5.3: Electron Arrangement in Atoms
Lesson Objectives
 Understand how to apply the Aufbau principle, the Pauli exclusion principle, and Hund’s rule to determine ground state electron configurations.
 Be able to write correct orbital filling diagrams and electron configurations for all elements.
 Know how to use the noble gas notation shorthand method.
 Be able to determine the number of valence electrons and the number of unpaired electrons in any atom.
 Understand that some electron configurations are exceptions to the normal Aufbau process.
Lesson Vocabulary
 Aufbau principle
 electron configuration
 Hund’s rule
 noble gas notation
 Pauli exclusion principle
 valence electron
Electron Configurations
The quantum mechanical model provides what is now recognized as the modern and accepted model of the atom. An atom’s electron configuration describes the arrangement of all electrons in that atom. Although we do not know the exact locations of any electrons, each electron will exist primarily in a region of most probable locations that is defined by one of the orbitals described in the previous section. Writing the electron configuration of an atom essentially amounts to listing which orbitals contain electrons and how many electrons are in each type of orbital. Since every element has a different number of electrons, each has a unique electron configuration. Recall that the natural tendency for all systems is to be in the lowest possible energy state, which is also known as the ground state. Thus, the ground state electron configuration for an element is the lowestenergy arrangement of electrons possible for that element. Most ground state electron configurations can be determined from the quantum number guidelines learned in the previous lesson, “The Quantum Mechanical Model,” and a few basic rules.
Aufbau Principle
To determine the ground state electron configuration for a given atom, it is first necessary to organize the atomic sublevels in order of increasing energy. Figure below shows the relative energies of various sublevels.
According to the Aufbau principle, all lower energy orbitals must be filled before electrons can be added to a higher energy orbital. The principal energy levels are color coded in this figure. Sublevels are grouped together by column, and each circle represents an orbital that is capable of holding two electrons.
The lowest energy sublevel is always the 1s sublevel, which consists of one orbital. The single electron of the hydrogen atom will occupy the 1s orbital when the atom is in its ground state. As we move on to atoms with more electrons, those electrons are sequentially added to the next lowest sublevels, first 2s, then 2p, then 3s, and so on. The Aufbau principle states that all lower energy orbitals must be filled before electrons can be added to a higher energy orbital. The Aufbau principle is sometimes referred to as the “buildingup” principle. It is worth noting that, in reality, atoms are not built by adding protons and electrons one at a time. This method is merely a way for us to predict and understand the end result.
As seen in Figure above, the energies of the sublevels in different principal energy levels eventually begin to overlap. After the 3p sublevel, it would seem logical that the 3d sublevel should be the next lowest in energy. However, the 4s sublevel is slightly lower in energy than the 3d sublevel, so the 4s orbital fills first. After the 3d sublevel is filled, the next lowest sublevels are 4p, 5s, and 4d. Note that the 4f sublevel does not fill until just after the 6s sublevel. Figure below is a useful and simple aid for keeping track of the order in which electrons are first added to each atomic sublevel.
The Aufbau principle is illustrated in the diagram by following each red arrow in order from top to bottom: 1s, 2s, 2p, 3s, etc.
Pauli Exclusion Principle
Recall that every orbital, no matter which type, is capable of containing two electrons, and the electrons in any completely filled orbital must have opposite spins. This is summed up in an alternate wording by the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers. The energy of the electron is specified by the principal, angular momentum, and magnetic quantum numbers. Because there are two possible values for the spin quantum number, each orbital can hold up to two electrons. Figure below describes how to depict electron configurations in an orbital filling diagram.
In an orbital filling diagram, a square represents an orbital, and arrows represent electrons. An arrow pointing upward represents one spin direction, while an arrow pointing downward represents the other spin direction.
View an animation of electron spin at http://www.dlt.ncssm.edu/core/Chapter8Atomic_Str_Part2/chapter8Animations/ElectronSpin.html.
Hund's Rule
