Atomic units

Atomic units (au) are a convenient system of units of measurement used in atomic physics, particularly for describing the properties of electrons. The atomic units have been chosen such that the fundamental electron properties are all equal to one atomic unit.

Related Topics:
System of units - Atomic physics - Electron

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The atomic units are:

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:length: the Bohr radius a_0 ? 5.291 772 108(18)×10-11 m

Related Topics:
Length - Bohr radius

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:mass: the electron rest mass m_e ? 9.109 3826(16)×10-31 kg

Related Topics:
Mass - Rest mass

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:charge: the elementary charge e ? 1.602 176 53(14)×10-19 C

Related Topics:
Charge - Elementary charge

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:angular momentum: the Dirac constant hbar ? 1.054 571 68(18)×10-34 J s

Related Topics:
Angular momentum - Dirac constant

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:energy: the Hartree energy E_h ? 4.359 744 17(75)×10-18 J

Related Topics:
Energy - Hartree energy

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The electrostatic force constant k = 1/4pi epsilon_0 is also equal to one in this system. In fact, these six quantities are not all independent; it is sufficient to define any four of these constants to be one.

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In atomic units, the Bohr magneton mu_B = 1/2, and the speed of light c = 1/lpha pprox 137.036, where lpha is the fine-structure constant.

Related Topics:
Bohr magneton - Speed of light - Fine-structure constant

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Here are other derived units:

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:time: rac{hbar}{E_h} ? 2.418 884 326 505(16)×10-17 s

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:velocity: rac{a_0 E_h}{hbar} ? 2.187 691 2633(73)×106 m s-1

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:force: rac{E_h}{a_o} ? 8.238 7225(14)×10-8 N

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The use of atomic units also simplifies the Schrödinger equation. For example the Hamiltonian for an electron in the hydrogen atom would be:

Related Topics:
Schrödinger equation - Hamiltonian - Hydrogen atom

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in SI units:

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:hat H = - {{{hbar^2} over {2 m_e}} abla^2} - {1 over {4 pi epsilon_0}}{{e^2} over {r}}

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in atomic units:

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:hat H = - {{{1} over {2}} abla^2} - {{1} over {r}}

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