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Arnold Sommerfeld

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Arnold Sommerfeld, Stuttgart 1935	Arnold Sommerfeld, Stuttgart 1935

Atom

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	Helium atom ground state.
Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808), one of the earliest scientific works on atomic theory	Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808), one of the earliest scientific works on atomic theory
Mendeleev's first periodic table (1869)	Mendeleev's first periodic table (1869)
A generic atomic planetary model, or the Rutherford model	A generic atomic planetary model, or the Rutherford model
A Bohr model of the hydrogen atom, showing an electron jumping between fixed orbits and emitting a photon of energy with a specific frequency	A Bohr model of the hydrogen atom, showing an electron jumping between fixed orbits and emitting a photon of energy with a specific frequency
Schematic diagram of a simple mass spectrometer	Schematic diagram of a simple mass spectrometer
The binding energy needed for a nucleon to escape the nucleus, for various isotopes	The binding energy needed for a nucleon to escape the nucleus, for various isotopes
Illustration of a nuclear fusion process that forms a deuterium nucleus, consisting of a proton and a neutron, from two protons. A positron (e+)—an antimatter electron—is emitted along with an electron neutrino.	Illustration of a nuclear fusion process that forms a deuterium nucleus, consisting of a proton and a neutron, from two protons. A positron (e+)—an antimatter electron—is emitted along with an electron neutrino.
A potential well, showing, according to classical mechanics, the minimum energy V(x) needed to reach each position x. Classically, a particle with energy E is constrained to a range of positions between x1 and x2.	A potential well, showing, according to classical mechanics, the minimum energy V(x) needed to reach each position x. Classically, a particle with energy E is constrained to a range of positions between x1 and x2.
Wave functions of the first five atomic orbitals. The three 2p orbitals each display a single angular node that has an orientation and a minimum at the center.	Wave functions of the first five atomic orbitals. The three 2p orbitals each display a single angular node that has an orientation and a minimum at the center.
This diagram shows the half-life (T½) of various isotopes with Z protons and N neutrons.	This diagram shows the half-life (T½) of various isotopes with Z protons and N neutrons.
These electron's energy levels (not to scale) are sufficient for ground states of atoms up to cadmium (5s2 4d10) inclusively. Do not forget that even the top of the diagram is lower than an unbound electron state.	These electron's energy levels (not to scale) are sufficient for ground states of atoms up to cadmium (5s2 4d10) inclusively. Do not forget that even the top of the diagram is lower than an unbound electron state.
An example of absorption lines in a spectrum	An example of absorption lines in a spectrum
Snapshots illustrating the formation of a Bose–Einstein condensate	Snapshots illustrating the formation of a Bose–Einstein condensate
Scanning tunneling microscope image showing the individual atoms making up this gold (100) surface. Reconstruction causes the surface atoms to deviate from the bulk crystal structure and arrange in columns several atoms wide with pits between them.	Scanning tunneling microscope image showing the individual atoms making up this gold (100) surface. Reconstruction causes the surface atoms to deviate from the bulk crystal structure and arrange in columns several atoms wide with pits between them.
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Atomic orbital

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The shapes of the first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz. The colors show the wave function phase. These are graphs of ψ(x, y, z) functions which depend on the coordinates of one electron. To see the elongated shape of ψ(x, y, z)2 functions that show probability density more directly, see the graphs of d-orbitals below.	The shapes of the first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz. The colors show the wave function phase. These are graphs of ψ(x, y, z) functions which depend on the coordinates of one electron. To see the elongated shape of ψ(x, y, z)2 functions that show probability density more directly, see the graphs of d-orbitals below.
The Rutherford–Bohr model of the hydrogen atom.	The Rutherford–Bohr model of the hydrogen atom.
Cross-section of computed hydrogen atom orbital (ψ(r, θ, φ)2) for the 6s (n = 6, ℓ = 0, m = 0) orbital. Note that s orbitals, though spherically symmetrical, have radially placed wave-nodes for n > 1. However, only s orbitals invariably have a center anti-node; the other types never do.	Cross-section of computed hydrogen atom orbital (ψ(r, θ, φ)2) for the 6s (n = 6, ℓ = 0, m = 0) orbital. Note that s orbitals, though spherically symmetrical, have radially placed wave-nodes for n > 1. However, only s orbitals invariably have a center anti-node; the other types never do.
The five d orbitals in ψ(x, y, z)2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus.	The five d orbitals in ψ(x, y, z)2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus.
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Electron atomic and molecular orbitals. The chart of orbitals (left) is arranged by increasing energy (see Madelung rule). Note that atomic orbits are functions of three variables (two angles, and the distance r from the nucleus). These images are faithful to the angular component of the orbital, but not entirely representative of the orbital as a whole.	Electron atomic and molecular orbitals. The chart of orbitals (left) is arranged by increasing energy (see Madelung rule). Note that atomic orbits are functions of three variables (two angles, and the distance r from the nucleus). These images are faithful to the angular component of the orbital, but not entirely representative of the orbital as a whole.
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Atomic theory

The following table shows images and captions on the left, and alt text and captions on the right: the right column is what a visually impaired reader will hear. This table was computed from the copy of Atomic theory cached on 13 May 2013 at 23:30.