The last of the three rules for determining ground state electron configurations gives information on how to arrange electrons in a set of orbitals that are all within the same sublevel. Hund’s rule states that orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all of the unpaired electrons must have the same spin. A slight preference for keeping electrons in separate orbitals helps minimize the natural repulsive forces that exist between any two electrons. Figure below shows how a set of three p orbitals would be filled with one, two, three, and four electrons.
The arrangement of electrons within the 2p sublevel for the elements boron (Z = 5), carbon (Z = 6), nitrogen (Z = 7), and oxygen (Z = 8). According to Hund’s rule, as electrons are added to a set of orbitals of equal energy, one electron enters each orbital before any orbital receives a second electron.
Orbital Filling Diagrams
An orbital filling diagram provides a more visual way to represent the arrangement of electrons in a particular atom. In an orbital filling diagram, the individual orbitals are shown as circles (or squares), and orbitals within the same sublevel are drawn next to each other horizontally. Sublevels can be shown as in Figure above, where energy increases as you move up the page, or to save space, all sublevels can simply be shown horizontally one after the other. Each sublevel is labeled by its principal energy level and sublevel. Electrons are indicated by arrows inside the circles. An arrow pointing upwards indicates one spin direction, while a downward pointing arrow indicates the other direction. The orbital filling diagrams for hydrogen, helium, and lithium are shown below.
According to the Aufbau principle, sublevels and orbitals are filled with electrons in order of increasing energy. Since the s sublevel consists of just one orbital, the second electron simply pairs up with the first electron, as in helium. The next element, lithium, requires the use of the next available sublevel. The third electron must be placed in a 2s orbital, because the 1s orbital is completely filled.
Electron Configuration Notation
Electron configuration notation eliminates the circles and arrows of orbital filling diagrams. Each occupied sublevel is written down, along with a superscript indicating the number of electrons present in that sublevel. For example, the configuration of a hydrogen atom is 1s^{1}, and the configuration of helium is 1s^{2}. Multiple occupied sublevels are written one after another. The electron configuration of lithium is 1s^{2}2s^{1}. The sum of the superscripts in an electron configuration is equal to the number of electrons in that atom, which is in turn equal to its atomic number.
Sample Problem 5.5: Orbital Filling Diagrams and Electron Configurations
Draw the orbital filling diagram for carbon and write its electron configuration.
Step 1: List the known quantities and plan the problem.
Known
 atomic number of carbon, Z = 6
Use the sublevel energy ordering from Figure above to draw an orbital filling diagram with a total of six electrons. Follow Hund’s rule. Write the electron configuration.
Step 2: Construct a diagram.
 Orbital filling diagram:
 Electron configuration: 1s^{2}2s^{2}2p^{2}
Step 3: Think about your result.
After the 2s sublevel is filled, the 2p sublevel is the next lowest in energy. p sublevels always consist of three orbitals, and all three orbitals need to be drawn, even if one or more is unoccupied. According to Hund’s rule, the sixth electron is placed in the second p orbital and exhibits the same direction of spin as the fifth electron.
You can watch video lectures on this topic from Khan Academy:
 Introduction to Orbitals at http://www.youtube.com/watch?v=yBrp8uvNAhI (13:38)
 More on Orbitals and Electron Configuration at http://www.youtube.com/watch?v=FmQoSenbtnU (14:31)
 Electron Configurations at http://www.youtube.com/watch?v=RJlEH5Jz80w (10:04)
 Electron Configurations 2 at http://www.youtube.com/watch?v=YURReI6OJsg (10:18)
Second Period Elements
Periods refer to the horizontal rows of the periodic table. Looking at a periodic table, you will see that the first period contains only the elements hydrogen and helium. This is because the first principal energy level consists of a single s orbital, so only two electrons are required to fill the entire level. Each time a new principal energy level begins to hold electrons, a new period is started on the periodic table. As one moves across the second period, electrons are successively added to orbitals in the second principal energy level. After beryllium (Z = 4), the 2s sublevel is complete, and the 2p sublevel begins to fill starting with boron (Z = 5). Since there are three 2p orbitals and each orbital holds two electrons, the 2p sublevel is filled after six elements. Table below shows the electron configurations of the elements in the second period.
Element Name  Symbol  Atomic Number  Electron Configuration 

