Rules for Filling Electron Shells

Introduction

Key Concepts

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's electron shells and subshells. Electrons occupy these shells in a manner that minimizes the atom's energy, following specific rules and principles. The arrangement of electrons determines an element's chemical properties and its position in the periodic table.

Aufbau Principle

The Aufbau principle, derived from the German word "Aufbau" meaning "building up," states that electrons fill atomic orbitals starting from the lowest energy level moving to higher levels. This sequential filling ensures that electrons occupy the most stable positions available.

For example, electrons fill the 1s orbital before the 2s orbital: $$ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 $$

Pauli Exclusion Principle

Proposed by Wolfgang Pauli, the Pauli Exclusion Principle asserts that no two electrons in an atom can have the same set of four quantum numbers. In simpler terms, an orbital can hold a maximum of two electrons, and these electrons must have opposite spins. This principle explains the electron pairing in orbitals.

Hund’s Rule

Hund’s Rule states that electrons will occupy degenerate orbitals (orbitals of the same energy) singly as far as possible before pairing up. This minimizes electron-electron repulsions and results in a lower energy state for the atom.

For instance, in the 2p subshell, electrons will fill each of the three p orbitals singly before any orbital gets a second electron: $$ \begin{align*} 2p_{x}^1 \, 2p_{y}^1 \, 2p_{z}^1 \end{align*} $$

Energy Levels and Subshells

Each electron shell is divided into subshells, designated as s, p, d, and f, each with a specific shape and energy. The s subshell contains one orbital, p has three, d has five, and f has seven. The energy levels increase in the order: s < p < d < f within the same principal quantum number.

For example, the fourth energy level contains the 4s, 3d, 4p, and 4f subshells, ordered by increasing energy: $$ 4s < 3d < 4p < 4f $$

Periodic Trends and Electron Configuration

Electron configuration explains many periodic trends observed in the periodic table, such as atomic radius, ionization energy, and electronegativity. As electrons fill into higher energy levels and subshells, these properties change predictably across periods and groups.

For instance, moving from left to right across a period, the increasing nuclear charge attracts electrons closer, decreasing the atomic radius: $$ \text{Na} \, ([Ne] \, 3s^1) \rightarrow \text{Mg} \, ([Ne] \, 3s^2) $$

Exceptions to the Aufbau Principle

While the Aufbau principle provides a general guideline for electron filling, there are notable exceptions due to electron-electron interactions and subshell stability. Elements such as chromium and copper exhibit electron configurations that deviate from the expected order to achieve greater stability.

For example: $$ \text{Chromium:} \, [Ar] \, 3d^5 \, 4s^1 \quad \text{instead of} \quad [Ar] \, 3d^4 \, 4s^2 $$ $$ \text{Copper:} \, [Ar] \, 3d^{10} \, 4s^1 \quad \text{instead of} \quad [Ar] \, 3d^9 \, 4s^2 $$

Quantum Numbers and Electron Arrangement

Quantum numbers describe the unique state of an electron within an atom. There are four quantum numbers: principal (n), angular momentum (l), magnetic (m_l), and spin (m_s). These numbers determine the electron's position, energy, and spin state, guiding the filling order of electrons in shells and subshells.

For example:

• Principal quantum number (n): Indicates the energy level (e.g., n=1, 2, 3).
• Angular momentum quantum number (l): Defines the subshell (s, p, d, f).
• Magnetic quantum number (m_l): Specifies the orbital within the subshell.
• Spin quantum number (m_s): Describes the electron's spin direction (+½ or -½).

Effective Nuclear Charge (Z_eff)

Effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge minus the shielding effect caused by other electrons. Z_eff influences the attraction between electrons and the nucleus, affecting electron configurations and periodic properties.

The formula for effective nuclear charge is: $$ Z_{\text{eff}} = Z - S $$ where \( Z \) is the atomic number and \( S \) is the shielding constant.

Electron Shielding and Penetration

Electron shielding occurs when inner-shell electrons reduce the effective nuclear charge experienced by outer-shell electrons. Penetration refers to the ability of an electron in a higher energy orbital to come closer to the nucleus, experiencing less shielding and a higher Z_eff.

For example, electrons in the 3s orbital penetrate closer to the nucleus compared to those in the 3p orbital, resulting in different shielding effects.

Stability of Half-Filled and Fully-Filled Subshells

Atoms achieve greater stability when their subshells are either half-filled or fully filled. This stability arises from symmetrical electron distribution and minimized electron-electron repulsions. As a result, elements with such configurations often exhibit unique chemical properties.

For example, nitrogen has a half-filled 2p subshell: $$ 2p^3 $$ and chromium achieves a fully filled 3d subshell: $$ 3d^{10} \, 4s^1 $$

Energy Level Diagrams

Energy level diagrams visually represent the order in which electrons fill the various orbitals of an atom. These diagrams help in predicting electron configurations and understanding the relative energies of different subshells.

An example of an energy level diagram for the first three shells:

Application of Electron Shells in Chemical Bonding

Electron shells play a crucial role in chemical bonding, determining how atoms share or transfer electrons to form molecules and compounds. Understanding electron shell configurations helps predict bonding behavior, bond angles, and molecular geometry.

For instance, the octet rule states that atoms tend to form bonds to achieve a full outer shell of eight electrons, leading to stable configurations:

• Sodium (Na) donates one electron to achieve [Ne] configuration.
• Chlorine (Cl) accepts one electron to achieve [Ne] 3s² 3p⁶ configuration.

Impact on Periodic Properties

The arrangement of electrons in shells influences various periodic properties such as metallic and non-metallic characteristics, reactivity, and electronegativity. Elements with similar electron configurations often exhibit similar chemical behaviors, grouping them into families or groups in the periodic table.

For example, the noble gases have fully filled electron shells, making them chemically inert: $$ \text{Ne:} \, [He] \, 2s^2 \, 2p^6 $$

Comparison Table

Summary and Key Takeaways