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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]
In the Bohr model, an n = 1 electron has a velocity given by =, where Z is the atomic number, is the fine-structure constant, and c is the speed of light. In non-relativistic quantum mechanics, therefore, any atom with an atomic number greater than 137 would require its 1s electrons to be traveling faster than the speed of light.
The principal quantum number was first created for use in the semiclassical Bohr model of the atom, distinguishing between different energy levels. With the development of modern quantum mechanics, the simple Bohr model was replaced with a more complex theory of atomic orbitals. However, the modern theory still requires the principal quantum ...
In 1913, Niels Bohr proposed a model of the atom, giving the arrangement of electrons in their sequential orbits. At that time, Bohr allowed the capacity of the inner orbit of the atom to increase to eight electrons as the atoms got larger, and "in the scheme given below the number of electrons in this [outer] ring is arbitrary put equal to the normal valency of the corresponding element".
Description: Stylised atom. Blue dots are electrons, red dots are protons and black dots are neutrons. Date: 14 February 2007: Source: Own work based on: of Image:Stylised Lithium Atom.png by Halfdan.
The azimuthal quantum number was carried over from the Bohr model of the atom, and was posited by Arnold Sommerfeld. [11] The Bohr model was derived from spectroscopic analysis of atoms in combination with the Rutherford atomic model. The lowest quantum level was found to have an angular momentum of zero.
Rutherford's model, being supported primarily by scattering data unfamiliar to many scientists, did not catch on until Niels Bohr joined Rutherford's lab and developed a new model for the electrons. [56]: 304 Rutherford model predicted that the scattering of alpha particles would be proportional to the square of the atomic charge.
Hence, the non-relativistic Bohr model is inaccurate when applied to such an element. Relativistic Dirac equation Energy eigenvalues for the 1s, 2s, 2p 1/2 and 2p 3/2 shells from solutions of the Dirac equation (taking into account the finite size of the nucleus) for Z = 135–175 (–·–), for the Thomas-Fermi potential (—) and for Z = 160 ...