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Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808).	Various atoms and molecules as depicted in John Dalton's A New System of Chemical Philosophy (1808).
The gold foil experiment Top: Expected results: alpha particles passing through the plum pudding model of the atom with negligible deflection. Bottom: Observed results: a small portion of the particles were deflected by the concentrated positive charge of the nucleus.	The gold foil experiment Top: Expected results: alpha particles passing through the plum pudding model of the atom with negligible deflection. Bottom: Observed results: a small portion of the particles were deflected by the concentrated positive charge of the nucleus.
The Bohr model of the atom	The Bohr model of the atom
The five filled atomic orbitals of a neon atom separated and arranged in order of increasing energy from left to right, with the last three orbitals being equal in energy. Each orbital holds up to two electrons, which most probably exist in the zones represented by the colored bubbles. Each electron is equally present in both orbital zones, shown here by color only to highlight the different wave phase.	The five filled atomic orbitals of a neon atom separated and arranged in order of increasing energy from left to right, with the last three orbitals being equal in energy. Each orbital holds up to two electrons, which most probably exist in the zones represented by the colored bubbles. Each electron is equally present in both orbital zones, shown here by color only to highlight the different wave phase.
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Bohr model

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Elliptical orbits with the same energy and quantized angular momentum	Elliptical orbits with the same energy and quantized angular momentum
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Cubical atom

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Density functional theory

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C60 with isosurface of ground-state electron density as calculated with DFT.	C60 with isosurface of ground-state electron density as calculated with DFT.

Drude model

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Drude Model electrons (shown here in blue) constantly bounce between heavier, stationary crystal ions (shown in red).	Drude Model electrons (shown here in blue) constantly bounce between heavier, stationary crystal ions (shown in red).
Complex conductivity for different frequencies assuming that and that .	Complex conductivity for different frequencies assuming that and that .
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Electronic band structure

The following table shows images and captions on the left, and alt text and captions on the right: the right column is what a visually impaired reader will hear. This table was computed from the copy of Electronic band structure cached on 20 May 2013 at 01:12.

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Simplified diagram of the filling of electronic band structure in various types of material, relative to the Fermi level EF (materials are shown in equilibrium with each other). In metals and semimetals the Fermi level lies inside at least one band, with semimetals containing far fewer charge carriers. In insulators the Fermi level is deep inside a forbidden gap, while in semiconductors the bands near the Fermi level are populated by thermally activated electrons and holes.	Simplified diagram of the filling of electronic band structure in various types of material, relative to the Fermi level EF (materials are shown in equilibrium with each other). In metals and semimetals the Fermi level lies inside at least one band, with semimetals containing far fewer charge carriers. In insulators the Fermi level is deep inside a forbidden gap, while in semiconductors the bands near the Fermi level are populated by thermally activated electrons and holes.
Figure 2: First Brillouin zone of FCC lattice showing symmetry labels	Figure 2: First Brillouin zone of FCC lattice showing symmetry labels
Figure 3: Bulk band structure for Si, Ge, GaAs and InAs generated with tight binding model. Note that Si and Ge are indirect, while GaAs and InAs are direct band gap materials.	Figure 3: Bulk band structure for Si, Ge, GaAs and InAs generated with tight binding model. Note that Si and Ge are indirect, while GaAs and InAs are direct band gap materials.

Ernest Rutherford

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Top: Expected results: alpha particles passing through the plum pudding model of the atom undisturbed. Bottom: Observed results: a small portion of the particles were deflected, indicating a small, concentrated charge. Note that the image is not to scale; in reality the nucleus is vastly smaller than the electron shell.	Top: Expected results: alpha particles passing through the plum pudding model of the atom undisturbed. Bottom: Observed results: a small portion of the particles were deflected, indicating a small, concentrated charge. Note that the image is not to scale; in reality the nucleus is vastly smaller than the electron shell.
A plaque commemorating Rutherford's presence at the Victoria University, Manchester	A plaque commemorating Rutherford's presence at the Victoria University, Manchester
A statue of a young Ernest Rutherford at his memorial in Brightwater, New Zealand.	A statue of a young Ernest Rutherford at his memorial in Brightwater, New Zealand.
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