Search results
Results From The WOW.Com Content Network
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 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 around an atomic nucleus. Bohr–Sommerfeld theory is named after Danish physicist Niels Bohr and German physicist Arnold Sommerfeld .
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 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]
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 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.
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 ...