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The Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus and where an electron jumps between orbits, is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). [1]
([2] page 364) The Sommerfeld extensions of the 1913 solar system Bohr model of the hydrogen atom showing the addition of elliptical orbits to explain spectral fine structure. 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 ...
The Bohr radius is one of a trio of related units of length, the other two being the Compton wavelength of the electron and the classical electron radius (). Any one of these constants can be written in terms of any of the others using the fine-structure constant α {\displaystyle \alpha } :
The Bohr model of the chemical bond took into account the Coulomb repulsion - the electrons in the ring are at the maximum distance from each other. [ 2 ] Thus, according to this model, the methane molecule is a regular tetrahedron , in which center the carbon nucleus locates, and in the corners - the nucleus of hydrogen.
With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen-like atoms, a Bohr electron "wavelength" could be seen to be a function of its momentum; so a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half ...
The last expression in the first equation shows that the wavelength of light needed to ionize a hydrogen atom is 4π/α times the Bohr radius of the atom. The second equation is relevant because its value is the coefficient for the energy of the atomic orbitals of a hydrogen atom: E n = − h c R ∞ / n 2 {\displaystyle E_{n}=-hcR_{\infty }/n ...
The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory. Spectral emission occurs when an electron transitions, or jumps, from a higher energy state to a lower energy state.
Weyl found a relativistic equation in terms of the Pauli matrices; the Weyl equation, for massless spin- 1 / 2 fermions. The problem was resolved by Dirac in the late 1920s, when he furthered the application of equation to the electron – by various manipulations he factorized the equation into the form: