A Brief Introduction to Quantum Chemistry - Part 2

Wave-Matter Duality of Light

In the early 1900’s, the fundamental nature of light was still a mystery. Light exhibited many properties that were consistent with both matter and waves/energy. For example, when light enters a prism, it divides into many colours, which are visual cues of electromagnetic radiation. Electromagnetic radiation is a form of energy, like UV rays and microwaves. However, light acts like matter when it is drawn into black holes. Attractive gravitational forces require that objects have mass, as matter does. As such, light remains a confusing amalgam of both being a wave and matter, but truly being neither.

In 1924, Louis deBroglie suggested an interesting claim. If light can show the characteristics of both matter and wave, why couldn’t matter show wave-like characteristics? deBroglie claimed that the wavelength of a moving object was Planck’s constant divided by p, its momentum. Later, this result was “proven” when both X-rays (a wave) and electrons (matter) were fired into a thin sheet of aluminum. The pattern that was observed from both was very similar, and wave-like in nature.

Heisenberg Uncertainty Principle

From deBroglie’s results, it could be seen that any moving object traveled in a wave-like path. While the result it generally inconsequential for large objects, the problem remained for smaller particles, such as electrons.

In order us to measure the location of a moving electron, at a single moment in time, light must be used to determine its location. Just as one sees by receiving light that has bounced off objects, one can “see” an electron by measuring light that has bounced off an electron.  The light needs to interact with the electron in someway, or there would be no detectable change, as it would be the same as light going through a vacuum. However, once the light hits the electron, it gives it an instantaneous boost of kinetic energy, which increases it momentum. Conversely, it we know an electron’s exact position, there is no way we can learn its momentum without colliding with light. At that moment, the electron becomes “displaced” from its original position. As such, it is impossible to know both the position and momentum of an object exactly with perfect accuracy.

The Heisenberg Uncertainty Principle is a key result used in Quantum Mechanics because it provides a boundary for the accuracy and limitations of measurement. In order for a measurement to be made, it requires interactions between the various objects. It is this fundamental interaction that causes this variability. Given the Uncertainty Principle, many results are given probabilistic interpretations where surfaces and ranges are often best representations of electron behaviour.

Introduction to Quantum Chemistry
Page 1
Page 2
Schrodinger Equation
Spherical Harmonics
Periodic Table
MO Theory