
Cs 1s22s22p63s23p63d104s24p64d105s25p66s1
During chemical reactions, elements like to gain or lose electrons in order to achieve the electron configuration of a noble gas.
The noble gases are the elements that have filled their orbitals completely.
They appear on the column on the far right side of the periodic table, and they include helium, neon, argon, krypton, xenon, and radon.
The elements above like to lose their s1 electron.
Because the noble gases have filled their orbitals, they are mostly inactive.
Simplifying Electron Configurations
Sometimes, electron configurations can get very long.
To simplify writing them, the core electron configuration can be substituted with the symbol of the noble gas which has the same core configuration.
For example, instead of writing
K 1s22s22p63s23p64s1
you can write
K [Ar] 4s1
because argon has the same electron configuration as the core configuration.
Unexpected Electron Configurations
There are a few exceptions to the rule for writing electron configurations.
They happen with the d subshell (the transition elements) and the f subshell (the inner transition elements).
It is because the d subshell sometimes will overlap with the proceeding s subshell, and the f subshell sometimes will overlap with the proceeding s or d subshells.
For example, chromium and copper have the following configurations:
Cr [Ar] 3d54s1
Cu [Ar] 3d104s1
The corresponding diagrams are:
Cr [Ar] 



Cu [Ar] 



One would expect the s subshells to be filled and have 2 electrons instead of 1.
But it is prefered to have the 3d subshell exactly half-filled or completely filled, and an s electron is borrowed to complete it.