Quantum Numbers and Electron Configuration

Introduction

• Electrons exhibit dual nature: particles and waves.
• Arrangement of electrons in an atom is determined by four quantum numbers.
• Quantum numbers describe atomic orbitals (regions where electrons are likely to be found).
• Types of orbitals: s, p, d, f (each can hold up to 2 electrons).

Quantum Numbers

Principal Quantum Number (n)

• Represents the energy level of an electron.
• Positive integer values (1, 2, 3, ...).
• Larger n means the orbital is further from the nucleus.

Angular Momentum Quantum Number (l)

• Describes the shape of the orbital.
• Values range from 0 to (n-1).
• Orbital shapes:
  • l = 0: s orbital (spherical, 1 per energy level)
  • l = 1: p orbital (lobed, 3 per energy level)
  • l = 2: d orbital (complex shapes, 5 per energy level)
  • l = 3: f orbital (more complex shapes, 7 per energy level)

Magnetic Quantum Number (m_l)

• Values range from -l to +l.
• Determines the specific orbital within a set.
• Number of values corresponds to number of orbitals:
  • l = 0: 1 value (1s orbital)
  • l = 1: 3 values (3p orbitals)
  • l = 2: 5 values (5d orbitals)
  • l = 3: 7 values (7f orbitals)

Spin Quantum Number (m_s)

• Values: +1/2 or -1/2.
• Describes the spin of an electron.

Pauli Exclusion Principle

• No two electrons in an atom can have identical quantum numbers.
• Each orbital can hold a maximum of 2 electrons with opposite spins.

Aufbau Principle

• Describes the order in which orbitals are filled based on energy levels.
• Electrons fill from lower to higher energy orbitals: 1s, 2s, 2p, 3s, 3p, etc.

Electron Configuration

• Describes how electrons are distributed among orbitals.
• Example: Chlorine (Cl) with 17 electrons: 1s² 2s² 2p⁶ 3s² 3p⁵.
• Hund’s Rule: Electrons fill each orbital singly before pairing.

Orbital Diagrams

• Visual representation of electron distribution in orbitals.
• Apply Hund's rule for filling.

Quick Tips

• Use the periodic table to determine electron configurations.
• Blocks: s-block, p-block, d-block, f-block.
• Use noble gas notation for simplification (e.g., [Ne] 3s² 3p⁵ for Cl).

Magnetic Properties

• Paramagnetic: Atoms with unpaired electrons; attracted to magnetic fields.
• Diamagnetic: Atoms with all electrons paired; not attracted to magnetic fields.

Summary

• n: Energy level
• l: Type of orbital
• m_l: Specific orbital in a set
• m_s: Spin of the electron
• Order of filling: governed by Aufbau principle

Additional Resources

• Watch tutorials for better understanding.
• Review orbital diagrams and electron configurations using the periodic table.