Electron Arrangement

Lesson ObjectivesThe student will:

state the relationship between the principal quantum number (n), the number of orbitals, and the maximum number of electrons in a principal energy level.

draw the orbital representation for selected atoms. write the electron configuration for selected atoms.

Vocabulary angular quantum number: describes the subshell, in basic terms by shape aufbau principle: named from the German word "aufbauen" which means "to build,"

electrons fill lower energy orbitals before higher energy orbitals are filled. degenerate orbitals: orbitals with similar energy electron configuration: a written representation of the electron arrangement within

orbitals and subshells Hund's rule: all the orbitals in a degenerate set must contain one electron (half filled)

before a second electron can be added noble gas notation (electron configuration shorthand): a shorthand method of

writing electron configuration in which the noble gas in the period above is used to denote the first part of the notation

orbital: a region within an energy level where there is a probability of finding an electron. Only two electrons are possible per orbital.

orbital representation: uses circles or lines to represent each orbital principal quantum number: indicates the main energy level of an electron within an

atom.  shell: equivalent to energy level (1, 2, 3, 4...) subshell: one or more orbitals within a shell that have the same energy level (s, p, d,

and f subshells)

 

Introduction 

The quantum mechanical model is now the modern and accepted model of the atom. Unlike previous models, the quantum mechanical model of the atom does not predict the path that an electron takes around the nucleus. To understand the properties of an atom, there are four quantum numbers that describe an electron's energy, orbital shape, orientation, and spin state.

According to the Pauli Exclusion Principle, named after Wolfgang Pauli, no two electrons in a given atom can have the same four quantum numbers. While there are four quantum numbers, you only need to know the first two:

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the principal quantum number (n) describes the energy level the angular quantum number (l) describes the shape of the orbital.

The electron cloud consists of several electron shells, or energy levels, described by the principal quantum number. The subshells within each energy level are described by the angular quantum numbers. Each subshell has a certain number of orbitals that can hold 2 electrons each. This can be compared to a school's campus: The campus is made up of buildings, the buildings contain multiple halls, and each hall contains classrooms. The most likely location of students is inside their assigned classrooms. In a similar fashion, an electron cloud is made up of levels. Each level has one or more sublevels, and each sublevel has at least one orbital. The electrons are most likely found in their orbitals.

 

Put the following in order from largest (5) to smallest (1): 

  

Energy Levels

The shell or level is generally symbolized by n, and denotes the probable distance of the electron from the nucleus; "n" is also known as the principle quantum number. The principal quantum number is a positive integer (1, 2, 3, . . .n) that indicates the main energy level of an electron within an atom.  Each energy level corresponds to a row on the periodic table.

 

 

Subshells

According to quantum mechanics, every principal energy level (or shell) has one or more subshells within it. There are four possible types of subshells, and each is identified by a letter.

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Beginning with the lowest energy subshell, the subshells are identified by the letters s, p, d, and f. These letters stand for the following:

s = sharp p = principal d = diffuse f = fundamental

Every energy level will have an s subshell, but only energy levels 2 and above will have p subshells. Similarly, d subshells occur in energy level 3 and above, and f subshells occur in energy level 4 and above. The shapes of the orbitals in the s, p, d, and f subshells are illustrated below.

 

Subshells p, d, and f are degenerate subshells. Although there is only one s orbital per energy level, there are three p orbitals, five d orbitals, and seven f orbitals. We will discuss these in more detail below.

 

Orbitals

An orbital is defined as an area in the electron cloud where the probability of finding the electron is high. An orbital can hold only two electrons. The number of orbitals in an energy level is equal to the square of the principal quantum number. So, level 1 has 1 orbital (12), energy level 2 will have 4 orbitals (22), energy level 3 will have 9 orbitals (32), and energy level 4 will have 16 orbitals (42).

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Energy level 1 contains only an s orbital which is shaped like a sphere:

 

 

Energy level 2 contains an s orbital and three p orbitals, px, py, and pz. The subscripts describe the orbital's orientation in a 3-dimensional space.

 

Energy level 3 contains an s orbital, three p orbitals, and five d orbitals. The p and d subshells are degenerate orbital sets, each orbital within a set having similar energy.

 

 

Energy level 4 contains an s orbital, three p orbitals, five d orbitals, and seven f orbitals. It can get quite messy as we add energy levels!

