Electron Configuration: Principles, Rules, and Applications

Electron Configuration

Introduction to Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's shells and subshells. Understanding electron configuration is essential for predicting chemical properties and reactivity of elements.

• Shells (or principal energy levels) are denoted by the quantum number n (1, 2, 3, ...).

• Each shell contains one or more sub-levels (subshells): s, p, d, f.

• The periods in the periodic table correspond to the principal energy levels.

Shells and Sub-levels

Electrons fill shells and sub-levels according to their energy, as described by quantum theory.

• The maximum number of electrons a shell can hold is given by $2n^2$.

• Sub-levels are assigned the letters s, p, d, f.

• Each principal energy level contains a specific set of sub-levels:

Principal Energy Level	Maximum Number of Electrons	Sub-levels Present
1	2	1 (1s)
2	8	2 (2s, 2p)
3	18	3 (3s, 3p, 3d)
4	32	4 (4s, 4p, 4d, 4f)

Sub-levels and Orbitals

Each sub-level contains a specific number of orbitals, and each orbital can hold up to 2 electrons.

Sub-level	Number of Orbitals	Name of Orbitals	Maximum Number of Electrons
s	1	s	2
p	3	px, py, pz	6
d	5	dxy, dyz, dzx, dx2-y2, dz2	10
f	7	not required (for general chemistry)	14

Shapes of Orbitals

The shapes of atomic orbitals are determined by their sub-level:

• s-orbitals: Spherical shape

• p-orbitals: Dumbbell shape, oriented along x, y, and z axes

• d-orbitals: Cloverleaf shapes and one with a donut-shaped ring

Order of Filling: The Aufbau Principle

Electrons fill orbitals in order of increasing energy, starting with the lowest energy sub-levels. This is known as the Aufbau Principle.

• The general order is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

• The 4s sub-level is filled before the 3d sub-level because it is lower in energy.

Mnemonic: Use diagonal arrows or the periodic table blocks to remember the order of filling.

Writing Electron Configurations

Electron configurations are written by listing the occupied sub-levels and the number of electrons in each as a superscript.

• Example for magnesium (Mg, Z = 12): $1s^2 2s^2 2p^6 3s^2$

• The sum of the superscripts equals the atomic number.

Exceptions to the Aufbau Principle

Certain elements (notably chromium, copper, and silver) have electron configurations that do not strictly follow the Aufbau Principle due to increased stability of half-filled or fully-filled sub-levels.

• Example: Chromium (Cr, Z = 24)

• Expected: $[Ar] 4s^2 3d^4$

• Actual: $[Ar] 4s^1 3d^5$ (half-filled d5 is more stable)

Electron Configurations for Ions

When atoms form ions, electrons are added or removed from the outermost sub-levels:

• Positive ions (cations): Electrons are lost from the highest energy level first.

• Negative ions (anions): Electrons are gained, filling the next available sub-level.

• Example: Sodium atom (Na): $1s^2 2s^2 2p^6 3s^1$

• Sodium ion (Na+): $1s^2 2s^2 2p^6$

• Example: Oxygen atom (O): $1s^2 2s^2 2p^4$

• Oxide ion (O2-): $1s^2 2s^2 2p^6$

Transition Metal Ions

For transition metals, electrons in the 4s sub-level are lost before those in the 3d sub-level when forming cations.

• Example: Titanium (Ti, Z = 22):

• Ti atom: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2$

• Ti2+ ion: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^2$

Condensed Electron Configurations

Electron configurations can be abbreviated using the symbol of the nearest preceding noble gas in brackets.

• Example: Titanium (Ti): $[Ar] 4s^2 3d^2$

• Example: Zinc (Zn): $[Ar] 4s^2 3d^{10}$

Orbital Diagrams

Orbital diagrams use boxes to represent orbitals and arrows to represent electrons. The direction of the arrow indicates the electron's spin.

• Electrons fill orbitals singly first (Hund's Rule), then pair up with opposite spins (Pauli Exclusion Principle).

• Example: Carbon (C, Z = 6):

Orbital diagram:

1s ↑↓ 2s ↑↓ 2p ↑ ↑

Summary Table: Maximum Electrons in Sub-levels and Shells

Main/Principle Energy Level	Sub-levels	Max. Electrons in Each Sub-level	Max. Electrons in Each Principle Energy Level
1	1s	2	2
2	2s, 2p	2, 6	8
3	3s, 3p, 3d	2, 6, 10	18
4	4s, 4p, 4d, 4f	2, 6, 10, 14	32

Practice Problems and Applications

• Write the full electron configuration and orbital diagram for the following elements:

• Lithium (Li): $1s^2 2s^1$

• Fluorine (F): $1s^2 2s^2 2p^5$

• Potassium (K): $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$

• Nitrogen (N): $1s^2 2s^2 2p^3$

• Oxygen (O): $1s^2 2s^2 2p^4$

Example: Selenium (Se, Z = 34)

• Number of protons and electrons: 34

• Group: 16 (chalcogens)

• Valence electrons: 6

• Se2- anion: 34 protons, 36 electrons

• Full electron configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^4$

• Condensed configuration: $[Ar] 4s^2 3d^{10} 4p^4$

• Orbital diagram: boxes for 4s, 3d, and 4p filled according to Hund's Rule and Pauli Exclusion Principle

Key Principles

• Aufbau Principle: Electrons fill the lowest energy sub-levels first.

• Hund's Rule: Electrons occupy orbitals singly before pairing up.

• Pauli Exclusion Principle: No two electrons in the same orbital can have the same spin.

Additional info: The notes also include visual aids for the order of filling, orbital shapes, and practice problems for further understanding.