 Lesson : Orbital diagrams and Electron Configurations

## LEARNING GOALS

3.2.1 Describe how Schrodinger advanced the understanding of atomic structure. Define orbital (electron cloud). Explain how the quantum mechanical model is based upon the idea that electrons travel in waves.

3.2.2 Explain the organization of energy levels, sub-levels (s, p, d, and f), and orbitals in atoms.

3.2.3 Describe and sketch the appearance of s and p orbitals.

3.2.4 State the maximum number of orbitals and electrons found in each sub-level.

3.2.5 Apply the Aufbau principle, Hund’s rule and Pauli exclusion principle to construct electron configurations (extended and noble gas format) and orbital diagrams to show the locations of electrons for atoms up to Z = 18.

3.2.6 Define valence electrons. Identify the valence electrons in orbital diagrams and electron configurations. Draw dot diagrams for elements.

## INTRODUCTION

If you take a look at the periodic table, what you'll notice is that hydrogen is a very special element. Hydrogen is the first element, and thus, it only has one electron. It turns out that Bohr's model of the atom worked very well provided it was used to describe atoms with only one electron. The moment that the Bohr model was applied to an element with more than one electron (which, unfortunately, includes every element except hydrogen), the Bohr model failed miserably. Bohr's model failed because it generalized the behavior of electrons to be like that of large objects, such as planets in orbit. Many of the differences between electrons and planets is how the objects interact. As a result, while Bohr's model worked for hydrogen, it became worse and worse at predicting the atomic spectra for atoms with more and more electrons. Even helium, with two electrons, was something of a disaster!

Another problem with Bohr's model was the predicted positions of the electrons in the electron cloud. If Bohr's model was correct, the hydrogen atom electron in ground state would always be the same distance from the nucleus. If we could take a series of photographic snapshots of a hydrogen electron cloud that would freeze the position of the electron so we could see exactly where it was located at different times, we still wouldn't know the path the electron followed to get from place to place, but we could see a few positions for the electron. Such an image of electron positions would show the electron could actually be various distances from the nucleus rather that at a constant distance. Also, he could not offer an explanation for why only the exact energy levels he calculated were present, that is, what is there about electrons in electron clouds that produce only a specific set of energy levels.

## DISCUSSION

Atomic Orbitals

The focus in this lesson will be on the current theory that describes and depicts the arrangement of electrons in atoms. In the Bohr model, the atom is viewed as a densely packed nucleus comprised of neutrons and protons that is surrounded by electrons at fixed distances, which correspond to specific energy levels. However, the quantum model, the current theory, is based on mathematics. Although it is more difficult to understand than the Bohr model, it can be used to explain observations made on complex atoms. This model shows that the distances between electrons and the nucleus are not really fixed. Due to their wave-like nature, we cannot pinpoint the exact location of an electron that is in motion, but we can determine the probability that a given electron will be in a particular region in three-dimensional space. Schrodinger’s equations are used to determine the position of a specific electron with respect to a nearby nucleus. The region in space in which an electron is most likely to be found is referred to as an orbital. The following is a video which depicts examples of orbitals.

s, p, d, and f Orbitals

The shapes corresponding to each orbital are designated by a single letter. You must be able to draw the shape of an s and a p orbital. The first orbital we will examine is the most basic orbital shape. It is an s orbital. This orbital is spherical in shape, as seen in Figure 1, and can contain a maximum of two electrons. FIGURE 1 An s orbital

The next orbital we will examine is more complicated than the s orbital, it is known as the p orbital. p orbitals can have three possible orientations each of which is perpendicular to the two others in three-dimensional space (Figure 2), and each of the p orbitals can contain a maximum of two electrons, for a total of six electrons. FIGURE 2 Three individual p orbitals are centered on the nucleus of the atom. This figure shows them both separately and together.

Continuing our exploration of orbitals is the d orbitals. These are even more complicated shapes than the s or the p orbital. The relative orientations for each of these orbitals are shown in Figure 3. Note that even though one of the d orbitals appears to have a different shape than the others, it is still mathematically equivalent and exhibits the same properties (such as total energy) as the other d orbitals.  Each of the five p orbitals can contain a maximum of two electrons in each, for a total of ten electrons. FIGURE 3 Relative geometry of the d orbitals

The most complex set of orbitals that we will encounter are the f orbitals. There are a total of seven distinct orbitals. The relative orientations for each of these orbitals are shown in Figure 4. Each of the seven d orbitals can contain a maximum of two electrons in each, for a total of fourteen electrons. FIGURE 4 Relative geometry of the f orbitals

Rules for Electron placement

Electrons fill energy levels with lower energy first.  Energy levels can be broken into sublevels.  The orbitals of one type (described above) make up a sublevel.  For example, the 3 p orbitals make up a p sublevel.

 sublevel # orbitals # of electrons in sublevel s 1 2 p 3 6 d 5 10 f 7 14

These sublevels can be present in more than one energy level.  The Energy Level (the #) only holds that # of sublevels. The break down of sublevels is in the following table.

