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The Bohr–Sommerfeld model (also known as the Sommerfeld model or Bohr–Sommerfeld theory) was an extension of the Bohr model to allow elliptical orbits of electrons around an atomic nucleus. Bohr–Sommerfeld theory is named after Danish physicist Niels Bohr and German physicist Arnold Sommerfeld .
With the advent of quantum mechanics, this picture was given a more formal interpretation in the form of the free electron model and its further extension, the nearly free electron model. In both models, the electrons are seen as a gas traveling through the structure of the solid with an energy that is essentially isotropic, in that it depends ...
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, [1] principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
The Bohr model gives an incorrect value L=ħ for the ground state orbital angular momentum: The angular momentum in the true ground state is known to be zero from experiment. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to revolve ...
This model explains the origin of the electronic dispersion relation, but the explanation for band gaps is subtle in this model. [2]: 121 The second model starts from the opposite limit, in which the electrons are tightly bound to individual atoms. The electrons of a single, isolated atom occupy atomic orbitals with discrete energy levels.
In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference (often expressed in electronvolts ) between the top of the valence band and the ...
The inverse of the resistance is known as the conductance. When we consider a metal of unit length and unit cross sectional area, the conductance is known as the conductivity, which is the inverse of resistivity. The Drude model attempts to explain the resistivity of a conductor in terms of the scattering of electrons (the carriers of ...
Bohr calculated that a 1s orbital electron of a hydrogen atom orbiting at the Bohr radius of 0.0529 nm travels at nearly 1/137 the speed of light. [11] One can extend this to a larger element with an atomic number Z by using the expression v ≈ Z c 137 {\displaystyle v\approx {\frac {Zc}{137}}} for a 1s electron, where v is its radial velocity ...