Quantum Theory and Electronic Structure: Electron Configuration, Orbital Diagrams, Aufbau’s Principle, and Hund’s Rule

Question

Consider magnesium (Mg), silicon (Si), and sulfur (S). Which of the following atoms has 2 unpaired electrons?

  1. Mg
  2. Si
  3. S
  4. Both Mg and S
  5. Both Si and S

 

Show/Hide Answer

e. Both Si and S

Refer to Section 2.6: Electronic Structure of Atoms (Electron Configurations) (1).

Strategy Map

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Check out the strategy map.

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Table 1: Strategy Map
Strategy Map Steps 
1. Find the element on the periodic table and note its atomic number.

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The atomic number (Z) describes the number of electrons the atom has.

This image shows the periodic table of the elements.

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Refer to Section 3.1: The Periodic Table (2).
2. Create an orbital box diagram for each element’s electrons.

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Orbital diagrams are pictorial representations of the electron configuration; it shows the individual orbitals as boxes and the pairing arrangement of electrons as arrows.

Begin to fill your box orbital diagram starting with the lowest energy ‘1s’ orbital, and stop when you “run out” of electrons.

Follow Hund’s Rule and Aufbau’s Principle.

When filling degenerate (same energy) orbitals, Hund’s Rule must be obeyed to maintain the most stable (lowest energy) electron configuration.

Hund’s Rule is shown below:

A box orbital diagram, showing the addition of electrons one through six. One upwards arrow is added to each of the three boxes from left to right, followed by a downwards arrow in each box, also from left to right. The complete box orbital diagram indicated in row six contains three separate boxes, each with one upwards arrow and one downwards arrow. The image contains six rows of boxes and each row contains three connected boxes. Below box one is the writing "npx", below box two is the writing "npy" and below box three is the writing "npz". In the first row, "first electron" is written at the centre above the three boxes and only the first box contains an upwards arrow which is highlighted in yellow. In the second row, "second electron" is written at the centre above the three boxes. The first two boxes of the second row contain an upwards arrow with the arrow in the second box being highlighted in yellow. In the third row, "third electron" is written at the centre above the three boxes. All three boxes of the third row contain an upwards arrow and the arrow in box three is highlighted. In the fourth row, "fourth electron" is written at the centre above the three boxes. All three boxes contain an upwards arrow and the first box also contains a highlighted downwards arrow. In the fifth row, "fifth electron" is written at the center above the three boxes. All three boxes in the fifth row contain an upwards arrow as well as a downwards arrow in the first and second box. The downwards arrow in the second box of the fifth row is highlighted. In the sixth row, "sixth electron" is written at the centre above the three boxes. All three boxes in the sixth row contain both an upwards and a downwards arrow. The downwards arrow in the third box of row six is highlighted.
3. Count the number of unpaired electrons.

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Any orbitals containing 1 single electron are described as unpaired electrons.

Solution

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Magnesium (Mg)

z = 12; 12 electrons

Mg has 0 unpaired electrons.

 

Silicon (Si)

z = 14; 14 electrons

Silicon has 2 unpaired electrons.

 

Sulfur (S)

z = 16; 16 electrons

Sulfur has 2 unpaired electrons.

 

Answer: Both Si and S

Guided Solution

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The guided solution below will give you the reasoning for each step to get your answer, with reminders and hints.

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Table 2: Guided Solution
Guided Solution Ideas
This question relies on concepts on the electronic structure of atoms.

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Refer to Section 2.6: Electronic Structure of Atoms (Electron Configurations) (1).
What does the question ask you to find?

Question: “Consider magnesium (Mg), silicon (Si), and sulfur (S). Which of the following atoms has 2 unpaired electrons?”

Consider the circumstances in which electrons are paired or unpaired.

Show/Hide Don’t Forget!
  • Aufbau Principle — Fill electrons into the lowest available energy orbital.
    • Paired electrons — If the lowest energy orbital available already has 1 electron, you will add a second electron to it with an opposite spin (represented by an arrow pointed in the opposite direction).
  • Hund’s Rule — When degenerate (same energy) orbitals are available, maximize the number of unpaired electrons with the same spin.
    • Unpaired electrons — Pay attention when filling the first, second, and third electrons into degenerate p-orbitals.
How many electrons does each element have?

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Find the atomic number (Z) on the periodic table to determine the number of electrons for each element.

Show/Hide Number of Electrons
  • Mg — 12 electrons
  • Si — 14 electrons
  • S — 16 electrons
Complete a box orbital diagram to determine the number of unpaired electrons for each element:

"Mg" is written at the top centre with an empty box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p" and a single box above the writing "3s."

"Si" is written at the top centre with an empty box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing.

"Si" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing "3p." The boxes above the writing 1s, 2s, 2p and 3s each contain one upwards arrow and one downwards arrow. Two of the three boxes above "3p" contain upward arrows only, both arrows being highlighted in yellow, with the third box left empty.

Show/Hide Watch Out!

Common Mistake: Having an even number of electrons does not always mean that they are all paired! The orbitals in the box diagram are arranged from left to right in order of increasing energy.

Refer to Figure 2.6.3 in Section 2.6: Electronic Structure of Atoms (Electron Configurations) (1)
Fill the appropriate number of electrons into each box diagram:

"Mg" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p" and a single box above the writing "3s." Each box contains one upwards arrow and one downwards arrow.

"Si" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing "3p." The boxes above the writing 1s, 2s, 2p and 3s each contain one upwards arrow and one downwards arrow. Two of the three boxes above "3p" contain upward arrows only, both arrows being highlighted in yellow, with the third box left empty.

