Problem 29 - Chemistry Matter and Change

Question

Apply the Pauli exclusion principle, the aufbau principle, and Hund's rule to write out the electron configuration and draw the orbital diagram for each of the following elements. a. silicon \(\quad\) b. fluorine \(\quad\) c. calcium \(\quad\) d. krypton

Step-by-Step Solution

Answer

Silicon: [Ne] 3s² 3p²; Fluorine: [He] 2s² 2p⁵; Calcium: [Ar] 4s²; Krypton: [Ar] 3d¹⁰ 4s² 4p⁶.

Step 1: Understanding the Given Task

To write the electron configurations and draw the orbital diagrams for silicon, fluorine, calcium, and krypton, we'll apply the Pauli exclusion principle, the aufbau principle, and Hund's rule. These principles help us understand how electrons are arranged in an atom's orbitals.

Step 1: Aufbau Principle Application

The aufbau principle states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. This is the sequence we will follow: 1s, 2s, 2p, 3s, 3p (continuing for elements with higher atomic numbers).

Step 2: Applying Hund's Rule

Hund's rule tells us that electrons will fill degenerate orbitals (orbitals of the same energy) singly before pairing up. For example, three electrons in a p subshell will each occupy one of the three p orbitals before any pairing occurs.

Step 3: Electron Configuration for Silicon

Silicon has an atomic number of 14, meaning it has 14 electrons. Its electron configuration is: 1s² 2s² 2p⁶ 3s² 3p². In the 3p subshell, Hund's rule requires that the two electrons remain unpaired in two separate orbitals until necessary to pair up.

Step 4: Drawing Orbital Diagram for Silicon

Silicon's orbital diagram is as follows: each orbital can hold 2 electrons (shown with opposite arrows). The 1s and 2s orbitals are full; 2p has 3 filled orbitals; 3s is full, and 3p has two separate electrons in its three orbitals: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑ ↑

Step 5: Electron Configuration for Fluorine

Fluorine has 9 electrons, with the electron configuration: 1s² 2s² 2p⁵. The 2p subshell will have five electrons, with the three orbitals having one pair in one orbital, and the others having single electrons.

Step 6: Drawing Orbital Diagram for Fluorine

Fluorine's orbital diagram looks like this: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑ ↑

Step 7: Electron Configuration for Calcium

Calcium has 20 electrons, with the following configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s². Here, the outermost filled shell is the 4s orbital, containing 2 electrons.

Step 8: Drawing Orbital Diagram for Calcium

The orbital diagram for calcium: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓

Step 9: Electron Configuration for Krypton

Krypton, with 36 electrons, has this configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶. The 3d subshell accommodates 10 electrons and the 4p is fully filled with 6 electrons.

Step 10: Drawing Orbital Diagram for Krypton

Krypton's orbital diagram is: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ 3d: ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 4p: ↑↓ ↑↓ ↑↓

Key Concepts

Pauli exclusion principle

The Pauli exclusion principle is a crucial rule in quantum mechanics. It states that no two electrons in an atom can have the same set of all four quantum numbers. Quantum numbers are like an address system for electrons within an atom's orbitals. These numbers are:

• Principal quantum number (n): Indicates the energy level or shell.
• Angular momentum quantum number (l): Determines the shape of the orbital.
• Magnetic quantum number (m): Specifies the orientation of the orbital.
• Spin quantum number (s): Has values of +1/2 or -1/2, which represent the two possible electron spins.

Due to this principle, an atomic orbital can hold a maximum of two electrons with opposite spins. This creates stability by ensuring electrons are paired with opposite spins within any given orbital. Understanding this principle helps explain the electron filling order and behavior in atoms.

Hund's rule

Hund's rule adds another layer of understanding for electron placement within orbitals. When electrons are distributed among degenerate orbitals (orbitals within the same subshell with the same energy level), Hund's rule states that electrons will occupy empty orbitals singly before pairing up. Think of it like riders getting into separate cars on a Ferris wheel before doubling up. This happens because electrons repel each other due to having the same negative charge. Placing them in separate orbitals minimizes this repulsion. For example, in the case of the 2p subshell, there are three p orbitals. Three electrons will each fill one of these orbitals on their own before any two start sharing an orbital. This rule helps in predicting the distribution of electrons and increasing stability within an atom's electron cloud.

Atomic orbitals

Atomic orbitals are regions around an atom's nucleus where electrons are likely to be found. Each orbital is defined by a specific energy level and shape, corresponding to different quantum mechanical properties:

• s orbitals: Spherical in shape and can hold up to two electrons.
• p orbitals: Dumbbell-shaped and consist of three different orientations, each holding up to two electrons, totaling six.
• d orbitals: More complex shapes with five orientations, allowing up to ten electrons in a d subshell.
• f orbitals: Even more complex, consisting of seven orientations, accommodating up to fourteen electrons.

Understanding atomic orbitals is essential for visualizing how electrons interact with each other and are arranged in atoms. Each element has its unique combination of orbitals, determining its chemical behavior and interaction with other elements.

Orbital diagram

An orbital diagram provides a visual representation of the electrons in an atom's orbitals. These diagrams help illustrate how electrons are arranged across the different energy levels and subshells, using a line or box for each orbital and arrows to signify the electrons. The arrows depict electron spin; one arrow pointing up (↑) and the other down (↓) indicates the opposite spins in a paired state. Consider the orbital diagram for silicon: its electron configuration is 1s² 2s² 2p⁶ 3s² 3p², translating to various boxes filled with paired and unpaired arrows according to the Pauli exclusion principle and Hund's rule. By following these guidelines, orbital diagrams provide a simplified way to see electron distribution, facilitating a deeper understanding of the chemical properties of elements.