Credits For ChemWiki

• Introduction To Electron Configuration

Before we begin assigning the electrons of an atom into orbitals, we must first familiarize ourselves with the basic concepts needed to become fluent in electron configurations. Every element on the periodic table consists of an atom which is composed of protons, neutrons, and electrons. In these situations, we are concerned with the electrons. Electrons exhibit a negative charge and are found around within the nucleus of the atom. Electron orbitals are the position of the electrons around the nucleus and is determined as the volume of space in which the electron can be found within 95% probability. The four different types of orbitals s,p,d, and f have different shapes and one orbital can hold a maximum of two electrons. The p, d, and f orbitals have different sublevels unlike the s orbital and thus can hold more electrons. Each of the these subshells can hold a different number of maximum number of electrons.

As stated, the electron configuration of each element is unique to its position on the periodic table. The energy level is determined by the period and amount of electrons by the atomic number of the element. Orbitals on different energy levels are similar to each other, but they occupy different areas in space. The 1s orbital and 2s orbital both have the characteristics of an s orbital (radial nodes, spherical volume probabilities, can only hold two electrons, etc.) but as they are found in different energy levels they occupy different spaces around the nucleus. Each orbital can be represented by specific blocks on the periodic table. The s-block is the region of the Alkali metals including Helium (groups 1 & 2), the d-block is the Transition metals (groups 3 to 12), the p-block are the main group elements from group 13 to 18, and the f-block are the Lanthanides and Actinides series.

Chemistry

sing the periodic table to determine the electron configurations of atoms is key, but also keep in mind that there are certain rules to follow when assigning electrons to different orbitals. The periodic table is an incredibly helpful tool in writing electron configurations.

• $S, P, D, and$ $F$ $Block$

• $S$ $Block$

The $S$ block in the periodic table of elements occupies the alkali metals and alkaline earth metals, also known as groups $1$ and $2$. Helium is also part of the $S$ block. The principal quantum number “n” fills the s orbital. There is a maximum of two electrons that can occupy the $S$ orbital.

• $P$ $Block$

The $P$ block contains groups $13, 14, 15, 16, 17,$ $and$ $18$, with the exception of Helium. (Helium is part of the $S$ block.) The principal quantum number “n” fills the p orbital. There is a maximum of six electrons that can occupy the $P$ orbital.

• $D$$Block$

The $D$ block elements are found in groups $3, 4, 5, 6, 7, 8, 9, 10, 11,$ $and$ $12$ of the periodic table. The $D$ block elements are also known as the transition metals. The $D$ orbital is filled with the electronic shell “n-1.” There is a maximum of ten electrons that can occupy the $D$ orbital.

• $F$$Block$

The $F$ block elements are the lanthanides and actinides. The $F$ orbitals of the electron shell are filled with “n-2.” There is a maximum of fourteen electrons that can occupy the $F$ orbital.

• Rules for Assigning Electron Orbitals

• Occupation of Orbitals

The first thing to keep in mind is that electrons fill orbitals in a way to minimize the energy of the atom. This would mean that the electrons in an atom would fill the principal energy levels in order of increasing energy (the electrons are getting farther from the nucleus). The order of levels filled would look like this:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p

One way to remember this pattern, probably the easiest, is to refer to the periodic table and remember where each orbital block falls to logically deduce this pattern. Another way is to make a table like the one below and use vertical lines to determine which subshells correspond to each other.

• #Pauli Exclusion Principle

The second major fact to keep in mind is the Pauli Exclusion Principle which states that no two electrons can have the same four quantum numbers. The first three $(n,l, and$ $(m_l)$ may be similar but the fourth quantum number must be different. We are aware that in one orbital a maximum of two electrons can be found and the two electrons must have opposing spins. That means one would spin up $\frac {+1}{2}$ and the other would spin down $\frac {-1}{2}$ . This tells us that each subshell has double the electrons per orbital. The $S$ subshell has $1$ orbital that can hold to $2$ electrons, the $P$ subshell has $3$ orbitals that can hold up to $6$ electrons, the $D$ subshell has $5$ orbitals that hold up to $10$ electrons, and the $F$ subshell has $7$ orbitals with $14$ electrons.

