5.2. The Quantum Mechanical Model http://www.ck12.org
5.2 The Quantum Mechanical Model
Lesson Objectives
- Understand the de Broglie wave equation and how it illustrates the wave nature of the electron.
- Explain the difference between quantum mechanics and classical mechanics.
- Understand how the Heisenberg uncertainty principle and Schrödinger’s wave equation led to the idea of
atomic orbitals. - Know the four quantum numbers and how they are related to the arrangement of electrons in an atom.
- Describe the interrelationships between principal energy level, sublevel, orbital and electron spin and how
they relate to the number of electrons of an atom.
Lesson Vocabulary
- angular momentum quantum number
- Heisenberg uncertainty principle
- magnetic quantum number
- orbital
- principal quantum number
- spin quantum number
- quantum mechanical model
- quantum mechanics
- quantum numbers
Wave Nature of the Electron
Bohr’s model of the atom was valuable in demonstrating how electrons are capable of absorbing and releasing energy
and how atomic emission spectra are created. However, the model did not really explain why electrons should exist
only in fixed circular orbits or why there would not be a limitless number of orbits with a continuum of possible
energies. In order to explain why atomic energy states are quantized, scientists needed to rethink the way in which
they viewed the nature of the electron and its movement.
de Broglie Wave Equation
Planck’s investigations into the emission spectra of hot objects and subsequent studies on the photoelectric effect
had proven that light was capable of behaving as a particle, even though it is also known to behave as a wave. It
seemed reasonable to wonder if matter that primarily acts as a particle, such as electrons, could also sometimes
exhibit behavior that is typical of waves. In 1924, French scientist Louis de Broglie (1892-1987) derived an equation