unified atomic mass unit

A very, very small unit of mass used to express the mass of atoms and molecules, conceptually equal to 1 gram divided by Avogadro’s constant. Since 1961, by definition the unified atomic mass unit is equal to one-twelfth of the mass of the nucleus of a carbon-12 atom. Referring to the definition of the mole, it must be assumed that the ¹²C atom referred to is at rest, unbound, and in the ground state.¹ Symbol, u. Although not an SI unit, the unified atomic mass unit is accepted by the CGPM for use with SI.

Some experts object to calling the unified atomic mass unit a unit:

The “unified atomic mass unit” is not really a unit at all but a physical quantity denoted by mu and defined as 1/12 of the mass of an atom of ¹²C. Alternatively it is the product L⁻¹ g mol⁻¹ of a physical quantity L⁻¹, the reciprocal of the Avogadro constant, and the unit g mol⁻¹.

M. L. McGlashan.
Physico-Chemical Quantities and Units.
London: Royal Institute of Chemistry, 1968.
Page 24.

The mass of the unified atomic mass unit is determined experimentally. According to the 2010 CODATA recommendations, one unified atomic mass unit is 1.660 538 921 × 10⁻²⁷ kilogram, with a one-standard deviation uncertainty of ± 0.000 000 073 × 10⁻²⁷ kilogram.²

The above definition was agreed upon by the International Union of Pure and Applied Physics in 1960³ and the International Union of Pure and Applied Chemistry (in 1961)⁴, resolving a longstanding difference between chemists and physicists. The unified atomic mass unit replaced the atomic mass unit (chemical scale) and the atomic mass unit (physical scale), both having the symbol amu. The amu (physical scale) was one-sixteenth of the mass of an atom of oxygen-16. The amu (chemical scale) was one-sixteenth of the average mass of oxygen atoms as found in nature.

1 u = 1.000 317 9 amu (physical scale) = 1.000 043 amu (chemical scale)

1. B. W. Petley.
The mole and the unified atomic mass unit.
Metrologia, volume 33, pages 261-264 (1996).

2. The 2010 value was taken from http://physics.nist.gov/cgi-bin/cuu/Value?tukg|search_for=atomic+mass+unit

3. International Union of Pure and Applied Physics.
Report of the 10th General Assembly.
Ottawa 1960.

Page 24.

4. A. E. Cameron and E. Wichers.
Report of the International Commission on Atomic Weights (1961).
Journal of the American Chemical Society, volume 84, page 4175 (1962).

History of the atomic mass unit

Stanislao Cannizzaro (1826–1910), the pioneer in this field, adopted the hydrogen atom as a standard of mass and set its atomic weight at 1. Others accepted the idea of using a specific atom as a standard of mass, but preferred a more massive standard in order to reduce experimental error.

As early as 1850, chemists used a unit of atomic weight based on saying the atomic weight of oxygen was 16. Oxygen was chosen because it forms chemical compounds with many other elements, simplifying determination of their atomic weights. Sixteen was chosen because it was the lowest whole number that could be assigned to oxygen and still have an atomic weight for hydrogen that was not less than 1.

The O = 16 scale was formalized when a committee appointed by the Deutsche Chemische Gesellschaft called for the formation of an international commission on atomic weights in March 1899. A commission of 57 members was formed. Since the commission carried on its business by correspondence, the size proved unwieldy, and the Gesellschaft suggested a smaller committee be elected. A 3-member International Committee of Atomic Weights was duly elected, and in 1903 issued its first report, using the O = 16 scale.⁵

Taking isotopes into account

The discovery of isotopes complicated the picture. In nature, pure oxygen is composed of a mixture of isotopes: some oxygen atoms are more massive than others.

This was no problem for the chemists’ calculations as long as the relative abundance of the isotopes in their reagents remained constant, though it confirmed that oxygen’s atomic weight was the only one that in principle would be a whole number (hydrogen’s, for example, was 1.000 8).

Physicists, however, dealing with atoms and not reagents, required a unit that distinguished between isotopes. At least as early as 1927⁶ physicists were using an atomic mass unit defined as equal to one-sixteenth of the mass of the oxygen-16 atom (the isotope of oxygen containing a total of 16 protons and neutrons).

In 1919, isotopes of oxygen with mass 17 and 18 were discovered.⁷ Thus the two amu’s clearly diverged: one based on one-sixteenth of the average mass of the oxygen atoms in the chemist’s laboratory, and the other based on one-sixteenth of the mass of an atom of a particular isotope of oxygen.

In 1956, Alfred Nier (at the bar in the Hotel Krasnapolski in Amsterdam) and independently A. Ölander⁸, both members of the Commission on Atomic Masses of the IUPAP, suggested to Josef Mattauch that the atomic weight scale be based on carbon-12. That would be okay with physicists, since carbon-12 was already used as a standard in mass spectroscopy. The chemists resisted making the amu one-sixteenth the mass of an oxygen-16 atom; it would change their atomic weights by about 275 parts per million. Making the amu one-twelfth the mass of a carbon-12 nucleus, however, would lead to only a 42 parts per million change, which seemed within reason.

Mattauch set to work enthusiastically proselytizing the physicists, while E. Wichers lobbied the chemists.⁹ In the years 1959–1961 the chemists and physicists resolved to use the isotope carbon-12 as the standard, setting its atomic mass at 12.

5. F. W. Clarke, T. E. Thorpe and K. Seubert.
Report of the International Commission on Atomic Weights.
Journal of the American Chemical Society, volume 25 (1903).

6. F. W. Aston.
Bakerian Lecture: A New Mass-Spectrograph and the Whole Number Rule.
Proceedings of the Royal Society (London) A115, page 487 (August 1927).

Page 500: “The choice of a standard of mass is at our disposal. From a theoretical point of view the neutral hydrogen atom, or the proton itself, would be a good unit, and would make all the divergences of the same, negative, sign. On the other hand, the fact that such masses as these lie at the extreme end of the scale makes them inconvenient as practical standards. For the present inquiry the neutral oxygen atom O16 has been adopted as standard. The identity of this scale with that of the chemical atomic weights depends on whether oxygen is a simple element or not. The absence of a very small percentage of an isotope is difficult to prove, and in oxygen particularly so, for the neighboring units 14, 15, 17, 18 are always liable to be present.”

7. W. F. Giaugue and H. L. Johnson.
An isotope of oxygen, mass 18.
Nature, volume 123, page 318 (1929).
W. F. Giaugue and H. L. Johnson.
An isotope of oxygen of mass 17 in the earth’s atmosphere.
Nature, volume 123, page 831 (1929).

8. According to remarks by H. E. Duckworth at the Nier Memorial Service, 2 November 1994. See John H. Reynolds, Alfred Otto Carl Nier, Biographical Memoirs, National Academy of Sciences.

9. Josef Mattauch.
The rational choice of a unified scale for atomic weights and nuclidic masses.
Supplement to:
E. Wichers.
Report on atomic weights for 1956-57.
Journal of the American Chemical Society, volume 80, page 4121 (1958).


The current IUPAC definition of unified atomic mass: http://goldbook.iupac.org/U06554.html

Norman E. Holden.
Atomic Weights and the International Committee—A Historical Review.
Chemistry International, volume 26, no. 1 (January-February 2004).

Very comprehensive. The complete article appears to be available only on the web, at www.iupac.org/publications/ci/2004/2601/1_holden.html

An English translation of Stanislao Cannizzaro's “Sunto di un corso di filosofia Chimica” is available on the web at www.archive.org/details/sketchofcourseof00cannrich. Originally published in Il Nuovo Cimento, vol. 7, pages 321-366 (1858)

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