Bohr radius

1 Bohr radius =
SI units
010−12 m010−3 nm
Natural units
01024 lP0103 le
US customary / Imperial units
010−12 ft010−9 in
In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy. In the simplest atom, hydrogen, a single electron orbits, and the smallest possible orbit for the electron, that with the lowest energy, is most likely to be found at a distance from the nucleus called the Bohr radius.

According to 2002 CODATA, the Bohr radius has a value of 5.291772108(18)10−11 m (i.e., approximately 53 pm or 0.53 Ã¥ngstrÃ¶ms). The number in parentheses (18) denotes the uncertainty of the last digits. This value can be computed in terms of other physical constants:

where:
is the permittivity of free space
is the reduced Planck's constant
is the electron rest mass
is the elementary charge
is the speed of light in vacuum
is the fine structure constant

While the Bohr model does not correctly describe an atom, the Bohr radius keeps its physical meaning as a characteristic size of the electron cloud in a full quantum-mechanical description. Thus the Bohr radius is often used as a unit in atomic physics, see atomic units.

Note that the definition of Bohr radius does not include the effect of reduced mass, and so it is not precisely equal to the orbital radius of the electron in a hydrogen atom in the more physical model where reduced mass is included. This is done for convenience: the Bohr radius as defined above appears in equations relating to atoms other than hydrogen, where the reduced mass correction is different. If the definition of Bohr radius included the reduced mass of hydrogen, it would be necessary to include a more complex adjustment in equations relating to other atoms.

The Bohr radius of the electron is one of a trio of related units of length, the other two being the Compton wavelength of the electron and the classical electron radius . The Bohr radius is built from the electron mass , Planck's constant and the electron charge . The Compton wavelength is built from , and the speed of light . The classical electron radius is built from , and . Any one of these three lengths can be written in terms of any other using the fine structure constant :

The Bohr radius including the effect of reduced mass can be given by the following equation:

,

where

is the Compton wavelength of the proton.
is the Compton wavelength of the electron.
is the fine structure constant.

In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together.

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1 metre =
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US customary / Imperial units
0 ft 0 in
The metre or meter[1](symbol: m) is the fundamental unit of length in the International System of Units (SI).
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1 nanometre =
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010−9 m 010−3 μm
US customary / Imperial units
010−9 ft 010−9 in
A nanometre (American spelling: nanometer, symbol nm
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In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units.
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The Planck length, denoted by , is the unit of length approximately 1.6 × 10−35 metres, 6.3 × 10-34 inches, or about 10-20 times the diameter of a proton. It is in the system of units known as Planck units.
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U.S. customary units, also known in the United States as English units[1] (but see English unit) or standard units, are units of measurement that are currently used in the USA, in some cases alongside units from SI (the International System of Units
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010−3 m 0 mm
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010−3 ft 010−3 yd

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In atomic physics, the Bohr model depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus — similar in structure to the solar system, but with electrostatic forces providing attraction, rather than
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atom (Greek ἄτομος or Ã¡tomos meaning "indivisible") is the smallest particle still characterizing a chemical element.
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Niels Bohr

Niels Henrik David Bohr
Born September 7 1885
Copenhagen, Denmark
Died November 18 1962 (aged 77)
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19th century - 20th century - 21st century
1880s  1890s  1900s  - 1910s -  1920s  1930s  1940s
1910 1911 1912 - 1913 - 1914 1915 1916

Year 1913 (MCMXIII
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Electron

Theoretical estimates of the electron density for the first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density
Composition: Elementary particle
Family: Fermion
Group: Lepton
Generation: First
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The nucleus of an atom is the very small dense region of an atom, in its center consisting of nucleons (protons and neutrons). The size (diameter) of the nucleus is in the range of 1.
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1, −1
(amphoteric oxide)
Electronegativity 2.20 (Pauling scale) More

Atomic radius 25 pm
Atomic radius (calc.) 53 pm
Covalent radius 37 pm
Van der Waals radius 120 pm
Miscellaneous

Thermal conductivity (300 K) 180.
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1 metre =
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0 ft 0 in
The metre or meter[1](symbol: m) is the fundamental unit of length in the International System of Units (SI).
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Distances shorter than 1 pm
• 1 pm = 1 picometre = 1,000 femtometres
• 2.4 pm — The compton wavelength of the electron.
• 5 pm — shorter X-ray wavelengths (approx.

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1 Ã¥ngstrÃ¶m =
SI units
010−12 m 010−3 nm
Natural units
01024 lPa0
US customary / Imperial units
010−12 ft 010−9
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In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma).
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Vacuum permittivity is the electric constant ε0 (also known as the permittivity of free space, or by the term dielectric constant of vacuum), which is a fundamental physical constant.
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Planck constant (denoted ) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory.
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Electron

Theoretical estimates of the electron density for the first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density
Composition: Elementary particle
Family: Fermion
Group: Lepton
Generation: First
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The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron.
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speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
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The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction.
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Electron cloud is a term used, if not originally coined, by the Nobel Prize laureate and acclaimed educator Richard Feynman in The Feynman Lectures on Physics for discussing "exactly what is an electron?".
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quantum mechanics is the study of the relationship between energy quanta (radiation) and matter, in particular that between valence shell electrons and photons. Quantum mechanics is a fundamental branch of physics with wide applications in both experimental and theoretical physics.
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Atomic units (au) form a system of units convenient for atomic physics, electromagnetism, and quantum electrodynamics, especially when the focus is on the properties of electrons.
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Reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. This is a quantity with the units of mass, which allows the two-body problem to be solved as if it were a one-body problem.
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