1. 5.2 Electron Arrangement in Atoms
Read the lesson title aloud to students.

2. Electron Configurations
The electron configuration is the way in which electrons are arranged in various orbitals about the nucleus of an atom.
Electron cloud
Electron orbitals
Pauli exclusion principle
Aufbau principle
Hund’s rule
Explain that in an atom, electrons and the nucleus interact to make the most stable arrangement possible, which is the arrangement with the lowest total energy. In the schematic shown of an atom, the electrons are depicted as forming a sort of “cloud” around the nucleus. Quantum mechanics reveals that the electrons occupy orbitals that have particular forms. The electron configuration is the way in which electrons are arranged in various orbitals about the nucleus of an atom.
Click to show the electron orbitals.
Tell students: There are three rules that tell you how to express the arrangement of electrons in atoms through electron configurations.
Click to reveal the three rules.
Have a volunteer read the three rules to the class.
Tell students: We will now discuss the three rules one at a time, then work some examples together.

3. Pauli Exclusion Principle
An atomic orbital describes at most two electrons. The 2 electrons will have opposite spins.
Sample
Electron orbital
“Spin-up” electron
“Spin-down” electron
Electron pair
Tell students: The Pauli exclusion principle states that an atomic orbital may describe at most two electrons.
Explain that, for example, either one or two electrons can occupy an s orbital or a p orbital. To occupy the same orbital, two electrons must have opposite spins; that is, the electron spins must be paired. Spin is a quantum mechanical property of electrons and may be thought of as clockwise or counterclockwise.
For advanced students, explain that the spin of electrons comes from combining relativity (Einstein) with quantum mechanics. By doing this, Pauli found that electrons can have a spin of either +1/2 or −1/2. Although some properties of electron spin are analogous to our macroscopic concept of spin, it is an entirely quantum phenomenon. For example, if you rotate an electron through 360 degrees, it only turns halfway around! A more precise version of the Pauli exclusion principle states that no two electrons in an atom can have identical quantum numbers (spin is a quantum number).
Tell students: A vertical arrow indicates an electron and its direction of spin.
Click to reveal the notation for electrons.
Explain that the arrow is meant to show the axis about which the electron spins. The direction of spin is determined by the right-hand rule: With your right thumb pointing up and your right fingers curled a bit, the fingers of your right hand point in the direction that the electron “spins.”
Ask: Which electron is rotating counterclockwise: the spin-up electron or the spin-down electron?
Answer: The spin-up electron is rotating counterclockwise.
Emphasize that “up” and “down” are relative terms and are not meant to be taken literally, but only to indicate that the two electrons spin in opposite directions with respect to each other.
Tell students: Because we can put at most a pair of electrons into a single orbital, we need a notation for a pair of electrons.
Ask: What do you think is the notation for a pair of electrons?
Answer: The up and down arrows are written side by side.
Click to show the notation for a pair of electrons.
Remind students that a pair of electrons is the most that we can put into a given orbital.
Click to show animation of electrons filling orbital.
Orbital full

4. Aufbau Principle Electrons first occupy the orbitals of lowest energy.
Tell students: Electrons occupy the orbitals of lowest energy first.
Explain that the orbitals for any sublevel of a principle energy level are always of equal energy. Within a principle energy level, the s sublevel is always the lowest-energy sublevel. However, the range of energy levels within a principle energy level can overlap the energy levels of another principle level.
Have students examine the Aufbau diagram on the screen. Explain that each box represents an atomic orbital and that the energy of the electrons in an orbital increases as you go up in the diagram.
Click to reveal the arrow indicating increasing energy.
Explain that the 1s orbital is the lowest-energy orbital, so it is filled first.
Ask for a volunteer to note an electron pair in the 1s box.
Click to reveal the response.
Ask for a volunteer to fill the next ten electrons. Again, student should use notation from the previous slide.
Ask for a volunteer to fill in the next ten electrons.
Explain that the 4s orbital is filled before the 3d orbitals because electrons in the 4s orbital are lower in energy than those in the 3d orbitals.
Explain that the two electrons in the 3d orbitals are in separate orbitals and are both pointing up because of Hund’s rule, which is discussed next.
Ask: What other orbitals are filled before other orbitals with lower principle quantum numbers?
Answer: The 5s orbital is filled before the 4d orbital. The 6s orbital is filled before the 5d and the 4f orbitals. The 4f orbital is filled before the 5d orbital.

