# Unified atomic mass unit

*See also Atomic mass.*

The **unified atomic mass unit** (* u*), or

**dalton**(

*), is a unit of atomic and molecular mass. By definition it is one twelfth of the mass of an unbound carbon-12 (*

**Da**^{12}C) atom, at rest and in its ground state.

The relationship of the unified atomic mass unit to the macroscopic SI base unit of mass, the kilogram, is given by Avogadro's number *N _{A}*. By the definition of Avogadro's number, the mass of

*N*carbon-12 atoms, at rest and in their ground state, is 12 gram ( = 12×10

_{A}^{−3}kg). The latest value of

*N*is the same numerical value as the Avagadro constant, the number of "elementary entities" in a mole of substance:

_{A}^{[1]}

*N*= 6.022 141 29(27) × 10_{A}^{23}/ mol,

where the symbol *mol* represents the mole, which can be defined for any substance as a sample containing the same number of "elementary entities" (atoms or molecules, for example) as there are atoms of ^{12}C in 0.012 kg of carbon-12.

From this value for *N _{A}* follows the latest value of the unified atomic mass unit:

^{[2]}

- 1
*u*≈ 1.660 538 921(73) × 10^{−27}kg

Future refinements in Avogadro's number by future improvements in counting large (on the order of 10^{27}) numbers of atoms, will give better accuracy of *u*. It is hoped that in the future the experimental accuracy of Avogadro's constant will improve so much that the unified atomic mass unit may replace the kilogram as the SI base unit. For instance, there is a proposal under consideration to define the kilogram in terms of a specified number of free carbon-12 (^{12}C) atoms, at rest and in their ground state, thereby fixing the Avagadro constant, and making an experimental determination unnecessary.^{[3]} See the article kilogram.

The unit *u* is convenient because one hydrogen atom has a mass of approximately 1 *u*, and more generally an atom or molecule that contains *p* protons and *n* neutrons will have a mass approximately equal to (*p* + *n*) *u*. The mass of a nucleus is not exactly equal to *p* + *n*, because the nuclear binding energy gives rise to a relativistic mass defect.

## Confusions

In the system of atomic units, the "atomic unit of mass" is the mass of the electron *m _{e}*.

^{[4]}But further confusion prevails:

In the literature one still finds the obsolete unit *amu* (atomic mass unit). This antiquated usage is deplorable, not only because the *amu* is __not__ a unit accepted for use with the SI, but also because two *different* standard masses are denoted by *amu*. There is the physicist's *amu* ( = 1/1.000 317 9 *u*) and there is the chemist's *amu* ( = 1/1.000 043 *u*). Because chemists and physicists now use the same atomic mass unit, today it is referred to as *unified*. It is a non-SI unit accepted for use with the SI, whose value in SI units is obtained experimentally.

## History

The different interpretations of the *amu* arose historically. Before 1960, in physics the amu was defined as 1/16 of the mass of one atom of oxygen-16, while in chemistry the amu was defined as 1/16 of the *average* mass of an oxygen atom (averaged over the natural abundance of the different oxygen isotopes). Both units are slightly smaller than the *unified atomic mass unit*, symbol *u*, that was adopted by the International Union of Pure and Applied Physics in 1960 and by the International Union of Pure and Applied Chemistry in 1961.

Much earlier, the first standardization of atomic mass was made by the chemist John Dalton in the early nineteenth century, who introduced the mass of one atom of hydrogen as the atomic mass unit. Later Francis Aston, inventor of the mass spectrometer, replace it by one sixteenth of the mass of one atom of oxygen-16.

## Examples

In the numerical values below, the numbers in parentheses refer to measurement uncertainties.

The atomic mass unit in MeV is (1 *u*) *c _{0}*

^{2}:

- 1
*u*= 931.494 061(21) MeV.^{[5]}

The proton mass is:

*m*= 1.007 276 466 812(90)_{p}*u*.^{[6]}

The neutron mass is:

*m*= 1.008 664 916 00(43)_{n}*u*.^{[7]}

The electron mass is:

*m*= 5.485 799 0946(22) × 10_{e}^{-4}*u*.^{[8]}

## References

- ↑
Fundamental physical constants: Avogadro constant
*N*. NIST. Retrieved on 2011-09-09._{A}, L - ↑
Fundamental physical constants: atomic mass unit-kilogram relationship 1
*u*. NIST. Retrieved on 2011-09-09. - ↑
P. Richard (2007). Theo W. Hänsch, ed:
*Metrology and fundamental constants: Volume 166 of Proceedings of the International School of Physics "Enrico Fermi"*. IOS Press, p. 511. ISBN 1586037846. - ↑
Fundamental physical constants: atomic unit of mass
*m*. NIST. Retrieved on 2011-09-09._{e} - ↑
Fundamental physical constants: atomic mass unit-electron volt relationship 1
*u*(*c*_{0}^{2}).*The NIST reference on constants, units, and uncertainty*. NIST. Retrieved on 2011-09-04. - ↑
Fundamental physical constants: proton mass in
*u*:*m*._{p}*The NIST reference on constants, units, and uncertainty*. NIST. Retrieved on 2011-09-04. - ↑
Fundamental physical constants: neutron mass in
*u*:*m*._{n}*The NIST reference on constants, units, and uncertainty*. NIST. Retrieved on 2011-09-09. - ↑
Fundamental physical constants: electron mass in
*u*:*m*._{e}*The NIST reference on constants, units, and uncertainty*. NIST. Retrieved on 2011-09-04.