Lecture Notes: Electronic Structure of Atoms

Overview

• Focus: Quantum Mechanical Model of an Atom
• Context: Following the limitations of Bohr’s model

Bohr’s Model

• Initially promising for hydrogen
• Failed for multi-electron atoms
• Marked an advancement but proved inadequate

Quantum Mechanical Model

• Developed by Schrödinger and Heisenberg
• Treats electrons as wavelike with probabilistic distributions
• Key Concepts:
  • Orbitals: Regions of space with a probability of finding an electron
  • Heisenberg Uncertainty Principle: Impossible to determine both position and momentum accurately

Quantum Mechanics and Orbitals

• Wave Equation and Functions:
  • Describes electron behavior
  • Wave Function: Solutions provide electron probability distributions
  • Atomic Orbitals: 3D shapes from wave functions

Quantum Numbers and Atomic Theory

• Describe electron distribution and chemical behavior
• Four Quantum Numbers:
  1. Principal Quantum Number (n):
  • Defines size and energy level of orbital
  • Larger n = higher energy and larger orbital
  • Electron capacity: (2n^2)
  2. Angular Momentum Quantum Number (l):
  • Defines orbital shape
  • Values from 0 to n-1 (e.g., s, p, d, f subshells)
  3. Magnetic Quantum Number (m_l):
  • Defines orbital orientation
  • Values range from -l to +l
  4. Spin Quantum Number (m_s):
  • Orientation of electron spin: +1/2 or -1/2

Principles Governing Electron Arrangement

• Aufbau Principle: Electrons fill lowest energy orbital first
• Pauli Exclusion Principle: Max two electrons per orbital with opposite spins
• Hund’s Rule: Fill degenerate orbitals singly first

Shells, Subshells, and Orbitals

• Shell: Defined by principal quantum number n
• Subshell: Defined by angular momentum quantum number
• Orbital: Region within a subshell; can hold 2 electrons

Electron Configuration

• Predicted using quantum numbers
• Notation:
  • Numbers and letters (e.g., 1s, 2p)
  • Follows periodic table to simplify
• Subshell Filling Order:
  • Order: 1s, 2s, 2p, 3s, etc.
  • Use periodic table blocks (s, p, d, f blocks)

Exceptions in Electron Configurations

• Chromium and Copper:
  • Favor half-filled or fully filled subshells for stability

Summary

Understanding the quantum mechanical model of atoms involves grasping the concept of orbitals, quantum numbers, and the principles that govern electron configurations. Special attention should be paid to the exceptions in filling orders for elements like chromium and copper. These foundations are crucial for predicting chemical behavior and electron arrangements.