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The chart below illustrates the relationships among the parts of the electron cloud. The maxiumum number of electrons per energy level is listed in the right column. Notice that if n equals the energy level, and the number of orbitals is n2 and each orbital can hold 2 electrons, then the maxiumum number of electrons per energy level is always 2n2. What is the total number of electrons that can be held in energy levels 1-4? Hover here to see the answer.

 

 

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Watch the video below to get a better understanding of orbitals and electron filling diagrams.

   

https://www.youtube.com/watch?v=2AFPfg0Como

Orbital Representation

Orbital representation uses circles or lines to represent each orbital.

In the figure below, all the energy levels, subshells, and orbitals are represented through 6s . The distance from the bottom of the chart indicates the energy of each energy level and subshell. The closer the energy level is to the bottom of the chart, the lower its energy. At the bottom of the chart, you will find the first energy level, n = 1. The chart shows only one square in the first energy level. This is because the first energy level contains only one s subshell, and s subshells have only one orbital.

 

 

Proceeding up the chart (higher energy), we see the second energy level, n= 2. The second energy level has both an s subshell and a p subshell. The s subshell in the second energy level, like all   s sub-levels, contains only one orbital and is represented by a single square. The second energy level also has a p subshell, which consists of three degenerate orbitals. The three orbitals in the p subshell all have the same energy. Therefore, the p subshell is represented by three squares equidistant from the bottom of the chart. This process is continued through the first four energy levels and partially into the fifth and sixth.

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Careful observation of the orbital representation chart will show that the next higher energy subshell is not always what you might expect. If you look closely at the relationship between the 3d and 4s subshells, you will notice that the 4s subshell is lower in energy than the 3d subshell. Therefore, when the energy subshells are being filled with electrons, the 4s orbital is filled before the 3d orbitals. As you go up the chart, there are more of these variations. The complete filling order is represented in the chart below. To determine the filling order, follow the top arrow from the base to the arrowhead. When you reach the arrowhead, move to the base of the next arrow and follow it to the arrowhead.

 

Filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. The numbers that precede the letters refer to the energy level, not the quantity of orbitals. For example, 2p means the p orbital set in the second energy level, and 4s means the s orbital in the fourth energy level.

Filling order is also evident by looking at the periodic table. Notice energy level 1 (period 1) only contains two elements, hydrogen and helium, and their electrons occupy the 1s shell only (as indicated on the table). Energy level 2 (period 2) contains eight elements that have electrons in the s and p orbitals of the second energy level. The same thing occurs with period 3. At period 4 things change slightly. As you move across the periodic table, you see that the 4s orbital is first, followed by the 3d orbitals, and finally the 4p orbitals. Notice that it looks as if the entire transition metal group has been dropped down a notch. It hasn't, but as long as you remember that the transition metals start filling in the 3d orbitals, you will always be able to decipher filling order by looking at the periodic table. The f orbitals are filled with electrons from the inner transition metals. Remember that lanthanides and actinides insert right into periods 6 and 7 of the periodic table, but f orbitals don't occur until energy level 4, so that's why these series must be labeled 4f and 5f. If you read the periodic table across, you will see the correct filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p...

The periodic table can now be broken up into blocks based on where the valence and other electrons reside. The alkali and alkaline earth metals of groups 1 and 2 (include helium) are part of the s block because their valence electrons are located in s orbitals. Groups 13-18 (except for helium) are part of the p block because their valence electrons reside in p orbitals. Similarly, the

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transition metals make up the d block, and the inner transition metals are in the f block. This will make more sense when we start looking at electron configurations next.

 

 Show/hide quiz group...

 

 

Rules for Determining Electron Configuration:

1. Following the Aufbau principle, each added electron enters the lowest energy orbital available.

2. No more than two electrons can be placed in any orbital.3. Before a second electron can be placed in any orbital, all the orbitals of that sub-level

must contain at least one electron. This is known as Hund's Rule .

Below is the orbital representation for the electron configuration of carbon. A carbon atom has six protons and six electrons. When placing the electrons in the appropriate orbitals, the first two electrons go into the 1s orbital, the second two go into the 2s orbital, and the last two go into the 2p orbitals. Since electrons repel each other, the electrons in the 2p orbitals go into separate orbitals before pairing up. Hund's rule is a statement of this principle, stating that no electrons are paired in a given orbital until all the orbitals of the same degenerate subshell have received at least one electron.