• $Example$

We have the first three quantum numbers $n=1$, $l=0$, $m_l=0$. Only two electrons can correspond to these, which would be either $m_s=\frac{-1}{2}$ or $m_s= \frac{+1}{2}$. As we already know from our studies of quantum numbers and electron orbitals, we can conclude that these four quantum numbers refer to $1s$ subshell. If only one of the ms values are given then we would have $1s^1$ (denoting Hydrogen) if both are given we would have $1s^2$ (denoting Helium). Visually this would be represented as:

As you can see, the 1s subshell can hold only two electrons and when filled the electrons have opposite spins.

• #Hund's Rule

When assigning electrons in orbitals, each electron will first fill all the orbitals with similar energy (also referred to as degenerate) before pairing with another electron in a half-filled orbital. Atoms at ground states tend to have as many unpaired electrons as possible. When visualizing this processes, think about how electrons are exhibiting the same behavior as the same poles on a magnet would if they came into contact; as the negatively charged electrons fill orbitals they first try to get as far as possible from each other before having to pair up.

• $Example$

If we look at the correct electron configuration of Nitrogen $(Z = 7)$, a very important element in the biology of plants: $1s^2 2s^2 2p^3$

We can clearly see that p orbitals are half filled as there are three electrons and three p orbitals. This is because Hund's Rule states that the three electrons in the $2p$ subshell will fill all the empty orbitals first before filling orbitals with electrons in them. If we look at the element after Nitrogen in the same period, Oxygen $(Z = 8)$ its electron configuration is: $1s^2 2s^2 2p^4$

Oxygen has one more electron than Nitrogen and as the orbitals are all half filled the electron must pair up.

• #The Aufbau Process

Aufbau comes from the German word "Aufbauen" which means "to build". When writing electron configurations, we are building up electron orbitals as we proceed from atom to atom. As we write the electron configuration for an atom, we will fill the orbitals in order of increasing atomic number. However, there are some exceptions to this rule.

• $Example$

If we follow the pattern across a period from $B$ $(Z=5)$ to $Ne$ $(Z=10)$ the number of electrons increase and the subshells are filled. Here we are focusing on the $P$ subshell in which as we move towards $Ne$, the $P$ subshell becomes filled.

$B$ $(Z=5)$ configuration: $1s^2 2s^2 2p^1$

$C$ $(Z=6)$ configuration:$1s^2 2s^2 2p^2$

$N$ $(Z=7)$ configuration:$1s^2 2s^2 2p^3$

$O$ $(Z=8)$ configuration:$1s^2 2s^2 2p^4$

$F$ $(Z=9)$ configuration:$1s^2 2s^2 2p^5$

$Ne$ $(Z=10)$ configuration:$1s^2 2s^2 2p^6$

• #Writing Electron Configurations

When writing the electron configuration we first write the energy level (the period) then the subshell to be filled and the superscript, which is the number of electrons in t hat subshell. The total number of electrons as mentioned before is the atomic number, Z. Using the rules from above, we can now start writing the electron configurations for all the elements in the periodic table.

There are three main methods used to write electron configurations: (1) orbital diagrams, (2) spdf notation, and (3) noble gas notation. Each method has its own purpose and each has its own drawbacks.

• #Orbital Diagrams

As seen in some examples above, the orbital diagram is a visual way to reconstruct the electron configuration by showing each of the separate orbitals and the spins on the electrons. This is done by first determining the subshell (s,p,d, or f) then drawing in each electron according to the stated rules above.

