Unified atomic mass unit

See also Atomic mass.

The unified atomic mass unit (u), or dalton (Da), is a unit of atomic and molecular mass. By definition it is one twelfth of the mass of an unbound carbon-12 (¹²C) 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_A carbon-12 atoms, at rest and in their ground state, is 12 gram ( = 12×10⁻³ kg). From the latest value of N_A follows the latest value of the unified atomic mass unit:

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 10²⁷) 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, see this article.

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. 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) c₀²:

1 u = 931.494 061(21) MeV.

The proton mass is:

m_p = 1.007 276 466 812(90) u.

The neutron mass is:

m_n = 1.008 664 916 00(43) u.

The electron mass is:

m_e = 5.485 799 0946(22) × 10^-4 u.