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The Bohr model of the atom was superseded by an electron probability cloud adhering to the Schrödinger equation as published in 1926. This is further complicated by spin and quantum vacuum effects to produce fine structure and hyperfine structure. Nevertheless, the Bohr radius formula remains central in atomic physics calculations, due to its ...
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.
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 ...
Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the Lyman (n f =1), Balmer (n f =2), and Paschen (n f =3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted. [30]: 34
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
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 ...
It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as n 2 (the n = 137 state of hydrogen has an atomic radius ~1 μm) and the geometric cross-section as n 4. Thus, Rydberg atoms are extremely large, with loosely bound valence electrons, easily perturbed or ionized by collisions or external fields.