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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 ...
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
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 radius is then defined to be the classical electron radius, , and one arrives at the expression given above. Note that this derivation does not say that is the actual radius of an electron. It only establishes a dimensional link between electrostatic self energy and the mass–energy scale of the electron.
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 fine-structure constant gives the maximum positive charge of an atomic nucleus that will allow a stable electron-orbit around it within the Bohr model (element feynmanium). [20] For an electron orbiting an atomic nucleus with atomic number Z the relation is mv 2 / r = 1 / 4πε 0 Ze 2 / r 2 .
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 ...
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.