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5.3: Electron Arrangement in Atoms

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Lesson Objectives

  • Understand how to apply the Aufbau principle, Pauli exclusion principle, and Hund’s rule to ground state electron configurations.
  • Write correct orbital filling diagrams and electron configurations for all elements.
  • Use the noble gas configuration 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 configuration
  • 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 is the arrangement of all of the electrons of that atom. Since every element has a different number of electrons, each has a unique electron configuration. Recall that the natural state for all systems is to be in the lowest energy state possible. Thus, the ground state electron configuration for an element is the lowest-energy arrangement of electrons possible for that element. The basis for determining electron configurations is the quantum number guidelines learned in the previous lesson, “The Quantum Mechanical Model,” along with a few basic rules.

Aufbau Principle

In order to create ground state electron configurations for any element, it is necessary to know the way in which the atomic sublevels are organized in order of increasing energy. Figure below shows the order of increasing energy of the sublevels.

Electrons are added to atomic orbitals in order from low energy to high according to the Aufbau principle. Principal energy levels are color coded, while sublevels are grouped together and each circle represents an orbital 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 proceed with atoms with multiple electrons, those electrons are added to the next lowest sublevel: 2s, 2p, 3s, and so on. The Aufbau principle states that an electron occupies orbitals in order from lowest energy to highest. The Aufbau principle is sometimes referred to as the “building-up” principle. It is worth noting that in reality atoms are not built by adding protons and electrons one at a time and that this method is merely an aid for us to 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 and thus fills first. Following the filling of the 3d sublevel is the 4p, then the 5s and the 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 of fill of the atomic sublevels.

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 that each must have opposite spin. This leads to 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. The two values of the spin quantum number allow each orbital to hold two electrons. Figure below shows how the electrons are indicated in a diagram.

In an orbital filling diagram, a square represents an orbital, while 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/Chapter8-Atomic_Str_Part2/chapter8-Animations/ElectronSpin.html.

Hund's Rule

The last of the three rules for constructing electron arrangements requires electrons to be placed one at a time in a set of orbitals within the same sublevel. This minimizes the natural repulsive forces that one electron has for another. 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 that each of the single electrons must have the same spin. Figure below shows how a set of three p orbitals is filled with one, two, three, and four electrons.

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 is the more visual way to represent the arrangement of all the electrons in a particular atom. In an orbital filling diagram, the individual orbitals are shown as circles (or squares) and orbitals within a sublevel are drawn next to each other horizontally. Sublevels can be shown as in Figure above with increasing energy proceeding 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 process, 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 is lithium and necessitates the use of the next available sublevel, the 2s.

Electron Configuration Notation

Electron configuration notation eliminates the circles and arrows of orbital filling diagrams. Each occupied sublevel designation is written followed by a superscript that is the number of electrons in that sublevel. For example, the hydrogen configuration is 1s1, while the helium configuration is 1s2. Multiple occupied sublevels are written one after another. The electron configuration of lithium is 1s22s1. 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 order of fill diagram to draw an orbital filling diagram with a total of six electrons. Follow Hund’s rule. Write the electron configuration.

Step 2: Construct diagram

  • Orbital filling diagram:
  • Electron configuration: 1s22s22p2

Step 3: Think about your result.

Following the 2s sublevel is the 2p, and p sublevels always consist of three orbitals. All three orbitals need to be drawn even if one or more is unoccupied. According to Hund’s rule, the sixth electron enters the second of those p orbitals and with the same spin as the fifth electron.

You can watch video lectures on this topic from Khan Academy:

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 only the s sublevel and so only two electrons are required in order to fill the entire principal energy level. Each time a new principal energy level begins, as with the third element lithium, a new period is started on the periodic table. As one moves across the second period, electrons are successively added. With beryllium (Z = 4), the 2s sublevel is complete and the 2p sublevel begins 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.

