# Atomic mass unit

Unified atomic mass unit
(Dalton)
Unit systemPhysical constant
(Accepted for use with the SI)
Unit ofmass
Symbolu or Da
Named afterJohn Dalton
Conversions
1 u or Da in ...... is equal to ...
kg   1.660539040(20)×10−27
MeV/c2   931.4940954(57)
me   1822.888486192(53)

The unified atomic mass unit or dalton (symbol: u, or Da or AMU) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol.[1] It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest,[2] and has a value of 1.660539040(20)×10−27 kg,[3] or approximately 1.66 yoctograms.[4] The CIPM has categorised it as a non-SI unit accepted for use with the SI, and whose value in SI units must be obtained experimentally.[2]

The atomic mass unit (amu) without the "unified" prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, many sources still use the term amu but now define it in the same way as u (i.e., based on carbon-12).[5][6] In this sense, most uses of the terms atomic mass units and amu, today, actually refer to unified atomic mass unit. For standardization, a specific atomic nucleus (carbon-12 vs. oxygen-16) had to be chosen because the average mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than (and not equal to) 1 u.

The atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass (me).

Until the 2019 redefinition of SI base units, the number of daltons in a gram is exactly the Avogadro number by definition, or equivalently, a dalton is exactly equivalent to 1 gram/mol. Thereafter, these relationships will no longer be exact, but they will still be extremely accurate approximations.[7][Note 1]

## History of amu

The standard atomic weight (or atomic weight) scale has traditionally been a relative value, that is without a unit, with the first relative atomic mass basis suggested by John Dalton in 1803 as 1H.[8] Despite the initial mass of 1H being used as the natural unit for relative atomic mass, it was suggested by Wilhelm Ostwald that relative atomic mass would be best expressed in terms of units of 1/16 mass of oxygen (1903). This evaluation was made prior to the discovery of the existence of elemental isotopes, which occurred in 1912.[8]

The discovery of isotopic oxygen in 1929 led to a divergence in relative atomic mass representation, with isotopically weighted oxygen (i.e., naturally occurring oxygen relative atomic mass) given a value of exactly 16 atomic mass units (amu) in chemistry, while pure 16O (oxygen-16) was given the mass value of exactly 16 amu in physics.

The divergence of these values could result in errors in computations, and was unwieldy. The chemistry amu, based on the relative atomic mass (atomic weight) of natural oxygen (including the heavy naturally-occurring isotopes 17O and 18O), was about 1.000282 as massive as the physics amu, based on pure isotopic 16O.

For these and other reasons, the reference standard for both physics and chemistry was changed to carbon-12 in 1961.[9] The choice of carbon-12 was made to minimise further divergence with prior literature.[8] The new and current unit was referred to as the unified atomic mass unit, u.[10] and given a new symbol, "u", which replaced the now deprecated "amu" that had been connected to the old oxygen-based system. The dalton (Da) is another name for the unified atomic mass unit.[11]

${\displaystyle 1\,\mathrm {u} =m_{\mathrm {u} }={\frac {1}{12}}m\left({}^{12}\mathrm {C} \right)}$

Despite this change, modern sources often still use the old term "amu" but define it as u (1/12 of the mass of a carbon-12 atom), as mentioned in the article's introduction. Therefore, in general, "amu" likely does not refer to the old oxygen standard unit, unless the source material originates from the 1960s or before.

## Terminology

The unified atomic mass unit and the dalton are different names for the same unit of measure. As with other unit names such as watt and newton, dalton is not capitalized in English, but its symbol, Da, is capitalized. With the introduction of the name dalton, there has been a gradual change towards using that name in preference to the name, unified atomic mass unit:

• In 1993, the International Union of Pure and Applied Chemistry (IUPAC) approved the use of the dalton with the qualification that the CGPM had not given its approval.[12]
• In 2003, the Consultative Committee for Units, part of the CIPM, recommended a preference for the usage of the "dalton" over the "unified atomic mass unit" as it "is shorter and works better with prefixes".[13]
• In 2005, the International Union of Pure and Applied Physics endorsed the use of the dalton as an alternative to the unified atomic mass unit.[14]
• In 2006, in the 8th edition of the formal definition of SI, the CIPM cataloged the dalton alongside the unified atomic mass unit as a "Non-SI unit whose values in SI units must be obtained experimentally: Units accepted for use with the SI".[2] The definition also noted that "The dalton is often combined with SI prefixes ..."
• In 2009, when the International Organization for Standardization published updated versions of ISO 80000, it gave mixed messages as to whether or not the unified atomic mass unit had been deprecated: ISO 80000-1:2009 (General), identified the dalton as having "earlier [been] called the unified atomic mass unit u",[15] but ISO 80000-10:2009 (atomic and nuclear physics) catalogued both as being alternatives for each other.[16]
• The 2010 version of the Oxford University Press style guide for authors in life sciences gave the following guidance: "Use the Système international d'unités (SI) wherever possible ... The dalton (Da) or more conveniently the kDa is a permitted non-SI unit for molecular mass or mass of a particular band in a separating gel."[17] At the same time, the author guidelines for the journal "Rapid Communications in Mass Spectrometry" stated "The dalton (Da) is a unit of mass normally used for the molecular weight ... use of the Da in place of the u has become commonplace in the mass spectrometry literature ... The 'atomic mass unit', abbreviated 'amu', is an archaic unit".[18]
• In 2012, in response to the proposed redefinition of the kilogram, it was proposed that the dalton be redefined as being 0.001/NA kg, thereby breaking the link with 12C. This would result in the dalton and the atomic mass unit having slightly different definitions, but the suggestion is that the older unit should be superseded by the "new" dalton.[19]
• In 2018, the draft Ninth SI Brochure[7] associated with the 2019 redefinition of SI base units retains the definition of the Dalton and atomic mass unit unchanged in term of the mass of a carbon-12 atom.