• $Example$

Electron configuration for aluminum. We known that aluminum is in the 3rd period and it has an atomic number of $Z=13$. If we look at the periodic table we can see that its in the p-block as it is in group 13. Now we shall look at the orbitals it will fill: $1s, 2s, 2p, 3s, 3p$. We know that aluminum completely fills the $1s, 2s, 2p, and$ $3s$ orbitals because mathematically this would be $2+2+6+2=12$. The last electron is in the $3p$ orbital. Also another way of thinking about it is that as you move from each orbital block, the subshells become filled as you complete each section of the orbital in the period. The block that the atom is in (in the case for aluminum: 3p) is where we will count to get the number of electrons in the last subshell (for aluminum this would be one electron because its the first element in the period 3 p-block). From this we can construct the following:

Note that in the orbital diagram, the two opposing spins of the electron can be seen. This is why it is sometimes useful to think about electron configuration in terms of the diagram. But because it is the most time consuming method, it is more common to write or see electron configurations in the spdf notation and noble gas notation. Another example is the electron configuration of iridium:

The electron configuration of iridium is much longer than aluminum. Though drawing out each orbital may prove to be helpful in determining unpaired electrons, its very time consuming and often not as practical as the spdf notation especially in the case of atoms with much longer configurations. The Hund's Rule is also present above as each electron fills up each 5d orbital before being forced to pair with another electron.

• #Electron Notation using spdf

The most common way to describe electron configurations is to write distributions in the spdf notation. Though, the distributions of electrons in each orbital may not be seen as in the diagram, the total number of electrons in each energy level is described by a superscript that follows the relating energy level. To write the electron configuration of an atom, we will first describe which energy level we are referring to and write the number of electrons in the energy level as its superscript like this: 1s2 This denotes a full s orbital and would refer to the electron configuration of helium. As usual, we will use the periodic table as a reference to accurately write the electron configurations of all atoms.

• $Example$

First we will start with a straight forward problem, finding the electron configuration of the element Yttrium. As always we will refer to our periodic table. The element Yttrium (symbolized as Y) is found in the fifth period and in group $3$ making it a transition metal. In total it has thirty-nine electrons. Its electron configuration would be:

$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^1$

This is a much simpler and efficient way to portray electron configuration of an atom. A logical way of thinking about it is that all we have to do is to fill orbitals as we move across a period and through orbital blocks. We know that the amount of elements in each block is the same as in the energy level it corresponds. For example, there are 2 elements in the s-block, and 10 elements in the d-block. As we move across we simply count how many elements fall in each block. We know that yttrium is the first element in the fourth period d-block, thus this corresponds to one electron in the that energy level. To check our answer we would just add all the superscripts to see if we get the atomic number. In this case $2+2+6+2+6+2+10+6+2+1= 39$ and $Z=39$ thus we have the correct answer.

Continuing :

A slightly more complicated example is the electron configuration of bismuth (symbolized as Bi with $Z = 83$). Looking at our periodic table we can get the following electron configuration:

A slightly more complicated example is the electron configuration of bismuth (symbolized as Bi with $Z = 83)$. Looking at our periodic table we can get the following electron configuration:

$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 6s^2 4f^14 5d^10 6p^3$

The reason why this electron configuration would seem to be more complex is because we must go through the f-block, the Lanthanide series. Most students who first learn electron configurations often have trouble with configurations that must pass through the f-block because they often overlook this break in the table and will skip that energy level. Its important to remember that when passing the 5d and 6d energy levels that we must pass through the f-block Lanthaniod and Actiniod series. If we keep this in mind, this "complex" problem will seem like second nature.