5. Hund’s Rule
Unpaired electrons in orbitals of the same energy all have the same spin. Electrons will enter each of the sublevels singly, then add a second if numbers permit.
Tell students: On the screen is shown the Aufbau diagram of a few of the lower sublevels.
Tell students: Unpaired electrons in orbitals of the same energy all have the same spin (that is, all spin up or all spin down). Because two electrons of the same spin cannot occupy the same orbital, this means that the orbitals of a given sublevel are filled with single electrons before pairing up an electron in any one of the orbitals.
Have students consider the example of the configuration for six electrons.
Ask for a volunteer to note the electron configuration for six electrons.
Click to reveal the response.
Explain that four of the electrons pair up into the two lowest-energy orbitals (1s and 2s) and the final two electrons go into different orbitals in the 2p sublevel. These two electrons are both drawn as spin up, but they could both be spin down. The important point is that both spins are in the same direction.
Have students consider adding one more electron to this configuration.
Ask for a volunteer to note where the next electron would go.
Explain that the added electron must go into an available orbital with the lowest possible energy and that its spin must be aligned to those of the other electrons in that sublevel.
Have students consider adding two more electrons to this configuration.
Ask for a volunteer to note where the next two electrons would go.
Explain that the two added electrons are colored in blue and that, because each orbital in the 2p sublevel has an electron, the next two electrons pair up with previous electrons.
Ask: Why are the two blue electrons spin down?
Answer: The Pauli exclusion principle says that two electrons can occupy the same orbital only if the electrons have opposite spins.

6. Electron Configuration of Elements
2px 2py 2pz 3s
Electron Configuration H O F Na
1s1
1s22s22p4
Tell students: Consider an oxygen atom with the electron configuration shown on the screen.
Explain that an oxygen atom contains eight electrons. The orbital of lowest energy, 1s, has one electron, then a second electron of opposite spin. The next orbital to fill is 2s. It also has one electron, then a second electron of opposite spin. One electron then occupies each of the three 2p orbitals of equal energy. The remaining electron now pairs with an electron occupying one of the 2p orbitals. The other two 2p orbitals remain only half filled, with one electron each.
Ask volunteers to fill in the electron configuration of the other three elements shown.
Click to reveal the responses.
Explain how Hund’s rule is followed for each atom.
Explain that you can express the arrangement of electrons in atoms through electron configurations by writing the energy level and the symbol for every sublevel occupied by an electron. You indicate the number of electrons occupying each sublevel with a superscript. For hydrogen, with one electron in a 1s orbital, the electron configuration is written 1s1.
Click to reveal the electron configuration for hydrogen.
Explain that for helium, with two electrons in a 1s orbital, the configuration is 1s2. For oxygen, with two electrons in a 1s orbital, two electrons in a 2s orbital, and four electrons in 2p orbitals, the electron configuration is 1s22s22p4 .
Click to reveal the electron configuration for oxygen.
Note that the sum of the superscripts equals the number of electrons in the atom.
Ask: What are the correct electron configurations for fluorine and sodium?
Click to reveal the answers.
1s22s22p5
1s22s22p63s1

7. Electron Configuration for Oxygen
Why is 1s22s22p4 the electron configuration of oxygen, not 1s22s22p33s1?
1s22s22p33s1
1s22s22p4
Ask: Why is 1s22s22p4 the electron configuration of oxygen, not 1s22s22p33s1?
Work through this example with the students.
Ask for volunteers to fill in the Aufbau diagrams for each electron configuration.
Click to reveal the responses.
Explain that electrons fill the orbitals with the lowest energy first (the Aufbau principle). The 2p sublevel of oxygen has less energy than the 3s sublevel and has space for six electrons. Because there are four electrons available for this energy sublevel, all four electrons go in the 2p orbital.

