Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Bohr radius
Summary
The Bohr radius (a0) 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
The Bohr radius is defined as
where
is the permittivity of free space,
is the reduced Planck constant,
is the mass of an electron,
is the elementary charge,
is the speed of light in vacuum, and
is the fine-structure constant.
The CODATA value of the Bohr radius (in SI units) is
In the Bohr model for atomic structure, put forward by Niels Bohr in 1913, electrons orbit a central nucleus under electrostatic attraction. The original derivation posited that electrons have orbital angular momentum in integer multiples of the reduced Planck constant, which successfully matched the observation of discrete energy levels in emission spectra, along with predicting a fixed radius for each of these levels. In the simplest atom, hydrogen, a single electron orbits the nucleus, and its smallest possible orbit, with the lowest energy, has an orbital radius almost equal to the Bohr radius. (It is not exactly the Bohr radius due to the reduced mass effect. They differ by about 0.05%.)
The Bohr model of the atom was superseded by an electron probability cloud obeying the Schrödinger equation as published in 1926.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 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 theory of the hydrogen atom, the Bohr radius is the value of the radial coordinate for which the radial probability density of the electron position is highest. The expected value of the radial distance of the electron, by contrast, is 3/2a0.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related concepts (21)
Muonium
Muonium (ˈmjuːoʊniəm) is an exotic atom made up of an antimuon and an electron, which was discovered in 1960 by Vernon W. Hughes and is given the chemical symbol Mu. During the muon's 2.2μs lifetime, muonium can undergo chemical reactions. Because a proton's mass is closer to the antimuon's mass than to the electron's mass, muonium (_Antimuon_Electron) is more similar to atomic hydrogen (_Proton+_Electron) than positronium (_Positron_Electron). Its Bohr radius and ionization energy are within 0.
Fine structure
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation. It was first measured precisely for the hydrogen atom by Albert A. Michelson and Edward W. Morley in 1887, laying the basis for the theoretical treatment by Arnold Sommerfeld, introducing the fine-structure constant. The gross structure of line spectra is the line spectra predicted by the quantum mechanics of non-relativistic electrons with no spin.
Fine-structure constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula 4πε_0ħcα = e^2. Its numerical value is approximately 0.