Lithium  Li  3 

Beryllium  Be  4 

Boron  B  5 

Carbon  C  6 

Nitrogen  N  7 

Oxygen  O  8 

Fluorine  F  9 

Neon  Ne  10 

Upon reaching the element neon, a 6^{th} electron is added to the 2p sublevel, and the second principal energy level is now filled. We will see that the electrons in the outermost principal energy level are very important for predicting and explaining chemical reactivity, so they are given a special name. Valence electrons are the electrons in the highest occupied principal energy level of an atom. In the second period elements listed above, the two electrons in the 1s sublevel are called innershell electrons, and they are not directly involved in the atom's reactivity or in the formation of compounds. Lithium has a single electron in the second principal energy level, so we say that lithium has one valence electron. Beryllium has two valence electrons. How many valence electrons does boron have? Because the second principal energy level consists of both the 2s and the 2p sublevels, the answer is three. The configuration of neon ends in 2s^{2}2p^{6}, so it has eight valence electrons.
The magnetic properties of various elements are related to the number of unpaired electrons in each atom. For example, hydrogen has only a single electron, so it is necessarily unpaired. Helium has no unpaired electrons, because both of its electrons are in the same orbital. To occupy the same orbital, they must have opposite spins, so in terms of their magnetic properties, the two electrons cancel each other out. Proceeding across the second period, we find the following numbers of unpaired electrons:


 Li = 1, Be = 0, B = 1, C = 2, N = 3, O = 2, F = 1, Ne = 0

In order to correctly identify the number of unpaired electrons, you may find it necessary to construct the orbital filling diagram. Correctly following Hund’s rule will have an effect on the number of unpaired electrons. Oxygen’s orbital filling diagram serves as an example:
The four electrons in the 2p sublevel are ordered such that two are paired up in the first orbital, while the single electrons in the second and third orbitals are unpaired.
Third Period Elements
Sodium, element number eleven, is the first element in the third period of the periodic table. Its electron configuration is 1s^{2}2s^{2}2p^{6}3s^{1}. The first ten electrons of the sodium atom are the innershell electrons, and the configuration of just those ten electrons is exactly the same as the configuration of the element neon (Z = 10). This provides the basis for a shorthand notation that is commonly used to abbreviate electron configurations for larger atoms. The elements that are found in the last column of the periodic table are an important group of elements called the noble gases. They include helium, neon, argon, krypton, xenon, and radon. The electron configuration of an atom can be abbreviated by using noble gas notation, in which the elemental symbol of the last noble gas prior to that atom is written first, followed by the configuration of the remaining electrons. For sodium, we can substitute [Ne] for the 1s^{2}2s^{2}2p^{6} part of the configuration. Sodium’s electron configuration can now be written [Ne]3s^{1}. Table below shows the electron configurations of the third period elements.
Element Name  Symbol  Atomic Number  Electron Configuration 

Sodium  Na  11 

Magnesium  Mg  12 

Aluminum  Al  13 

Silicon  Si  14 

Phosphorus  P  15 

Sulfur  S  16 

Chlorine  Cl  17 

Argon  Ar  18 

Again, the number of valence electrons increases from one to eight across the third period.
Fourth and Fifth Period Elements
The element potassium begins the fourth period. The last electron in the potassium atom goes into the 4s sublevel, which fills before the 3d sublevel. From this point onward, it is important to consult the diagram in Figure above in order to follow the Aufbau process correctly. The fourth period elements are shown in Table below.
Element Name  Symbol  Atomic Number  Electron Configuration 

