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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 radius ( ) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.291 772 105 44 (82) × 10 −11 m. [1] [2]
The Bohr model posits that electrons revolve around the atomic nucleus in a manner analogous to planets revolving around the Sun. In the simplest version of the Bohr model, the mass of the atomic nucleus is considered to be infinite compared to the mass of the electron, [ 7 ] so that the center of mass of the system, the barycenter , lies at ...
Bohr radius: the radius of the lowest-energy electron orbit predicted by Bohr model of the atom (1913). [15] [16] It is only applicable to atoms and ions with a single electron, such as hydrogen, singly ionized helium, and positronium. Although the model itself is now obsolete, the Bohr radius for the hydrogen atom is still regarded as an ...
Notable results from this period include Max Planck's calculation of the blackbody radiation spectrum, Albert Einstein's explanation of the photoelectric effect, Einstein and Peter Debye's work on the specific heat of solids, Niels Bohr and Hendrika Johanna van Leeuwen's proof that classical physics cannot account for diamagnetism, Bohr's model ...
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.
where is the reduced Planck constant, and α is the fine-structure constant (a relativistic correction for the Bohr model). 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]
The Bohr model exhibits difficulty for atoms with atomic number greater than 137, for the speed of an electron in a 1s electron orbital, v, is given by v = Z α c ≈ Z c 137.04 {\displaystyle v=Z\alpha c\approx {\frac {Zc}{137.04}}}