Table 7 contains units whose values in SI units have to be determined experimentally, and thus have an associated uncertainty. Except for the astronomical unit, all other units in Table 7 are related to fundamental physical constants. The first three units, the nonSI units electronvolt, symbol eV, dalton or unified atomic mass unit, symbol Da or u, respectively, and the astronomical unit, symbol ua, have been accepted for use with the SI by the CIPM. The units in Table 7 play important roles in a number of specialized fields in which the results of measurements or calculations are most conveniently and usefully expressed in these units. For the electronvolt and the dalton the values depend on the elementary charge e and the Avogadro constant N_{A}, respectively.
There are many other units of this kind, because there are many fields in which it is most convenient to express the results of experimental observations or of theoretical calculations in terms of fundamental constants of nature. The two most important of such unit systems based on fundamental constants are the natural unit (n.u.) system used in high energy or particle physics, and the atomic unit (a.u.) system used in atomic physics and quantum chemistry. In the n.u. system, the base quantities for mechanics are speed, action, and mass, for which the base units are the speed of light in vacuum c_{0}, the Planck constant h divided by 2, called the reduced Planck constant with symbol , and the mass of the electron m_{e}, respectively. In general these units are not given any special names or symbols but are simply called the n.u. of speed, symbol c_{0}, the n.u. of action, symbol , and the n.u. of mass, symbol m_{e}. In this system, time is a derived quantity and the n.u. of time is a derived unit equal to the combination of base units /m_{e}c_{0}^{2}. Similarly, in the a.u. system, any four of the five quantities charge, mass, action, length, and energy are taken as base quantities. The corresponding base units are the elementary charge e, electron mass m_{e}, action , Bohr radius (or bohr) a_{0}, and Hartree energy (or hartree) E_{h}, respectively. In this system, time is again a derived quantity and the a.u. of time a derived unit, equal to the combination of units /E_{h}. Note that a_{0} = /(4R_{}), where is the finestructure constant and R_{} is the Rydberg constant; and E_{h} = e^{2}/(4_{0}a_{0}) = 2R_{}hc_{0} = ^{2}m_{e}c_{0}^{2}, where _{0} is the electric constant and has an exact value in the SI.
For information, these ten natural and atomic units and their values in SI units are also listed in Table 7. Because the quantity systems on which these units are based differ so fundamentally from that on which the SI is based, they are not generally used with the SI, and the CIPM has not formally accepted them for use with the International System. To ensure understanding, the final result of a measurement or calculation expressed in natural or atomic units should also always be expressed in the corresponding SI unit. Natural units (n.u.) and atomic units (a.u.) are used only in their own special fields of particle and atomic physics, and quantum chemistry, respectively. Standard uncertainties in the least significant digits are shown in parenthesis after each numerical value.
Table 7. NonSI units whose values in SI units must be obtained experimentally

Quantity 
Name of unit 
Symbol for unit 
Value in SI units ^{(a)} 

Units accepted for use with the SI 
energy 
electronvolt ^{(b)} 
eV 
1 eV = 1.602 176 565(35) x 10^{–19} J 
mass 
dalton, ^{(c)} 
Da 
1 Da = 1.660 538 921(73) x 10^{–27} kg 

unified atomic mass unit 
u 
1 u = 1 Da 
Natural units (n.u.) 
speed 
n.u. of speed (speed of light in vacuum) 
c_{0} 
299 792 458 m/s (exact) 
action 
n.u. of action (reduced Planck constant) 

1.054 571 726(47) x 10^{–34} J s 
mass 
n.u. of mass (electron mass) 
m_{e} 
9.109 382 91(40) x 10^{–31} kg 
time 
n.u. of time 
/(m_{e}c_{0}^{2}) 
1.288 088 668 33(83) x 10^{–21} s 
Atomic units (a.u.) 
charge 
a.u. of charge (elementary charge) 
e 
1.602 176 565(35) x 10^{–19} C 
mass 
a.u. of mass (electron mass) 
m_{e} 
9.109 382 91(40) x 10^{–31} kg 
action 
a.u. of action (reduced Planck constant) 

1.054 571 726(47) x 10^{–34} J s 
length 
a.u. of length, bohr (Bohr radius) 
a_{0} 
0.529 177 210 92(17) x 10^{–10} m 
energy 
a.u. of energy, hartree (Hartree energy) 
E_{h} 
4.359 744 34(19) x 10^{–18} J 
time 
a.u. of time 
/E_{h} 
2.418 884 326 502(12) x 10^{–17} s 
(a) 
The values in SI units of all units in this table are taken from the 2010 CODATA set of recommended values of the fundamental physical constants, P.J. Mohr, B.N. Taylor and D.B. Newell, Rev. Mod. Phys., 2012, 84, 15271605. The standard uncertainty in the last two digits is given in parentheses (see section 5.3.5). 
(b) 
The electronvolt is the kinetic energy acquired by an electron in passing through a potential difference of one volt in vacuum. The electronvolt is often combined with the SI prefixes. 
(c) 
The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 times the mass of a free carbon 12 atom, at rest and in its ground state. The dalton is often combined with SI prefixes, for example to express the masses of large molecules in kilodaltons, kDa, or megadaltons, MDa, or to express the values of small mass differences of atoms or molecules in nanodaltons, nDa, or even picodaltons, pDa. 


[ updated 2014 ] 