Potassium  K  19 

Calcium  Ca  20 

Scandium  Sc  21 

Titanium  Ti  22 

Vanadium  V  23 

Chromium  Cr  24 

Manganese  Mn  25 

Iron  Fe  26 

Cobalt  Co  27 

Nickel  Ni  28 

Copper  Cu  29 

Zinc  Zn  30 

Gallium  Ga  31 

Germanium  Ge  32 

Arsenic  As  33 

Selenium  Se  34 

Bromine  Br  35 

Krypton  Kr  36 

Beginning with scandium (Z = 21), the 3d sublevel begins to fill. Note that it is customary for the lower principal energy level (the 3^{rd}) to be written first in the electron configuration even though it fills after the outer (4^{th}) principal energy level. Titanium and vanadium follow scandium. We would expect that the next element, chromium, would have an outer configuration of 3d^{4}4s^{2}. However, in this case, one of the 4s electrons is shifted to the last of the empty 3d orbitals, resulting in an outer configuration of 3d^{5}4s^{1}. This has a slightly lower energy, because having six unpaired electrons instead of four minimizes electronelectron repulsions. As a result, the ground state of chromium has a different arrangement than the one we might expect based on the Aufbau principle.
Proceeding onward, manganese (Mn) pairs up the single electron in the 4s orbital. Iron (Fe), cobalt (Co), and nickel (Ni) follow, with electrons now pairing up in the 3d orbitals. Copper (Cu) is another element with an unexpected configuration. This time, the second 4s electron is shifted into the last available spot in the 3d sublevel, completely filling it. This is the lowest energy configuration for Cu. Electron configurations that do not quite follow the usual order of filling orbitals, like those of Cr and Cu, occur frequently among the heavier elements, and such exceptions are not always easy to explain. It is important to be aware of them, but it is not necessary to memorize every exception. From gallium (Ga) through the noble gas krypton (Kr), electrons fill the 4p sublevel in a straightforward manner.
Recall that valence electrons are only those electrons in the outermost principal energy level. For elements 2130, electrons are being added to the 3d sublevel. However, the 3d sublevel is not the outermost energy level, because the 4s orbital contains one or more electrons. Therefore, the atoms of elements 2130 have two valence electrons, except for chromium and copper, which each have only one valence electron. Because the d and f sublevels always fill behind s sublevels of a higher principal energy level, they can never be valence electrons. The maximum possible number of valence electrons in an atom is eight, which results from a full set of s and p orbitals.
The fifth period consists of the elements rubidium (Rb) through xenon (Xe). The pattern of sublevel filling is the same as in the fourth period: 5s followed by 4d followed by 5p. Several more exceptional configurations occur, as seen in Table below.
Element Name  Symbol  Atomic Number  Electron Configuration 

Rubidium  Rb  37 

Strontium  Sr  38 

Yttrium  Y  39 

Zirconium  Zr  40 

Niobium  Nb  41 

Molybdenum  Mo  42 

Technetium  Tc  43 

Ruthenium  Ru  44 

Rhodium  Rh  45 

Palladium  Pd  46 

Silver  Ag  47 

Cadmium  Cd  48 

Indium  In  49 

Tin  Sn  50 

Antimony  Sb  51 

Tellurium  Te  52 

Iodine  I  53  \begin{align*}[\text{Kr}]4d^{10}5s^25p^5\end{align*} 
Xenon  Xe  54  \begin{align*}[\text{Kr}]4d^{10}5s^25p^6\end{align*} 
Sixth and Seventh Period Elements
The sixth period contains 32 elements and begins with cesium (Cs) filling the 6s sublevel. The 6s sublevel is followed by 4f, then 5d, and finally 6p. See Table below for the electron configurations of the sixth period elements, noting again the large number of exceptions.
Element Name  Symbol  Atomic Number  Electron Configuration 