Another way (but less commonly used) to write the spdf notation is the expanded notation format. Its basically the same concept except that each individual orbital is represented with a subscript. We know that in the $P$, $D$, and $F$ orbitals have different sublevels. The $P$ orbitals are $px py pz$ and if represented on the $2p$ energy with full orbitals would look like: $2p_x^2 2p_y^2 2p_z^2$ . If we look at the expanded notation for neon $(Ne)$, $Z=10)$ it would look like the following:

$1s^2 2s^2 2p_x^2 2p_y^2 2p_z^2$

The individual orbitals are represented here but the spins on the electrons are not; we assume opposite spins. When representing the configuration of an atom with half filled orbitals we would just write the two half filled orbitals. For carbon the expanded notation would look like the following:

$1s^2 2s^2 2p_x^1 2p_y^1$

As this is form of the spdf notation is not usually used, its not as important to dwell on this detail as it is to understand how to use the general spdf notation.

• #Noble Gas Notation

This brings up an interesting point about elements and electron configurations. As the p subshell is filled in the above example about the Aufbau Principal (trend from boron to neon), it reaches the group commonly known as the noble gases. The noble gases have the most stable electron configurations (as all their subshells are filled) and are known for being relatively inert. We can conclude from this that all noble gases have their subshells filled and we can used them as a short hand way of writing electron configurations for subsequent atoms. This method of writing configurations is called the noble gas notation in which the noble gas in the period above the element that is being analyzed is used to denote the subshells that element has filled and after which the valence electrons (electrons filling orbitals in the outer most shells) are written. We will write this notation slightly different than the spdf notation because we must denote our reference noble gas being used.

• $Example$ :

Vanadium ($V$, $Z=23$) lies in the transition metals at the four period in the fifth group. The noble gas before it is argon, ($Ar$, $Z=18$) and knowing that vanadium has filled those orbitals before it, we will use argon as our reference noble gas. We denote the noble gas in the configuration as the symbol, E, in brackets: $[E]$ Now, to find the valance electrons that follow, we will simply do some simple math by subtracting the atomic numbers: $23 - 18 = 5$ Now instead of having $23$ electrons to distribute in orbitals, we have $5$. Now we have enough information to write the electron configuration:

Vanadium :

V : [Ar] $4s^2 3d^3$

This method streamlines the process of distributing electrons by showing the valence electron which are determinants in the chemical properties of atoms. Also, when determining the number of unpaired electrons in an atom, this method will allow us to quickly visualize the configurations of the valance electrons. In the example above, we clearly see that we have a full s orbital and three half filled d orbitals.

• #Electron Configurations of Ions

Writing electron configurations for ions, whether it be cation or anion, is basically exactly the same as writing them for normal elements. All the same rules apply, except you must take into account the gained or lost electrons. For instance, when Potassium $(K)$ loses an electron it becomes $K^+$ and has the noble gas configuration of $[Ar]$.

K [Ar] \\\(4s^1\\\)

$\Rightarrow$ $K^{+}$ $[Ar] + e^{-}$

Therefore, the electron configuration for the $K^{+}$ ion is simply $[Ar]$.

When an atom, such as Chlorine $(Cl)$ gains an electron, it becomes $Cl^{-}$ and also has the electron configuration of $[Ar]$.

$Cl$ ($[Ne]$ $(3s^{2} 3p^{5})$ $+$ $e^{-}$ $\Rightarrow$ $Cl^{-}$ $([Ar])$

Yet again, the electron configuration is $[Ar]$. For more complex ionic electron configurations, such as an ion from the transition metals, the answer isn't always a noble gas. Take Iron $(Fe)$. The most common irons for Iron are $Fe^{2+})$ and $Fe^{3+}$. Lets focus on $Fe^{2+}$.

$Fe$ ($[Ar] 3d^64s^2$) $\Rightarrow$ $Fe^{2+}$ ($[Ar] 3d^6$) - $2e^{-}$

Here Iron loses two electrons. So thats two less electrons to fill orbitals. When you backtrack two electrons in Fe's original electron configuration you get $[Ar]3d^6$ as $Fe^{2+}$ 's new configuration

When writing the electron configuration for ions, treat it like any normal element. Just remember to simply add or subtract the gained or lost electrons when filling out shells.