Quantum Numbers and Electron Configuration

Introduction

• Understanding Quantum Numbers: Essential for describing the arrangement of electrons in an atom.
• Electrons as both particles and waves: Electrons are arranged in orbitals, regions of probability around the nucleus.
• Types of Orbitals: s, p, d, f orbitals with different shapes. Each can hold up to two electrons.

Principal Quantum Number (n)

• Symbol: n
• Values: Any positive integer
• Represents: Energy level of electron
• Relation to Bohr Model: Larger n value indicates electron is further from the nucleus.

Angular Momentum Quantum Number (l)

• Symbol: l
• Values: Ranges from 0 to (n-1)
• Describes: Shape of the orbital
  • l = 0: s orbital (spherical, 1 per energy level)
  • l = 1: p orbital (lobes on three axes, 3 per energy level)
  • l = 2: d orbital (complex shapes, 5 per energy level)
  • l = 3: f orbital (more complex, 7 per energy level)

Magnetic Quantum Number (m_l)

• Symbol: m_l
• Values: From -l to +l
• Defines: Specific orbital within a set
  • Example: If l = 2, m_l = -2, -1, 0, 1, 2
  • m_l = 0 for l = 0: Only 1 s orbital per energy level
  • m_l = 3 values for l = 1: Three p orbitals
  • m_l = 5 values for l = 2: Five d orbitals
  • m_l = 7 values for l = 3: Seven f orbitals

Spin Quantum Number (m_s)

• Symbol: m_s
• Values: +1/2 or -1/2
• Describes: Electron spin direction
• Pauli Exclusion Principle: No two electrons can have the same set of four quantum numbers.

Electron Configuration

• Example Analysis:
  • n = 1: l = 0, m_l = 0 (1s orbital, 2 electrons with spins +1/2 and -1/2)
  • n = 2: l = 0 (2s orbital) or l = 1 (2p orbitals, 3 values for m_l)
  • n = 3: l = 0 (3s orbital), l = 1 (3p orbitals), l = 2 (3d orbitals)
• Aufbau Principle: Orbitals filled in order of increasing energy: 1s, 2s, 2p, 3s, 3p, etc.
• Hund’s Rule: Electrons occupy empty orbitals singly before pairing up.

Example: Chlorine (Cl) Electron Configuration

• Total Electrons: 17
• Configuration: 1s² 2s² 2p⁶ 3s² 3p⁵
• Using Periodic Table: Identify elements by their electron addition sequence.
• Noble Gas Notation: Use the noble gas from the previous row for compact notation (e.g., [Ne] 3s² 3p⁵ for Cl).

Orbital Diagrams

• Visual Representation: Shows how electrons occupy orbitals.
• Paramagnetic vs. Diamagnetic:
  • Paramagnetic: Atoms with unpaired electrons (attracted by magnetic field)
  • Diamagnetic: Atoms with paired electrons (not affected by magnetic field)

Summary

• n: Energy level
• l: Orbital shape
• m_l: Specific orbital
• m_s: Spin direction
• Remember: Unique quantum numbers per electron, following Aufbau Principle and Hund's Rule.
• Confusion: Rewatch or reread for better understanding.

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