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 b. fluorine c. calcium d. krypton

Short answer

Electron configurations and orbital diagrams for the given elements are as follows: a. Silicon (Si): Electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^2\) Orbital diagram: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑ ↑ b. Fluorine (F): Electron configuration: \(1s^2 2s^2 2p^5\) Orbital diagram: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑ c. Calcium (Ca): Electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\) Orbital diagram: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ d. Krypton (Kr): Electron configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) Orbital diagram: 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ 3d: ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 4p: ↑↓ ↑↓ ↑↓

Step-by-step solution

(Pauli exclusion principle)

The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. In simpler terms, in any given orbital, there can be at most two electrons with opposite spins.

(Aufbau principle)

The aufbau principle states that electrons fill orbitals with the lowest energy levels first, and then move to higher energy orbitals only after the lower energy orbitals are filled.

(Hund's rule)

Hund's rule states that electrons will occupy orbitals of the same energy (also called degenerate orbitals) in a way that maximizes the number of parallel spins. In simple terms, when filling orbitals with the same energy, electrons will fill each orbital with one electron before pairing up with opposite spins. Now we'll apply these principles and rules to write the electron configurations and draw the orbital diagrams for each given element. a. Silicon (Si): Atomic number = 14 (14 electrons)

(Electron configuration for Si)

\(1s^2 2s^2 2p^6 3s^2 3p^2\)

(Orbital diagram for Si)

1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑ ↑ b. Fluorine (F): Atomic number = 9 (9 electrons)

(Electron configuration for F)

\(1s^2 2s^2 2p^5\)

(Orbital diagram for F)

1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑ c. Calcium (Ca): Atomic number = 20 (20 electrons)

(Electron configuration for Ca)

\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\)

(Orbital diagram for Ca)

1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ d. Krypton (Kr): Atomic number = 36 (36 electrons)

(Electron configuration for Kr)

\(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\)

(Orbital diagram for Kr)

1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ 3d: ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 4p: ↑↓ ↑↓ ↑↓

Key concepts

Pauli Exclusion Principle

The Pauli exclusion principle is a fundamental rule in quantum mechanics that plays a critical role in the arrangement of electrons around the nucleus of an atom. This principle asserts that no two electrons within an atom can possess the same set of four quantum numbers.

In simpler terms, this means each electron in an atom has a unique identity. The unique identity is ensured by having electrons within the same orbital possess opposite spins. An orbital can house at most two electrons.

To better visualize this, consider an atomic orbital as a small space where an electron lives. By having opposite spins, represented often by arrows pointing in opposite directions (↑↓), the electrons share the same spatial environment in compliance with the Pauli exclusion principle. This rule is crucial as it dictates the specific arrangement of electrons in multi-electron atoms, influencing the overall electronic configuration and the chemical properties of elements.

Aufbau Principle

The Aufbau principle is a guideline used to determine the electron configuration of an atom. Derived from the German word "aufbauen," meaning "to build up," this principle describes how electrons fill the atomic orbitals.

According to the Aufbau principle, electrons fill orbitals starting with the lowest energy level available and gradually fill higher energy levels. This is because electrons reside in the most stable and lowest energy configuration possible.

For example, in the electron configuration for silicon, with an atomic number of 14, electrons will first fill the lower energy levels beginning with the 1s orbital, followed by the 2s, 2p, and so forth. A complete electron configuration for silicon in terms of the Aufbau principle looks like this:

• 1s: two electrons
• 2s: two electrons
• 2p: six electrons
• 3s: two electrons
• 3p: two electrons

This principle helps us predict the order of filling, providing clarity on how electrons occupy orbitals in atoms of different elements.

Hund's Rule

Hund's rule is a key principle used alongside the Pauli exclusion and Aufbau principles to determine the electron configurations of atoms, particularly when multiple orbitals of the same energy are available. This rule helps decide how electrons are distributed among orbitals of equal energy (degenerate orbitals).

Hund's rule states that electrons will fill each degenerate orbital singly before any electron pairing occurs within those orbitals. Additionally, within a subshell, electrons prefer to exist with parallel spins, which means having all spins in the same direction before they pair up.

An example illustrating Hund's rule can be seen in the 2p orbital of fluorine, which follows the configuration 1s² 2s² 2p⁵. Within the 2p orbital, there are three identical energy levels, and thus, the electrons will spread out one in each orbital before pairing up, aiming to minimize electron-electron repulsions and stabilize the atom.

Remember, a single electron in an orbital will be represented by either an up (↑) or down (↓) arrow. Applying Hund's rule correctly results in the most stable arrangement for electrons in atoms, leading to significant implications for the chemical behavior and reactivity of elements.