 Energy Level # of Sublevels sublevels 1 1 1s 2 2 2s  2p 3 3 3s 3p 3d 4 4 4s 4p 4d 4f n n -----

Using the break down of energy levels, sublevels, and orbitals the atomic model can be represented.  See the following diagrams to grasp the complexity of the models and how they fit together. Hydrogen through NeonHydrogen has a single electron in a 1s orbital.This is the only atom for which Bohr's planetary model gave accurate results.Helium also just has a 1s orbital. It has two electrons but also two protons. So the stronger attraction of the nucleus makes the helium s orbital only a little more than half the radius of the hydrogen s orbital. Lithium and beryllium have a 2s as well. Since lithium has three protons and beryllium has four protons, the attraction of the nucleus on the electrons is is greater so the 1s radius is about a third that of hydrogen.Neon is the first element with a stable octet with complete p and s orbitals. The reason the octet is so stable is that the only way to add electrons is to add the next s orbital outward. There is no way to add electrons to the 2 shell of neon, period.   Period 3 (Sodium to Argon)With sodium, we add a 3s orbital and at aluminum we begin adding 3p orbitals. Note that the 3p orbitals are larger than the 3s orbital.Argon is the next element with a stable octet with complete p and s orbitals. The reason the octet is so stable is that the only way to add electrons is to add the next s orbital outward. It is possible to add 3d orbitals, but not until the 4s orbital is full. So it's all but impossible to make reactive ions out of the noble gases.    Period 4: Potassium  With potassium and calcium we begin adding the 4s sublevel.
http://www.uwgb.edu/dutchs/Petrology/ScaleAtomsHeKr.HTM

Beyond 20 electrons atoms, the filling of orbitals is electrons does not follow the order above provided above.
 Energy Level # of Sublevels sublevels 1 1 1s 2 2 2s  2p 3 3 3s 3p 3d 4 4 4s 4p 4d 4f n n -----

The electrons actually fill in the following order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p

Rules for Determining Electron Configurations

As evidenced by the diagrams above, the quantum model representations of atoms can be very complex. Scientists have come up with a simplistic representation to show the placement of electrons in sublevels. An orbital diagram provides a visual representation of the way in which an atom’s electrons are distributed into various orbitals. Each orbital is shown as a single square, and orbitals within the same sub-level are drawn directly next to each other. Each sub-level is labeled by its energy level number and by its sub-level. Electrons are indicated by arrows inside the squares. An arrow pointing upwards indicates one spin direction, while a downward pointing arrow indicates the other direction. The representation on the right is called an orbital diagram.  The left diagram shows the deviated order, 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p. Follow the arrows from the top 1s 2s 2p 3s 3p.  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. You will need to be able to construct orbital diagrams that go up to the 3p sub-level. When constructing an orbital diagram three rules must be followed.  The three rules are described below.

Aufbau Principle

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 “building-up” 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.

Pauli Exclusion Principle

The Pauli exclusion principle states that two electrons occupying the same orbital must have opposite spins. To denote this we will use up and down arrows in orbital diagrams. Hund’s Rule

Hund’s rule states that, in a set of orbitals that are energetically equivalent, each orbital is occupied by a single electron before any orbital within the set is occupied by a second electron. Additionally, all electrons in singly occupied orbitals prefer to have the same spin (all arrows up or all arrows down when representing electrons). We will see more concrete examples of how this rule works below in our discussion of orbital filling diagrams. Electron Configuration Notation

The set of orbitals occupied by electrons in a given atom is referred to as its electron configuration. An electron configuration essentially provides a map of where each electron is likely to be located in a given atom. In the case of a free, electrically neutral atom, the atom is considered to be in a ground state. This means its electrons are in the lowest energy locations. The rules above should be used to determine the lowest energy locations of the various electrons in a free atom. Electron configuration notation is a shorthand version of the information contained in orbital diagrams. The squares and arrows are eliminated and replaced with the name of each occupied level, sub-level and a superscript indicating the number of electrons present in that sub-level. For example, the configuration of a hydrogen atom is 1s1, and the configuration of helium is 1s2. Multiple occupied sub-levels are placed one after another, so the electron configuration of lithium is written 1s22s1. The sum of all 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.

Examples: Electron Configurations - The First 10 Elements

Hydrogen and Helium - The 1s Orbital

We start with hydrogen, which has only one electron. According to the Aufbau principle, this should be placed into the 1s orbital, which is the lowest energy orbital. The configuration of hydrogen is 1s1.

Helium has two electrons. The lowest energy orbital (1s) has enough room to accommodate both electrons, so Helium has a 1s2 configuration.

Lithium and Beryllium - The 2s Orbital

Now that we have filled the 1s shell, we move to the 2nd energy level and start to work on the second shell with lithium. Lithium has a configuration of 1s22s1.

Beryllium has a configuration of 1s22s2.

Boron Through Neon - The 2p Orbitals

Now that the 1s and 2s orbitals are filled, the next lowest energy orbitals are the three 2p orbitals.

Boron has a configuration of 1s22s22p1.

Beginning with carbon, we start to see Hund’s rule come into play. The rule states that orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin.

Carbon has a configuration of 1s22s22p2.

Nitrogen has a third 2p electron, Nitrogen has a configuration of 1s22s22p3.

Now that we have no more empty orbitals within this subshell, we need to start putting electrons in orbitals that are already partially occupied. For oxygen, one of the 2p orbitals will contain two electrons, while the others will still each have one. The electrons in the doubly occupied 2p orbital must have different spins to avoid violating the Pauli exclusion principle. Oxygen has a configuration of 1s22s22p4.

Adding another 2p electron gives us fluorine’s configuration of 1s22s22p5.

Once we reach neon, a noble gas, all of the 2p orbitals will be completely full. Neon has a configuration of 1s22s22p6. Any further electrons will need to go in the next highest energy orbital, which would be the 3s orbital.

Electron configurations and orbital filling diagrams for lithium through neon are provided below. Lesson Review Questions

1. Draw orbital diagrams and then the electron configurations for the following atoms:

a. H
b. Li
c. N
d. F
e. Br

2. List the total number of electrons needed to fully occupy energy levels 1-4.

3. State the Aufbau principle, the Pauli exclusion principle, and Hund’s rule (you will not need to have th names of the rules memorized).

Adapted from 2014 CK-12 Foundation, www.ck12.org