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Atomic units
From Wikipedia, the free encyclopedia
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. There are two different kinds of
atomic units, which one might name Hartree atomic units and Rydberg atomic units, which differ in the
choice of the unit of mass and charge. This article deals with Hartree atomic units. In au, the numerical
values of the following six physical constants are all unity by definition:
Two properties of the electron, its mass and charge;
Two properties of the hydrogen atom, its Bohr radius and the absolute value of its electric potential
energy in the ground state;
Two constants, Dirac's and that for Coulomb's Law.
Contents
1 Fundamental units
2 Some derived units
3 Comparison with Planck units
4 Quantum mechanics and electrodynamics simplified
5 See also
6 References
7 External links
Fundamental units
Fundamental Atomic Units
Quantity
Name
Symbol
SI value
Planck unit
scale
length
Bohr radius
a0
5.291 772 108(18)!10-11
m
10-35 m
mass
electron rest mass
me
9.109 3826(16)!10-31 kg
10-8 kg
charge
elementary charge e
1.602 176 53(14)!10-19 C 10-18 C
angular momentum
Planck's constant
1.054 571 68(18)!10-34 J s (same)
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Atomic units - Wikipedia, the free encyclopedia
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energy
Hartree energy
Eh
4.359 744 17(75)!10-18 J
109 J
electrostatic force
constant
Coulomb's
constant
1/(4"#0 )
8.9875516!10 9 C-2 N m 2
(same)
These six quantities are not independent; to normalize all six quantities to 1, it suffices to normalize any four
of them to 1. The normalizations of the Hartree energy and Coulomb's constant, for example, are only an
incidental consequence of normalizing the other four quantities.
Some derived units
Derived Atomic Units
Quantity
Expression SI value
Planck unit scale
time
2.418 884 326 505(16)!10-17 s 10-43 s
velocity
2.187 691 2633(73)!106 m s -1 108 m s -1
force
8.238 7225(14)!10-8 N
1044 N
current
6.623 617 82(57)!10-3 A
1026 A
temperature
3.157 7464(55)!105 K
1032 K
pressure
2.942 1912(19)!1013 N m -2
10114 Pa
Comparison with Planck units
Both Planck units and au are derived from certain fundamental properties of the physical world, and are free
of anthropocentric considerations. To facilitate comparing the two systems of units, the above tables show the
order of magnitude, in SI units, of the Planck unit corresponding to each atomic unit. Generally, when an
atomic unit is "large" in SI terms, the corresponding Planck unit is "small", and vice versa. It should be kept
in mind that au were designed for atomic-scale calculations in the present-day Universe, while Planck units
are more suitable for quantum gravity and early-Universe cosmology.
Both au and Planck units normalize the Dirac constant and the Coulomb force constant to 1. Beyond this,
Planck units normalize to 1 the two fundamental constants of general relativity and cosmology: the
gravitational constant G and the speed of light in a vacuum, c. Letting $ denote the fine structure constant, the
au value of c is $-1 % 137.036.
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Atomic units - Wikipedia, the free encyclopedia
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Atomic units, by contrast, normalize to 1 the mass and charge of the electron, and a0 , the Bohr radius of the
hydrogen atom. Normalizing a0 to 1 amounts to normalizing the Rydberg constant, R& , to 4"/$ = 4"c. Given
au, the Bohr magneton 'B=1/2. The corresponding Planck value is e/2me. Finally, au normalize a unit of
atomic energy to 1, while Planck units normalize to 1 Boltzmann's constant k, which relates energy and
temperature.
Quantum mechanics and electrodynamics simplified
The (non-relativistic) Schrödinger equation for an electron in SI units is
.
The same equation in au is
.
For the special case of the electron around a hydrogen atom, the Hamiltonian in SI units is:
,
while atomic units transform the preceding equation into
.
Finally, Maxwell's equations take the following elegant form in au:
(There is actually some ambiguity in defining the atomic unit of magnetic field. The above Maxwell equations
use the "Gaussian" convention, in which a plane wave has electric and magnetic fields of equal magnitude. In
the "Lorentz force" convention, a factor of $ is absorbed into B.)
See also
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Atomic units - Wikipedia, the free encyclopedia
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Planck units
Natural units
References
H. Shull and G. G. Hall, Atomic Units, Nature, volume 184, no. 4698, page 1559 (Nov. 14, 1959)
External links
CODATA Internationally recommended values of the Fundamental Physical Constants.
(http://physics.nist.gov/cuu/Constants/index.html)
Retrieved from "http://en.wikipedia.org/wiki/Atomic_units"
Categories: Systems of units | Natural units | Atomic physics
This page was last modified 15:16, 22 October 2007.
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