Electron Configurations of Second-Period Elements
Element Name Symbol Atomic Number Electron Configuration
Lithium Li 3 1s^22s^1
Beryllium Be 4 1s^22s^2
Boron B 5 1s^22s^22p^1
Carbon C 6 1s^22s^22p^2
Nitrogen N 7 1s^22s^22p^3
Oxygen O 8 1s^22s^22p^4
Fluorine F 9 1s^22s^22p^5
Neon Ne 10 1s^22s^22p^6

Upon reaching the element neon, the last electron to add to the atom is the p6 electron and so the sublevel and the principal energy level are now filled. In the study of chemical reactivity, we will find that the electrons in the outermost principal energy level are very important and 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 inner-shell electrons and are not involved directly in the element’s reactivity or in the formation of compounds. Lithium has a single electron in the second principle energy level and so we say that lithium has one valence electron. Beryllium has two valence electrons . How many valence electrons does boron have? You must recognize that the second principal energy level consists of both the 2s and the 2p sublevels and so the answer is three. In fact, the number of valence electrons goes up by one for each step across a period until the last element is reached. Neon, with its configuration ending in s2p6, has eight valence electrons.

The magnetic properties of elements are related to the number of electrons in the atom that are unpaired. For example, hydrogen has only a single electron, so it is necessarily unpaired. Helium has no unpaired electrons because its second electron is matched up, with opposite spin, in the same orbital as the first electron. Proceeding across the second period, we come up with 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. Hund’s rule must be followed and that will affect 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 1s22s22p63s1. The first ten electrons of the sodium atom are the inner-shell 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 for electron configurations called the noble gas configuration. The elements that are found in the last column of the periodic table are an important group of elements that are called the noble gases. They are helium, neon, argon, krypton, xenon, and radon. A noble gas configuration of an atom consists of the elemental symbol of the last noble gas prior to that atom, followed by the configuration of the remaining electrons. So for sodium, we make the substitution of [Ne] for the 1s=22s22p6 part of the configuration. Sodium’s noble gas configuration becomes [Ne]3s1. Table below shows the noble gas configurations of the third period elements.

Electron Configurations of Third-Period Elements
Element Name Symbol Atomic Number Noble Gas Electron Configuration
Sodium Na 11 [\text{Ne}]3s^1
Magnesium Mg 12 [\text{Ne}]3s^2
Aluminum Al 13 [\text{Ne}]3s^23p^1
Silicon Si 14 [\text{Ne}]3s^23p^2
Phosphorus P 15 [\text{Ne}]3s^23p^3
Sulfur S 16 [\text{Ne}]3s^23p^4
Chlorine Cl 17 [\text{Ne}]3s^23p^5
Argon Ar 18 [\text{Ne}]3s^23p^6

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.

Electron Configurations of Fourth-Period Elements
Element Name Symbol Atomic Number Noble Gas Electron Configuration
Potassium K 19 [\text{Ar}]4s^1
Calcium Ca 20 [\text{Ar}]4s^2
Scandium Sc 21 [\text{Ar}]3d^14s^2
Titanium Ti 22 [\text{Ar}]3d^24s^2
Vanadium V 23 [\text{Ar}]3d^34s^2
Chromium Cr 24 [\text{Ar}]3d^54s^1
Manganese Mn 25 [\text{Ar}]3d^54s^2
Iron Fe 26 [\text{Ar}]3d^64s^2
Cobalt Co 27 [\text{Ar}]3d^74s^2
Nickel Ni 28 [\text{Ar}]3d^84s^2
Copper Cu 29 [\text{Ar}]3d^{10}4s^1
Zinc Zn 30 [\text{Ar}]3d^{10}4s^2
Gallium Ga 31 [\text{Ar}]3d^{10}4s^24p^1
Germanium Ge 32 [\text{Ar}]3d^{10}4s^24p^2
Arsenic As 33 [\text{Ar}]3d^{10}4s^24p^3
Selenium Se 34 [\text{Ar}]3d^{10}4s^24p^4
Bromine Br 35 [\text{Ar}]3d^{10}4s^24p^5
Krypton Kr 36 [\text{Ar}]3d^{10}4s^24p^6

Beginning with scandium (Z = 21), the 3d sublevel begins to fill. Note that it is customary for the lower principal energy level (the 3rd) to be written first in the electron configuration even though it fills after the outer 4th principal energy level. Titanium and vanadium follow scandium. We would expect that the next element, chromium, would have an outer configuration of 3d44s2. 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 3d54s1. This is of slightly lower energy and thus is more stable than the arrangement we would expect according to the Aufbau principle. The reason is because having six unpaired electrons instead of four minimizes electron-electron repulsions.

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. Exceptional electron configurations like those of Cr and Cu occur frequently among the heavier elements and are not always easy to explain. It is important to be aware of them, but not necessary to memorize every exception. From gallium, Ga, through the noble gas krypton, Kr, electrons fill the 4p sublevel.