If you look below at the orbital representation for the electron configuration of oxygen which has eight electrons, you will see that all three 2p orbitals have at least one electron and only one 2p

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orbital has two electrons. The electron configuration lists the number of the principal energy level followed by the letter of the subshell type. A superscript is placed on the subshell letter to indicate the number of electrons in that subshell. The electron configuration for carbon is 1s22s22p2 meaning that two electrons occupy the 1s orbital, two electrons occupy the 2s orbital, and two electrons occupy the 2p orbital set.

 

 

A carbon atom has six protons and six electrons. When placing the electrons in the appropriate orbitals, the first two electrons go into the 1s orbital, the second two go into the 2s orbital, and the last two go into the 2p orbitals. Since electrons repel each other, the electrons in the 2p orbitals go into separate orbitals before pairing up. Hund's rule is a statement of this principle, stating that no electrons are paired in a given orbital until all the orbitals of the same degenerate subshell have received at least one electron. If you look below at the orbital representation for the electron configuration of oxygen which has eight electrons, you will see that all three 2p orbitals have at least one electron and only one 2 p orbital has two electrons. The electron configuration for oxygen is 1s22s22p4 meaning that two electrons occupy the 1s orbital, two electrons occupy the 2s orbital, and four electrons occupy the 2p orbital set.

 

The image below shows an example of the orbital representation for zinc. The electron configuration for zinc is 1s22s22p63s23p64s23d10 meaning that two electrons occupy the 1s orbital, two electrons occupy the 2s orbital, six electrons occupy the 2p orbital set, two electrons occupy the 3s orbital, six electrons occupy the 3p orbital set, two electrons occupy the 4s orbital, and ten electrons occupy the 3d orbital set.

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The chart below shows the electron configuration and the orbital representation for the first seven elements in the periodic table. Notice that the sum of the superscripts not only equals the total number of electrons in the atom, but for neutral atoms, it equals the proton number. So, by adding up the subscripts, you can identify the element. For example, what element is represented by the following electron configuration notation?

1s22s22p63s23p64s23d104p5

 

 

 

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Noble Gas Notation (Electron Configuration Shorthand)

As the electron configurations get longer and longer, it becomes tedious to write them out. A shortcut has been devised to make this process less tedious. Consider the electron configuration for potassium:

1s22s22p63s23p64s1

The electron configuration for argon is similar, except that it has one less electron than potassium:  1s22s22p63s23p6. It is acceptable to use [Ar] to represent the electron configuration for argon and [Ar]4s1 to represent the configuration for potassium. Using this shortcut, the electron configuration for calcium would be [Ar]4s2, and the configurations for scandium would be [Ar]4s23d1. Note that generally only noble gases (the last column on the periodic table) have their electron configurations abbreviated in this form. For example, aluminum would rarely (if ever) be represented as [Na] 3p1. Instead, the electron configuration would be written as [Ne]3s23p1.

 

Practice:

What is the electron configuration shorthand for iodine?

What is the electron configuration shorthand for barium?

 

What element is represented by the electron configuration [Ne]3s23p2?

What element is represented by the electron configuration [Kr]5s24d2?

 

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Lesson Summary

The quantum numbers are used to describe the size and shape of the electron shells and sublevels.

The electron cloud consists of several electron shells or energy levels. Within the levels are sublevels and within the sublevels are orbitals.

The orbital representation uses circles or lines to represent each atomic orbital. In the orbital representation, the distance from the bottom of the chart indicates the

energy of each energy level and sub-level. The Aufbau principle states that as electrons are added to "build up" the elements, each

electron is placed in the lowest energy orbital available. Hund's rule states that no electrons are paired in a given orbital until all the orbitals of

the same sub-level have received at least one electron. A shorthand method of representing electron arrangement is called the electron

configuration.

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The electron configuration lists the number of the principal energy level followed by the letter of the subshell type. A superscript is placed on the subshell letter to indicate the number of electrons in that sub-level.

Further Reading / Supplemental Links

Here are the Khan Academy videos on this topic, which are very helpful!

More on orbitals and electron configuration

Electron Configurations 2

 

This video provides an introduction to the electron configuration of atoms.

http://www.youtube.com/watch?v=fv-YeI4hcQ4

 

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