Overview
This lecture introduces the development of quantum theory, focusing on wave-particle duality, the quantum mechanical model of electrons in atoms, and the four quantum numbers that describe electrons’ states.
Wave-Particle Duality and de Broglie Hypothesis
- Macroscopic objects follow classical physics; microscopic objects display both particle and wave behavior.
- Louis de Broglie proposed material particles have a wavelength: λ = h / (mv), where h is Planck's constant, m is mass, and v is velocity.
- Electron interference experiments confirmed electrons exhibit wavelike properties.
Heisenberg’s Uncertainty Principle
- It is impossible to simultaneously and exactly know both the position and momentum of a particle.
- The product of these uncertainties is ≥ ħ/2, where ħ = h/(2π).
- Uncertainty is significant only for microscopic particles.
Quantum Mechanical Model and Schrödinger Equation
- Schrödinger developed an equation to describe electrons as wavefunctions (ψ), representing probability distributions of particles.
- The square of the wavefunction’s magnitude (|ψ|²) gives the probability density of finding an electron.
Quantization of Electron Energy and Orbitals
- Electron energies in atoms are quantized; transitions between levels involve absorption or emission of photons.
- Principal quantum number (n) labels shells and determines electron energy and distance from the nucleus.
The Four Quantum Numbers
- Principal quantum number (n): Specifies energy and size of orbital (n = 1, 2, 3, ...).
- Angular momentum quantum number (l): Defines shape of orbital (l = 0 to n–1; s, p, d, f, etc.).
- Magnetic quantum number (ml): Specifies orientation in space; can range from –l to +l.
- Spin quantum number (ms): Electron spin can be +½ or –½, reflecting two allowed spin states.
Pauli Exclusion Principle
- No two electrons in an atom can have the same set of four quantum numbers.
- Each orbital holds a maximum of two electrons with opposite spins.
Shells, Subshells, and Orbital Capacity
- Subshells (l values) within each shell (n) have: s=1, p=3, d=5, f=7 orbitals, each orbital holds 2 electrons.
- Maximum electrons in a shell: 2n² (e.g., n=2 ⇒ 8 electrons; n=5 ⇒ 50 electrons).
Key Terms & Definitions
- de Broglie wavelength (λ) — wavelength associated with a particle: λ = h/(mv).
- Uncertainty Principle — states Δx·Δp ≥ ħ/2; limits precision of measuring position and momentum.
- Wavefunction (ψ) — describes probability distribution of an electron’s position.
- Orbital — region around nucleus with high probability of finding an electron.
- Principal quantum number (n) — energy and size of orbital.
- Angular momentum quantum number (l) — shape of orbital (s, p, d, f).
- Magnetic quantum number (ml) — orientation of orbital.
- Spin quantum number (ms) — intrinsic electron spin (+½ or –½).
- Pauli exclusion principle — rule that no two electrons can have identical quantum numbers.
Action Items / Next Steps
- Watch the Dr. Quantum Double Slit Experiment cartoon for wave-particle duality visualization.
- Review quantum number properties and complete practice problems on electron configurations.
- Calculate maximum electrons in a shell with given n values as practice.