"Si" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing "3p." The boxes above the writing 1s, 2s, 2p and 3s each contain one upwards arrow and one downwards arrow. Two of the three boxes above "3p" contain upward arrows only, both arrows being highlighted in yellow, with the third box left empty.

Show/Hide Don’t Forget!

Add electrons from left to right:

  • Maximize the number of electrons in each lowest energy available orbital before moving on.
    • Each orbital can hold a maximum of 2 electrons; the 2 electrons must have opposite spin (pointed up and down).
  • If degenerate empty orbitals are available, fill those first with unpaired electrons with the same spin before pairing electrons.

Refer to Example 2.6.1: Quantum Numbers and Electron Configurations in Section 2.6 (1)
Table 3: Complete Solution
Complete Solution 
Magnesium (Mg) is atomic number 12 and has a total of 12 electrons. The diagram is filled starting with a pair of electrons in the 1s orbital box, followed by 2s, the 2p then 3s.

All electrons are paired in magnesium.

"Si" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing "3p." The boxes above the writing 1s, 2s, 2p and 3s each contain one upwards arrow and one downwards arrow. Two of the three boxes above "3p" contain upward arrows only, both arrows being highlighted in yellow, with the third box left empty.

Silicon (Si) is atomic number 14 and has a total of 14 electrons. The diagram is filled starting with the 1s orbital box, followed by 2s, 2p, 3s then 3p.

The 3p orbital has 2/6 electrons, meaning silicon has 2 unpaired electrons.

"Si" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing "3p." The boxes above the writing 1s, 2s, 2p and 3s each contain one upwards arrow and one downwards arrow. Two of the three boxes above "3p" contain upward arrows only, both arrows being highlighted in yellow, with the third box left empty.

Sulfur (S) is atomic number 16 and has a total of 16 electrons. The diagram is filled starting with the 1s orbital box, followed by 2s, 2p, 3s then 3p.

The 3p orbital has 4/6 electrons, meaning sulfur has 2 unpaired electrons.

"S" is written at the top centre with a filled box orbital diagram below it. From left to right this contains a single box above the writing "1s" , a single box above the writing "2s", three connected boxes above the writing "2p", a single box above the writing "3s" and three connected boxes above the writing "3p." The boxes above the writing 1s, 2s, 2p and 3s each contain one upwards arrow and one downwards arrow. The first of the connected boxes above the writing "3p" contains one upwards arrow and one downwards arrow. The second and third connected boxes above the writing "3p" contain only one arrow, both facing upwards and highlighted in yellow

Answer: Both Si and S have 2 unpaired electrons

Check Your Work

Summary of what we would expect based on the related chemistry theory.

Show/Hide Watch Out!

Be sure that your box orbital diagram adheres to the guidelines:

  • The lowest energy available orbitals should be filled first.
  • Box orbitals on the left are lower energy than the right (Aufbau’s Principle).
  • All paired arrows should have opposite spin (Pauli’s Exclusion Principle).
  • When same energy orbitals are available (3 ‘p’ orbitals, or 5 ‘d’ orbitals), electrons remain unpaired with the same spin until no unoccupied orbitals remain (Hund’s Rule).

Does your answer make chemical sense?

Show/Hide Answer

When completing the box orbital diagram, count the number of arrows representing electrons; be sure it matches the number of electrons determined from the atomic number (z)!

PASS Attribution

Media Attributions

Unless otherwise noted, all figures by the authors (Brewer S. and Blackstock L.) are free to use under a CC0 license.

  • Periodic Table of Elements Black and White [adapted from Dmarcus100] by Thompson Rivers University Open Learning (7) is used under a CC BY-SA 4.0 license.

References

1. OpenStax. 2.6: Electronic Structure of Atoms (Electron Configurations). In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/02%3A_Quantum_Theory_and_Electronic_Structure_of_Atoms/2.06%3A_Electronic_Structure_of_Atoms_(Electron_Configurations).

2. OpenStax. 3.1 The Periodic Table. In CHEM1500: Chemical Bonding  and Organic Chemistry. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/CHEM_1500%3A_Chemical_Bonding_and_Organic_Chemistry/03%3A_Periodic_Relationships_Among_the_Elements/3.01%3A_The_Periodic_Table.

3. Blackstock, L.; Brewer, S.; Jensen, A. PASS Chemistry Book CHEM 1500; LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1510%2F%2F1520.

4. Blackstock, L.; Brewer, S.; Jensen, A. 2.4: Question 2.E.58 PASS – Electron Configuration, Orbital Diagrams, Aufbau’s Principle Hund’s Rule. In PASS Chemistry Book CHEM 1500. LibreTexts, 2023. https://chem.libretexts.org/Courses/Thompson_Rivers_University/PASS_Chemistry_Book_CHEM_1500/02%3A_Quantum_Theory_and_Electronic_Structure/2.04%3A_Question_2.E.58_PASS_-_electron_configuration_orbital_diagrams_Aufbau’s_Principle_Hund’s_Rule.

5. OpenStax. 6.E: Electronic Structure and Periodic Properties (Exercises). In Chemistry 1e (OpenSTAX). LibreTexts, 2023. https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX).

6. Flowers, P.; Robinson, W. R.; Langley, R.; Theopold, K. Ch. 6 Exercises. In Chemistry 2e; OpenStax, 2019. https://openstax.org/books/chemistry-2e/pages/6-exercises.

7. Thompson Rivers University Open Learning. Periodic Table Of Elements Black And White [adapted from Dmarcus100].

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