8. Warning: Notation Does Not Give Energy
Consider bromine, which has 35 electrons:
1s2
2s2
2p6
3s2
3p6
4s2
4p5
3d10
Explain that when electron configurations are written, the sublevels within the same principle energy level are generally written together. These configurations are not always in the same order as shown on the Aufbau diagram.
Tell students: We shall work through the example of bromine, which is a gas at standard temperature and pressure, as shown in the photo. Bromine has 35 electrons.
Tell students: Up the to 3p level, the energy of the sublevels increases in the order in which the configuration is noted.
Click to show the notation for a filled 3p sublevel and the corresponding Aufbau diagram.
Ask: What is the next sublevel to be filled with electrons?
Answer: the 4s sublevel
Click to show the notation for the filled 4s sublevel.
Explain that the gap before the 4s2 notation in the configuration exists because the 3d sublevel will go there, even if the 3d sublevel is higher in energy than the 4s sublevel.
Click to show the filled 3d sublevel and its notation.
Explain that the final sublevel to be filled is the 4p sublevel.
Ask: How many electrons go into the 4p sublevel?
Answer: There are 30 electrons in the diagram, so there are 35 – 30 = 5 more electrons to place.
Click to show the five electrons in the 4p sublevel and its notation.

9. Several Possible Notations
Example: Bromine (Br)
Ordered by principle energy level
4p5
3d10
4s2
1s2
2s2
2p6
3s2
3p6
4p5
3d10
4s2
1s2
2s2
2p6
3s2
3p6
Ordered by energy of sublevel
Shorthand notation for Br
4p5
3d10
4s2
[Ar]
Explain that there are several possible notations for the electron configuration of atoms. The notation seen on the previous slide gives the occupancy of the sublevels ordered by principle energy level. This is shown on the screen.
Ask: How would this notation change if it is ordered by the energy of the sublevel?
Answer: The 4s2 sublevel would precede the 3d10 sublevel.
Click to show the response.
Explain that from left to right, the energy of electrons in each sublevel increases in this notation.
Tell students that a shorthand notation may also be seen.
Click to reveal the shorthand notation.
Explain that in the shorthand notation, the first noble gas with fewer electrons than the atom in question is used as a base, and the electron configuration for the subsequent electrons is noted after the noble gas.
Ask: From the shorthand notation for Br, what is the electron configuration of argon?
Answer: 1s22s22p63s23p6

10. Exceptions for Electron Configurations
Consider Cu (29 electrons):
Aufbau principle gives
1s22s22p63s23p63d94s2
Correct configuration is
Tell students: In a few cases, the Aufbau principle gives the incorrect electron configuration. In other words, filling the sublevels with electrons starting with the lowest-energy sublevel does not lead to the correct electron configuration.
Explain that you can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the Aufbau diagram for orbital filling. If you were to continue in that fashion, however, you would assign chromium and copper incorrect configurations.
Tell students: We shall consider the electron configuration of Cu first.
Ask a volunteer to fill in the Aufbau diagram for Cu using the Aufbau principle.
Click to reveal the response.
Ask a volunteer to write the electron configuration for Cu on the write-on line.
Explain that this configuration gives copper a partially filled 3d sublevel (see 3d9 in black on screen). Filled energy sublevels are more stable than partially filled sublevels. Some actual electron configurations differ from those assigned using the Aufbau principle because although half-filled sublevels are not as stable as filled sublevels, they are more stable than other configurations. This tendency overcomes the small difference between the energies of the 3d and 4s sublevels in copper and chromium. Thus, in copper, the total energy of the electrons is lower if the 3d shell is filled and the 4s shell is singly occupied.
Click to reveal the correct electron configuration for copper.
1s22s22p63s23p63d104s1

11. Chromium: Another Exception to Aufbau
The Aufbau principle gives the incorrect electron configuration for chromium (24 electrons).
Aufbau principle gives
1s22s22p63s23p63d44s2
Correct configuration is
Tell students: Chromium is another example where the Aufbau principle gives the incorrect electron configuration.
Ask a volunteer to fill in the Aufbau diagram for chromium using the Aufbau principle.
Click to reveal the response.
Ask a volunteer to write the electron configuration for chromium on the write-on line.
Explain that this configuration gives chromium a partially filled 3d sublevel and a filled 4s sublevel (see 3d4 in black on screen). However, because the 4s sublevel and the 3d sublevel are very close in energy, it turns out that a lower-energy configuration is to have one electron in the 4s sublevel and add an electron to the 3d sublevel.
Click to reveal the correct electron configuration for chromium.
Explain that at higher principal quantum numbers, energy differences between some sublevels (such as 5f and 6d, for example) are even smaller than in the chromium and copper examples. As a result, there are other exceptions to the Aufbau principle. Although it is worth knowing that exceptions to the Aufbau principle occur, it is more important to understand the general rules for determining electron configurations in the many cases in which the Aufbau principle applies.
1s22s22p63s23p63d54s1