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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]
The Bohr model explains the atomic spectrum of hydrogen (see Hydrogen spectral series) as well as various other atoms and ions. It is not perfectly accurate, but is a remarkably good approximation in many cases, and historically played an important role in the development of quantum mechanics. The Bohr model posits that electrons revolve around ...
This result can be generalized to other systems, such as positronium (an electron orbiting a positron) and muonium (an electron orbiting an anti-muon) by using the reduced mass of the system and considering the possible change in charge. Typically, Bohr model relations (radius, energy, etc.) can be easily modified for these exotic systems (up ...
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 .
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
When Bohr analyzes his model for the atom he writes [5] = where he uses frequency (proportional to wavenumber). Thus he has been able to compute the value of Rydberg's heuristic constant N 0 {\displaystyle N_{0}} from his atom theory and set the integers μ 1 {\displaystyle \mu _{1}} and μ 2 {\displaystyle \mu _{2}} to zero.
A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron.These atoms are isoelectronic with hydrogen.Examples of hydrogen-like atoms include, but are not limited to, hydrogen itself, all alkali metals such as Rb and Cs, singly ionized alkaline earth metals such as Ca + and Sr + and other ions such as He +, Li 2+, and Be 3+ and isotopes of any of the above.
An atom in a Rydberg state has a valence electron in a large orbit far from the ion core; in such an orbit, the outermost electron feels an almost hydrogenic Coulomb potential, U C, from a compact ion core consisting of a nucleus with Z protons and the lower electron shells filled with Z-1 electrons. An electron in the spherically symmetric ...