Cesium  Cs  55  \begin{align*}[\text{Xe}]6s^1\end{align*} 
Barium  Ba  56  \begin{align*}[\text{Xe}]6s^2\end{align*} 
Lanthanum  La  57  \begin{align*}[\text{Xe}]5d^16s^2\end{align*} 
Cerium  Ce  58  \begin{align*}[\text{Xe}]4f^15d^16s^2\end{align*} 
Praseodymium  Pr  59  \begin{align*}[\text{Xe}]4f^36s^2\end{align*} 
Neodymium  Nd  60  \begin{align*}[\text{Xe}]4f^46s^2\end{align*} 
Promethium  Pm  61  \begin{align*}[\text{Xe}]4f^56s^2\end{align*} 
Samarium  Sm  62  \begin{align*}[\text{Xe}]4f^66s^2\end{align*} 
Europium  Eu  63  \begin{align*}[\text{Xe}]4f^76s^2\end{align*} 
Gadolinium  Gd  64  \begin{align*}[\text{Xe}]4f^75d^16s^2\end{align*} 
Terbium  Tb  65  \begin{align*}[\text{Xe}]4f^96s^2\end{align*} 
Dysprosium  Dy  66  \begin{align*}[\text{Xe}]4f^{10}6s^2\end{align*} 
Holmium  Ho  67  \begin{align*}[\text{Xe}]4f^{11}6s^2\end{align*} 
Erbium  Er  68  \begin{align*}[\text{Xe}]4f^{12}6s^2\end{align*} 
Thulium  Tm  69  \begin{align*}[\text{Xe}]4f^{13}6s^2\end{align*} 
Ytterbium  Yb  70  \begin{align*}[\text{Xe}]4f^{14}6s^2\end{align*} 
Lutetium  Lu  71  \begin{align*}[\text{Xe}]4f^{14}5d^16s^2\end{align*} 
Hafnium  Hf  72  \begin{align*}[\text{Xe}]4f^{14}5d^26s^2\end{align*} 
Tantalum  Ta  73  \begin{align*}[\text{Xe}]4f^{14}5d^36s^2\end{align*} 
Tungsten  W  74  \begin{align*}[\text{Xe}]4f^{14}5d^46s^2\end{align*} 
Rhenium  Re  75  \begin{align*}[\text{Xe}]4f^{14}5d^56s^2\end{align*} 
Osmium  Os  76  \begin{align*}[\text{Xe}]4f^{14}5d^66s^2\end{align*} 
Iridium  Ir  77  \begin{align*}[\text{Xe}]4f^{14}5d^76s^2\end{align*} 
Platinum  Pt  78  \begin{align*}[\text{Xe}]4f^{14}5d^96s^1\end{align*} 
Gold  Au  79  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^1\end{align*} 
Mercury  Hg  80  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^2\end{align*} 
Thallium  Tl  81  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^26p^1\end{align*} 
Lead  Pb  82  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^26p^2\end{align*} 
Bismuth  Bi  83  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^26p^3\end{align*} 
Polonium  Po  84  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^26p^4\end{align*} 
Astatine  At  85  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^26p^5\end{align*} 
Radon  Rn  86  \begin{align*}[\text{Xe}]4f^{14}5d^{10}6s^26p^6\end{align*} 
The seventh period starts with francium (Fr) and the 7s sublevel. This is followed by the 5f and 6d sublevels. The seventh period is incomplete and consists largely of artificial and very unstable elements. Electron configurations for the known seventh period elements are listed in Table below.
Element Name  Symbol  Atomic Number  Electron Configuration 