## Relationship to SI

The former definition of the mole, an SI base unit, was accepted by the CGPM in 1971 as:

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12; its symbol is "mol".
2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

However, the first part of this definition will be changed on 20 May 2019 to:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number.[20][21]

One consequence of this change is that the current defined relationship between the mass of the 12C atom, the dalton, the kilogram, and the Avogadro number will no longer be valid. One of the following must change:

• The mass of a 12C atom is exactly 12 dalton.
• The number of dalton in a gram is exactly the numerical value of the Avogadro number: (i.e., 1 g/Da = 1 mol ⋅ NA).

The wording of the ninth SI Brochure[7][Note 1] implies that the first statement remains valid, which means that the second is no longer true. The molar mass constant, while still with great accuracy remaining 1 g/mol, is no longer exactly equal to that. Given that the unified atomic mass unit is one twelfth the mass of one atom of carbon-12, meaning the mass of such an atom is 12 u, it follows that there are only approximately NA atoms of carbon-12 in 0.012 kg of carbon-12. This can be expressed mathematically as

12 u ⋅ NA ≈ 0.012 kg/mol, or
1 u ⋅ NA ≈ 0.001 kg/mol

## Usage

Molecular masses of proteins are often expressed in kilodaltons (kDa or kD). For example, a molecule of a protein with molar mass 64000 g⋅mol−1 has a mass of 64 kDa.[1]

In research and commerce, the degree of polymerization of synthetic polymers is conventionally expressed in daltons.

The US Supreme Court based a major precedent of appellate law on a disputed case of counting daltons for a molecular distribution.[22]

## Notes

1. ^ a b A footnote in Table 8 on non-SI units states: "The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state."

## References

1. ^ a b Berg, Jeremy M.; Tymoczko, John L.; Stryer, Lubert (2007). "2". Biochemistry (6th ed.). New York: Freeman. p. 35. ISBN 978-0-7167-8724-2.
2. ^ a b c International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 126, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
3. ^ "CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-25. 2014 CODATA recommended values
4. ^
5. ^ Chang, Raymond (2005). Physical Chemistry for the Biosciences. p. 5. ISBN 978-1-891389-33-7.
6. ^ Kelter, Paul B.; Mosher, Michael D.; Scott, Andrew (2008). Chemistry: The Practical Science. 10. p. 60. ISBN 0-547-05393-2.
7. ^ a b c "Draft of the ninth SI Brochure" (PDF). BIPM. 5 February 2018. Retrieved 12 November 2018.
8. ^ a b c Petley, B. W. (1989), "The atomic mass unit", IEEE Trans. Instrum. Meas., 38 (2): 175–79, doi:10.1109/19.192268
9. ^ Holden, Norman E. (2004), "Atomic Weights and the International Committee—A Historical Review", Chem. Int., 26 (1): 4–7
10. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "unified atomic mass unit". doi:10.1351/goldbook.U06554
11. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "dalton". doi:10.1351/goldbook.D01514
12. ^ Mills, Ian; Cvitaš, Tomislav; Homann, Klaus; Kallay, Nikola; Kuchitsu, Kozo (1993). Quantities, Units and Symbols in Physical Chemistry International Union of Pure and Applied Chemistry; Physical Chemistry Division (PDF) (2nd ed.). International Union of Pure and Applied Chemistry and published for them by Blackwell Science Ltd. ISBN 0-632-03583-8.
13. ^
14. ^ "IUPAP: C2: Report 2005". Retrieved 2018-07-15.
15. ^ International Standard ISO 80000-1:2009 – Quantities and Units – Part 1: General, International Organization for Standardization, 2009
16. ^ International Standard ISO 80000-10:2009 – Quantities and units – Part 10: Atomic and nuclear physics, International Organization for Standardization, 2009
17. ^ "Instructions to Authors". AoB Plants. Oxford journals; Oxford University Press. Retrieved 2010-08-22.
18. ^ "Author guidelines". Rapid Communications in Mass Spectrometry. Wiley-Blackwell. 2010.[full citation needed]
19. ^ Leonard, B P (2012). "Why the dalton should be redefined exactly in terms of the kilogram". Metrologia. 49 (4): 487–491. Bibcode:2012Metro..49..487L. doi:10.1088/0026-1394/49/4/487.
20. ^ CIPM Report of 106th Meeting Archived 27 January 2018 at the Wayback Machine Retrieved 7 April 2018
21. ^ "Redefining the Mole". NIST. NIST. 23 October 2018. Retrieved 24 October 2018.
22. ^
23. ^ Opitz CA, Kulke M, Leake MC, Neagoe C, Hinssen H, Hajjar RJ, Linke WA (October 2003). "Damped elastic recoil of the titin spring in myofibrils of human myocardium". Proc. Natl. Acad. Sci. U.S.A. 100 (22): 12688–93. Bibcode:2003PNAS..10012688O. doi:10.1073/pnas.2133733100. PMC 240679. PMID 14563922.