FACTOID #151: The five countries with the highest coffee consumption are also the five countries whose citizens trust one another the most. Coincidence? Probably.
In physics, the free electron model is a possible model for the behaviour of electrons in a crystal structure. The core idea is that the valence electrons detach themselves completely from their ions and form an "electron gas". The willingness to question previously held truths and search for new answers resulted in a period of major scientific advancements, now known as the Scientific Revolution. ... Properties The electron is a subatomic particle. ... Rose des Sables (Sand Rose), formed of gypsum crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... In chemistry, valence electrons (vay-luhhn-cee) are the electrons contained in the valence shell of an atom, and which are likely to participate in a chemical reaction through bonding with other atoms, molecules, or ions. ... An ion is an atom or group of atoms with a net electric charge. ...
While this model is the simplest model, it reproduces the main electronic properties of metals. The two fundamental asumptions are:
the independent electron approximation that considers the electrons as independent. Electron screening is one justification for ignoring electron-electron interactions.
the electrons move in a constant energy potential (the structure of the material is completely ignored). The Bloch theorem states that a periodic potential (such as a regular array of atoms) cannot scatter a travelling wave electron.
The electronic Hamiltonian for a multi-electron molecule in atomic units is: where is the vector position of electron with vector components in Bohr radii, is the charge of fixed nucleus a in units of the elementary charge, is the vector position of nucleus with vector components in Bohr radii. ... In physics, a potential is a scalar quantity that can be used to analyze the effects of complicated vectorial forces and similar quantities by means of simple conservation laws. ...
Predictions of the model
This very simple model of metals more or less correctly predicts:
In physics, the freeelectron model is a simple model for the behaviour of electrons in a crystal structure of a metallic solid.
The freeelectron model is a quantum model as opposed to the Drude model, which is classical.
The freeelectron model should be contrasted with the tight-binding model, which uses the opposite simplification of treating the electrons as tightly bound to the atomic cores.
Today, a freeelectron laser requires the use of an electron accelerator with its associated shielding, as accelerated electrons are a radiation hazard.
Usually, the electron beam must be maintained in a vacuum which requires the use of numerous pumps along the beam path.
In a gyrotron or freeelectron laser the EM-wavelength is smaller than the electron beam and the electrons have to be manipulated.
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