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Atomic Units
When you are working with expressions that have many small valued constants, it may
be easier to simply set the constant or group of constants equal to 1. All constants have
the value of 1 in some unit system. Here is a summary of quantities and their atomic unit
definitions:
Quantity
constant(s)
SI value
mass of an electron
m=1
9.109382 x 10-31 kg
charge of an electron
e=1
1.6021765 x 10-19 C
angular momentum
quantization constant
permittivity of a
vacuum
distance which is the
most probable radius of a 1s
electron in hydrogen atom
(called a Bohr)
energy which is equal to
twice the ionization
energy of hydrogen atom
(called a Hartree)
time it takes for an electron
to travel one period in the
first Bohr orbit
speed the electron is
traveling in the first
Bohr orbit
electric potential (energy which
is minus the potential energy of
an electron in the first Bohr orbit)
ħ=1
1.0545716 x 10-34 J·sec
4o = 1
1.11265 x 10-10
C2
Jm
4 o  2
 ao  1
me2
5.2917721 x 10-11 m
me4
1
(4 o ) 2
4.359744 x 10-18 J
(4 o ) 2  3
1
me4
2.4188843 x 10-17 s
e2
4 o 
1
me3
1
(4 o ) 2
2.1876913 x 106 m/s
27.21138 V (J/C)
Notice that the energy atomic unit (Hartree) will simplify the expression for the energy
levels of hydrogen atom to,
1
EnH atom   2 [a.u.] n  1,2,3,...
2n
and that potential and kinetic energy of the hydrogen atom will always add according to
the Virial theorem:
1
1
EnH atom  E pot  Ekin   2  2
n
2n