Quantum Theory and Electronic Structure

Electromagnetic radiation (light)

• Originally, a form of energy thought of ass waves travelling through space

• Travels (in a vacuum) as the sepped of light (c = 3.00 × 10⁸ m/s)

Wave characteristics

1. Wavelength (lambda)

2. Frequency (nu)

3. Amplitude: height of wave

Wavelength

Distance between 2 peaks and 2 troughs

Frequency

Number of waves per second that pass through a given point

Amplitude

Height of wave

• Classically related to energy (intensity) of light

  • Light of greater amplitude appears brighter

Diffraction

An interference of waves

Constructive wave interference

When two waves overlap, combining to form a wave with a larger amplitude than the original waves

Destructive wave interference

When two waves meet and their crests and troughs align in a way that causes them to cancel each other out, resulting in a wave with a reduced or even zero amplitude

Light

• Has many wave properties but does not behave like a classical wave

• Comes in “packets” (particles) of energy (photons)

Matter (originally)

Discrete particles with determinate mass, position, etc

The double-slit experiment

Demonstrates wave-particle duality, showing that particles like light and matter exhibit both wave-like and particle-like behaviours

Wave-particle duality

Light: both wave and particulate characteristics

Matter: both particulate and wave characteristics

Schrodinger model of the atom

H ^ ψ = E ψ

• ψ - “wavefunction” or “orbital”

• ψ² - probability of finding the electron at any point about the nucleus

Quantum number that describes orbitals 

• Principle quantum number

• Angular momentum quantum number

• Magnetic quantum number

• Electron spin quantum number

Principle quantum number (n)

Size of the orbital

Angular momentum quantum number (l)

Shape of the orbital

Magnetic quantum number (m)

Orientation of the orbital

Electron spin quantum number (s)

s = -1/2 or s = +1/2

Orbitals

Max of two electrons; must have opposing spins

Pauli exclusion principle

No two electrons in an atom can have the same values of all 4 quantum numbers

Effective nuclear charge 

The nuclear charge actually felt by an electron

Two factors that determine an atom’s energy

• Electron-nuclear attraction

• Electron-electron replusion

Aufbau principle

Electrons will fill orbitals of lowest energy first

Hund’s rule

If two or more degenerate orbitals are available, one electron goes into each until they are half full. All electrons in half-filled orbitals have the same spin quantum number