2.3 Rules of Electronic Configuration

This topic explains the three main rules used to determine the electronic configuration of elements: the Aufbau Principle, the n+l Rule, Pauli's Exclusion Principle, and Hund's Rule.

Definition

Electronic Configuration: The distribution of electrons in an atom's orbitals and subshells.

Main Idea

Electrons are distributed in orbitals and subshells according to specific rules. These rules determine the order in which orbitals are filled, the maximum number of electrons in each orbital, and the arrangement of electrons within degenerate orbitals.

Core Concept

• Aufbau Principle: Electrons fill orbitals in order of increasing energy.
• Pauli's Exclusion Principle: No two electrons can have the same four quantum numbers.
• Hund's Rule: Electrons occupy degenerate orbitals singly first, with parallel spins.

Additionally, the n+l Rule helps determine the order of orbital energies.

Detailed Explanation

1. Aufbau Principle

• Electrons are distributed in orbitals/subshells in order of increasing energy.
• Firstly, low-energy orbitals are filled, then electrons are filled in high-energy orbitals.
• The energies of orbitals are calculated using quantum mechanical principles.
• This calculation provides information about the allowed energy levels and spatial distribution of electrons in an atom.

Increasing Energy Order of Orbitals: 1s < 2s < 2p < 3s < 3p < 4s < 3d < …

It is apparent that sometimes the electron is filled first in a higher shell (n) and then in a lower shell. This can be explained on the basis of the n+l rule.

2. n+l Rule

• Higher the n+l value, higher will be the energy of the orbital.
• This rule helps determine which orbital is filled first when there is a conflict.

Examples:

Since 4 + 0 = 4 (for 4s) and 3 + 2 = 5 (for 3d), the 3d orbital has greater energy than the 4s orbital. Therefore, 4s is filled before 3d.

3. Pauli's Exclusion Principle

• No two electrons in an atom can have the same values of all four quantum numbers.
• At least the spin quantum number will be different.
• If two electrons are present in the same orbital (n, l, and m are same), their spins will be opposite.

• Two electrons in the 3p_x orbital have the following sets of quantum numbers:
• Electron 1: n=3, l=1, m=-1, s=+12
• Electron 2: n=3, l=1, m=-1, s=-12

4. Hund's Rule

• According to this rule, if degenerate orbitals (orbitals with equal energy) are available, the electrons will tend to reside separately with the same spin, instead of pairing up in the same orbital with opposite spin.
• This minimizes electron-electron repulsion.

Examples:

Two electrons in p orbitals: p_x¹ p_y¹ p_z⁰

Three electrons in p orbitals: p_x¹ p_y¹ p_z¹

• Energy of an orbital is also related to the number of electrons present in it.
• Half-filled and completely filled orbitals are more stable with less energy.
• This is obvious in the configuration of many elements like chromium (Cr) and copper (Cu).

Intermediate Level

Aufbau Principle

• Electrons fill orbitals in order of increasing energy.
• Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < …

n+l Rule

• Higher the n+l value, higher the energy of the orbital.
• Example: 4s (n+l=4) is filled before 3d (n+l=5).

Pauli's Exclusion Principle

• No two electrons can have the same four quantum numbers.
• Two electrons in the same orbital must have opposite spins.

Hund's Rule

• Electrons occupy degenerate orbitals singly first, with parallel spins.
• Example: For p³, the configuration is p_x¹ p_y¹ p_z¹, not p_x² p_y¹.

Stability of Half-Filled and Completely Filled Orbitals

• Half-filled and completely filled orbitals are more stable.
• Examples: Chromium (3d⁵ 4s¹) and Copper (3d¹⁰ 4s¹).

Important Points

• 1. Aufbau Principle: Electrons fill orbitals in order of increasing energy.
• 2. n+l Rule: Higher n+l value → higher energy.
• 3. Pauli's Exclusion Principle: No two electrons can have the same four quantum numbers.
• 4. Hund's Rule: Electrons occupy degenerate orbitals singly first, with parallel spins.
• 5. Half-filled and completely filled orbitals are more stable.
• 6. Examples of anomalous configurations: Chromium and Copper.

Remember

• - Aufbau Principle: Lowest energy first
• - n+l Rule: Higher n+l → higher energy
• - Pauli's Exclusion Principle: Opposite spins in same orbital
• - Hund's Rule: Singly first, then pair
• - Stability: Half-filled and completely filled orbitals
• - Examples: Cr, Cu

Common Mistakes

• 1. Forgetting the n+l rule: It explains why 4s is filled before 3d.
• 2. Violating Pauli's Exclusion Principle: Two electrons in the same orbital must have opposite spins.
• 3. Violating Hund's Rule: Electrons occupy degenerate orbitals singly first.
• 4. Ignoring the stability of half-filled and completely filled orbitals: This explains anomalous configurations.

Quick Revision

• Aufbau Principle: Electrons fill orbitals in order of increasing energy.
• n+l Rule: Higher n+l value → higher energy.
• Pauli's Exclusion Principle: No two electrons can have the same four quantum numbers.
• Hund's Rule: Electrons occupy degenerate orbitals singly first, with parallel spins.
• Half-filled and completely filled orbitals are more stable.
• Examples of anomalous configurations: Chromium and Copper.

60-Second Revision

• Aufbau Principle: Lowest energy first
• n+l Rule: Higher n+l → higher energy
• Pauli's Exclusion Principle: Opposite spins in same orbital
• Hund's Rule: Singly first, then pair
• Stability: Half-filled and completely filled orbitals
• Examples: Cr, Cu

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