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Nevertheless, the Bohr radius formula remains central in atomic physics calculations, due to its simple relationship with fundamental constants (this is why it is defined using the true electron mass rather than the reduced mass, as mentioned above). As such, it became the unit of length in atomic units. In Schrödinger's quantum-mechanical ...
For more recent data on covalent radii see Covalent radius. Just as atomic units are given in terms of the atomic mass unit (approximately the proton mass), the physically appropriate unit of length here is the Bohr radius, which is the radius of a hydrogen atom. The Bohr radius is consequently known as the "atomic unit of length".
The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius.
Atomic units are chosen to reflect the properties of electrons in atoms, which is particularly clear in the classical Bohr model of the hydrogen atom for the bound electron in its ground state: Mass = 1 a.u. of mass; Charge = −1 a.u. of charge; Orbital radius = 1 a.u. of length; Orbital velocity = 1 a.u. of velocity [44]: 597
The atomic (covalent) radii of phosphorus, sulfur, and chlorine are about 1 angstrom, while that of hydrogen is about 0.5 angstroms. Visible light has wavelengths in the range of 4000–7000 Å. In the late 19th century, spectroscopists adopted 10 −10 of a metre as a convenient unit to express the wavelengths of characteristic spectral lines ...
The two ratios of three characteristic lengths: the classical electron radius r e, the reduced Compton wavelength of the electron ƛ e, and the Bohr radius a 0: r e = αƛ e = α 2 a 0. In quantum electrodynamics, α is directly related to the coupling constant determining the strength of the interaction between electrons and photons. [18]
Ionic radius, r ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice .
The Planck mass is the order of mass for which the Compton wavelength and the Schwarzschild radius = / are the same, when their value is close to the Planck length (). The Schwarzschild radius is proportional to the mass, whereas the Compton wavelength is proportional to the inverse of the mass.