Recall that valence electrons are only those electrons in the outermost principal energy level. For elements 21-30, electrons are being added to the 3d sublevel which is not the outermost energy level since the 4s electrons entered those atoms first. Therefore, the atoms of elements 21-30 have two valence electrons, with the exception of chromium and copper which 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 number of valence electrons possible is eight, 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.

Electron Configurations of Fifth-Period Elements
Element Name Symbol Atomic Number Noble Gas Electron Configuration
Rubidium Rb 37 [\text{Kr}]5s^1
Strontium Sr 38 [\text{Kr}]5s^2
Yttrium Y 39 [\text{Kr}]4d^15s^2
Zirconium Zr 40 [\text{Kr}]4d^25s^2
Niobium Nb 41 [\text{Kr}]4d^45s^1
Molybdenum Mo 42 [\text{Kr}]4d^45s^1
Technetium Tc 43 [\text{Kr}]4d^55s^2
Ruthenium Ru 44 [\text{Kr}]4d^75s^1
Rhodium Rh 45 [\text{Kr}]4d^85s^1
Palladium Pd 46 [\text{Kr}]4d^{10}
Silver Ag 47 [\text{Kr}]4d^{10}5s^1
Cadmium Cd 48 [\text{Kr}]4d^{10}5s^2
Indium In 49 [\text{Kr}]4d^{10}5s^25p^1
Tin Sn 50 [\text{Kr}]4d^{10}5s^25p^2
Antimony Sb 51 [\text{Kr}]4d^{10}5s^25p^3
Tellurium Te 52 [\text{Kr}]4d^{10}5s^25p^4
Iodine I 53 [\text{Kr}]4d^{10}5s^25p^5
Xenon Xe 54 [\text{Kr}]4d^{10}5s^25p^6

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 the 4f, then the 5d and finally the 6p. See Table below for the electron configurations of sixth period elements, noting again the large number of exceptions.

Electron Configurations of Sixth-Period Elements
Element Name Symbol Atomic Number Noble Gas Electron Configuration
Cesium Cs 55 [\text{Xe}]6s^1
Barium Ba 56 [\text{Xe}]6s^2
Lanthanum La 57 [\text{Xe}]5d^16s^2
Cerium Ce 58 [\text{Xe}]4f^15d^16s^2
Praseodymium Pr 59 [\text{Xe}]4f^36s^2
Neodymium Nd 60 [\text{Xe}]4f^46s^2
Promethium Pm 61 [\text{Xe}]4f^56s^2
Samarium Sm 62 [\text{Xe}]4f^66s^2
Europium Eu 63 [\text{Xe}]4f^76s^2
Gadolinium Gd 64 [\text{Xe}]4f^75d^16s^2
Terbium Tb 65 [\text{Xe}]4f^96s^2
Dysprosium Dy 66 [\text{Xe}]4f^{10}6s^2
Holmium Ho 67 [\text{Xe}]4f^{11}6s^2
Erbium Er 68 [\text{Xe}]4f^{12}6s^2
Thulium Tm 69 [\text{Xe}]4f^{13}6s^2
Ytterbium Yb 70 [\text{Xe}]4f^{14}6s^2
Lutetium Lu 71 [\text{Xe}]4f^{14}5d^16s^2
Hafnium Hf 72 [\text{Xe}]4f^{14}5d^26s^2
Tantalum Ta 73 [\text{Xe}]4f^{14}5d^36s^2
Tungsten W 74 [\text{Xe}]4f^{14}5d^46s^2
Rhenium Re 75 [\text{Xe}]4f^{14}5d^56s^2
Osmium Os 76 [\text{Xe}]4f^{14}5d^66s^2
Iridium Ir 77 [\text{Xe}]4f^{14}5d^76s^2
Platinum Pt 78 [\text{Xe}]4f^{14}5d^96s^1
Gold Au 79 [\text{Xe}]4f^{14}5d^{10}6s^1
Mercury Hg 80 [\text{Xe}]4f^{14}5d^{10}6s^2
Thallium Tl 81 [\text{Xe}]4f^{14}5d^{10}6s^26p^1
Lead Pb 82 [\text{Xe}]4f^{14}5d^{10}6s^26p^2
Bismuth Bi 83 [\text{Xe}]4f^{14}5d^{10}6s^26p^3
Polonium Po 84 [\text{Xe}]4f^{14}5d^{10}6s^26p^4
Astatine At 85 [\text{Xe}]4f^{14}5d^{10}6s^26p^5
Radon Rn 86 [\text{Xe}]4f^{14}5d^{10}6s^26p^6

The seventh period starts with francium (Fr) and the 7s sublevel. This is followed by the 5f, and 6d. 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.

