The quantum mechanical model

Warm up: Sketch the model of the atom throughout history Dalton’s Atomic Model Plum Pudding Model (Thomson)

Bohr’s Model Quantum Mechanical Model

• 1920’s • Werner Heisenberg (Uncertainty Principle) • Louis de Broglie (electron has wave properes) • Erwin Schrodinger (mathemacal equaons using probability, quantum numbers)

Werner Heisenberg: Uncertainty Principle

• We can not know both the posion and momentum of a parcle at a given me.

Balloon in a dark room

Louis de Broglie, (France, 1892-1987) Wave Properes of Maer (1923) •Since light waves have a parcle behavior (as shown by Einstein in the Photoelectric Effect), then parcles could have a wave behavior. •de Broglie wavelength λ= h mv Electron Moon Around Atom Shown as a de Broglie Wave

Erwin Schrodinger, 1925 Quantum (wave) Mechanical Model of the Atom

• Derived an equaon that treated the electron as a wave • Was successful in describing the electrons in all atoms – not just the one electron in hydrogen as in the Bohr model Schrodinger’s wave funcon

The quantum mechanical model predicts a three dimensional region around the nucleus, where the electron is likely found, called the atomic orbital Atomic Orbital

• Region in space where there is a high probability of finding an electron Atomic Orbital s

2s Degenerate Orbitals

• Equal energy orbitals • Oriented differently in space Example of degenerate orbitals: p orbitals

hp://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif

• The d orbitals f orbitals The Electron Cloud

• The electron cloud represents posions where there is probability of finding an electron. The Electron Cloud The higher the electron density, the higher the probability that an electron may be found in that region. The Electron Cloud for Hydrogen

90% probability of finding the electron within this space Probability Curve for Hydrogen FYI: Schrodinger’s Equaon

• ψ is called the wave function and indicates the probability of where an electron may be found. Summary: Quantum Mechanical Model • Electrons are located in specific energy levels.

• There is no exact path around the nucleus.

• The model esmates the probability of finding an electron in a certain posion. Homework

• Create a table comparing and contrasng the Bohr model with the Quantum Mechanical Model • Read “Tiny Tweezers” on p. 163 for an applicaon of light interacng with maer

Bohr Model Quantum Mechanical Model