Francium  Fr  87  \begin{align*}[\text{Rn}]7s^1\end{align*} 
Radium  Ra  88  \begin{align*}[\text{Rn}]7s^2\end{align*} 
Actinium  Ac  89  \begin{align*}[\text{Rn}]6d^17s^2\end{align*} 
Thorium  Th  90  \begin{align*}[\text{Rn}]6d^27s^2\end{align*} 
Protactinium  Pa  91  \begin{align*}[\text{Rn}]5f^26d^17s^2\end{align*} 
Uranium  U  92  \begin{align*}[\text{Rn}]5f^36d^17s^2\end{align*} 
Neptunium  Np  93  \begin{align*}[\text{Rn}]5f^46d^17s^2\end{align*} 
Plutonium  Pu  94  \begin{align*}[\text{Rn}]5f^67s^2\end{align*} 
Americium  Am  95  \begin{align*}[\text{Rn}]5f^77s^2\end{align*} 
Curium  Cm  96  \begin{align*}[\text{Rn}]5f^76d^17s^2\end{align*} 
Berkelium  Bk  97  \begin{align*}[\text{Rn}]5f^97s^2\end{align*} 
Californium  Cf  98  \begin{align*}[\text{Rn}]5f^{10}7s^2\end{align*} 
Einsteinium  Es  99  \begin{align*}[\text{Rn}]5f^{11}7s^2\end{align*} 
Fermium  Fm  100  \begin{align*}[\text{Rn}]5f^{12}7s^2\end{align*} 
Mendelevium  Md  101  \begin{align*}[\text{Rn}]5f^{13}7s^2\end{align*} 
Nobelium  No  102  \begin{align*}[\text{Rn}]5f^{14}7s^2\end{align*} 
Lawrencium  Lr  103  \begin{align*}[\text{Rn}]5f^{14}7s^27p^1\end{align*} 
Rutherfordium  Rf  104  \begin{align*}[\text{Rn}]5f^{14}6d^27s^2\end{align*} 
Dubnium  Db  105  \begin{align*}[\text{Rn}]5f^{14}6d^37s^2\end{align*} 
Seaborgium  Sg  106  \begin{align*}[\text{Rn}]5f^{14}6d^47s^2\end{align*} 
Bohrium  Bh  107  \begin{align*}[\text{Rn}]5f^{14}6d^57s^2\end{align*} 
Hassium  Hs  108  \begin{align*}[\text{Rn}]5f^{14}6d^67s^2\end{align*} 
Meitnerium  Mt  109  \begin{align*}[\text{Rn}]5f^{14}6d^77s^2\end{align*} 
Lesson Summary
 The ground state electron configurations of most atoms can be predicted based on the Aufbau principle, the Pauli exclusion principle, and Hund’s rule.
 Orbital filling diagrams are drawn to show how electrons fill up various energy levels. In these diagrams, orbitals are arranged from lowest to highest energy.
 The electron configuration is unique for each element.
 Valence electrons are the electrons in the outermost principal energy level. An atom can have a maximum of eight valence electrons.
 Unpaired electrons influence the magnetic properties of an atom.
 Some electron configurations, such as those of chromium and copper, do not strictly follow the Aufbau principle.
Lesson Review Questions
Reviewing Concepts
 Electron configurations:
 What do the superscripts in an electron configuration represent?
 What is the atomic number of an element with the electron configuration 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{5}?
 Arrange these sublevels in order of increasing energy: 3p, 5s, 4f, 2s, 3d.
 Which rule is violated by the electron configuration 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{2}? Explain.
 Which rule is violated by each of the orbital filling diagrams below? Explain.
Problems
 Using only the atomic number, construct orbital filling diagrams for the following elements. Note: none are exceptions to the Aufbau principle.
 boron (Z = 5)
 sulfur (Z = 16)
 nickel (Z = 28)
 rubidium (Z = 37)
 Using only the atomic number, write full electron configurations for the following elements.
 fluorine (Z = 9)
 calcium (Z = 20)
 zirconium (Z = 40)
 europium (Z = 63)
 Write the electron configurations for the four elements in question #6 using noble gas notation.
 How many electrons are in the second principal energy level of each element below?
 sodium
 nitrogen
 beryllium
 How many principal energy levels are completely filled in atoms of each of the following elements?
 argon
 ruthenium
 barium
 How many principal energy levels are occupied in atoms of the elements listed in question #9?
 How many sublevels are occupied in an atom of aluminum? How many are completely filled?
 Which elements have completely filled s and p sublevels in their outermost principal energy level?
 Fill in the following table (Table below). Use a periodic table to find the atomic numbers. All elements in this problem follow the conventional Aufbau order for filling sublevels.
O  K  Fe  Kr  Cd  I  Pu  

Total number of occupied principal energy levels  
Number of completely filled principal energy levels  
Total number of occupied sublevels  
Number of completely filled sublevels  
Number of unpaired electrons  
Number of valence electrons 
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