Electron Configurations of Seventh-Period Elements
Element Name Symbol Atomic Number Noble Gas Electron Configuration
Francium Fr 87 [\text{Rn}]7s^1
Radium Ra 88 [\text{Rn}]7s^2
Actinium Ac 89 [\text{Rn}]6d^17s^2
Thorium Th 90 [\text{Rn}]6d^27s^2
Protactinium Pa 91 [\text{Rn}]5f^26d^17s^2
Uranium U 92 [\text{Rn}]5f^36d^17s^2
Neptunium Np 93 [\text{Rn}]5f^46d^17s^2
Plutonium Pu 94 [\text{Rn}]5f^67s^2
Americium Am 95 [\text{Rn}]5f^77s^2
Curium Cm 96 [\text{Rn}]5f^76d^17s^2
Berkelium Bk 97 [\text{Rn}]5f^97s^2
Californium Cf 98 [\text{Rn}]5f^{10}7s^2
Einsteinium Es 99 [\text{Rn}]5f^{11}7s^2
Fermium Fm 100 [\text{Rn}]5f^{12}7s^2
Mendelevium Md 101 [\text{Rn}]5f^{13}7s^2
Nobelium No 102 [\text{Rn}]5f^{14}7s^2
Lawrencium Lr 103 [\text{Rn}]5f^{14}6d^17s^2
Rutherfordium Rf 104 [\text{Rn}]5f^{14}6d^27s^2
Dubnium Db 105 [\text{Rn}]5f^{14}6d^36s^2
Seaborgium Sg 106 [\text{Rn}]5f^{14}6d^47s^2
Bohrium Bh 107 [\text{Rn}]5f^{14}6d^57s^2
Hassium Hs 108 [\text{Rn}]5f^{14}6d^67s^2
Meitnerium Mt 109 [\text{Rn}]5f^{14}6d^77s^2

Lesson Summary

  • Electrons occupy atomic orbitals in the ground state of atoms according to the Aufbau principle, the Pauli exclusion principle, and Hund’s rule.
  • Orbital filling diagrams are drawn to show how electrons fill up energy levels and orbitals from low energy to high.
  • The electron configuration is unique for each element.
  • Valence electrons are the electrons in the outermost principal energy level and there is a maximum of eight.
  • Unpaired electrons are important to an atom’s magnetic properties.
  • Some electron configurations such as those of chromium and copper, do not strictly follow the Aufbau principle.

Lesson Review Questions

Reviewing Concepts

  1. What do the superscripts in an electron configuration represent?
    1. What is the atomic number of an element with the full electron configuration of 1s22s22p23s23p63d104s24p5?
  2. Arrange these sublevels in order of increasing energy: 3p, 5s, 4f, 2s, 3d.
  3. Which rule is violated with the electron configuration 1s22s22p63s23p63d2? Explain.
  4. Which rule is violated by the orbital filling diagrams below? Explain.

Problems

  1. Using only the atomic number, construct orbital filling diagrams for the following elements. Note: none are exceptions to the Aufbau principle.
    1. boron (Z = 5)
    2. sulfur (Z = 16)
    3. nickel (Z = 28)
    4. rubidium (Z = 37)
  2. Using only the atomic number, write full electron configurations for the following elements.
    1. fluorine (Z = 9)
    2. calcium (Z = 20)
    3. zirconium (Z = 40)
    4. europium (Z = 63)
  3. Write the noble gas configurations for the same four elements from question #6.
  4. How many electrons are in the second principal energy level of each element below?
    1. sodium
    2. nitrogen
    3. beryllium
  5. How many completely filled principal energy levels in atoms of each element?
    1. argon
    2. ruthenium
    3. barium
  6. How many principal energy levels are occupied in atoms of the elements listed in question #9?
  7. How many sublevels are occupied in an atom of aluminum? How many are completely filled?
  8. Which elements have completely filled outermost s and p sublevels?
  9. Fill in the following table (Table below). Use a periodic table to find the atomic numbers. All follow the conventional Aufbau order of filling sublevels.
Table for Problem 13
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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