2.4: Question 2.E.58 PASS - electron configuration, orbital diagrams, Aufbau's Principle Hund's Rule

Exercise \(\PageIndex{2.E.58}\)

Consider magnesium (Mg), silicon (Si), and sulfur (S).

Which of the following atoms has two unpaired electrons?

a) Mg

b) Si

c) S

d) Both Mg and S

e) Both Si and S

Answer

e) Both Si and S

See LibreText 2.6 Electronic Structure of Atoms

Strategy Map

Step	Hint
1. Find your element on the Periodic Table and note its atomic number	The atomic number (Z) describes the number of electrons the atom has Recall (LibreText section 3.1): The Periodic Table
2. Create an orbital box diagram for each elements electrons	Orbital diagrams are pictorial representations of the electron configuration, showing 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 Principle
3. Count the number of unpaired electrons	Any orbitals containing one single electron are described as unpaired electrons

Solution

Magnesium (Mg): 12 electrons

Mg has no unpaired electrons

Silicon (Si): 14 electrons

Silicon has two unpaired electrons

Sulfur (S): 16 electrons

Sulfur has 2 unpaired electrons

Answer

e) Both Si and S

Guided Solution

Guided Solution	Hint
This problem relies on concepts from Electronic Structure of Atoms (Electron Configurations)	Refer to LibreText 2.6, Electronic Structure of Atoms (Electron Configurations)
What does the question ask you to find? Question Consider magnesium (Mg), silicon (Si), and sulfur (S). Which of the following atoms has two unpaired electrons? Consider the circumstances in which electrons are paired or unpaired	Aufbau Principle: Fill electrons into the lowest available energy orbital Paired electrons: If the lowest energy orbital available already has one 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? Mg: 12 electrons Si: 14 electrons S: 16 electrons	Find the atomic number (Z) on the Periodic Table to determine the number of electrons for each element
Complete a Box Orbital diagram to determine the number of unpaired electrons for each element	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 See LibreText Figure 2.6.2 - The Aufbau Principle
Fill the appropriate number of electrons into each box diagram	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 two electrons the two 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 See LibreText Example 2.6.1: Quantum Numbers and Electron Configurations
Complete Solution: Mg Magnesium, atomic number 12, has a total of twelve 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 Silicon, atomic number 14, has a total of fourteen 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 two unpaired electrons. S Sulfur, atomic number 16, has a total of sixteen 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 two unpaired electrons.	When filling degenerate (same enegy) orbitals, Hund's Rule must be obeyed to maintain the most stable (lowest energy) electron configuration. Hund's Rule is shown below:
Check your work! When completing the box orbital diagram, count the number of arrows; be sure it matches the number of electrons determined from the atomic number!

(question source adapted question 6.4.14 from 6.E: Electronic Structure and Periodic Properties (Exercises): https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_1e_(OpenSTAX)/06%3A_Electronic_Structure_and_Periodic_Properties_of_Elements/6.E%3A_Electronic_Structure_and_Periodic_Properties_(Exercises), shared under a CC BY 4.0 license, authored, remixed, and/or curated by OpenStax, original source question 59 https://openstax.org/books/chemistry-2e/pages/6-exercises, Access for free at https://openstax.org/books/chemistry/pages/1-introduction)