Thedalton orunified atomic mass unit (symbols:Da oru, respectively) is a unit ofmass defined as1/12 of the mass of anunbound neutral atom ofcarbon-12 in its nuclear and electronicground state andat rest.[1][2][3] It is anon-SI unit accepted for use with SI. The word "unified" emphasizes that the definition was accepted by bothIUPAP andIUPAC.[4] Theatomic mass constant, denotedmu, is an atomic-scale reference mass, defined identically, but it is not a unit of mass. Expressed in terms ofma(12C), theatomic mass of carbon-12:mu =ma(12C)/12 = 1 Da.[5] The dalton's numerical value in terms of the fixed-h kilogram is an experimentally determined quantity that, along with its inherent uncertainty, is updated periodically. As listed in the 9th edition, version 3.02, of theSI Brochure, the 2022CODATA recommended value of the atomic mass constant expressed in the SI base unitkilogram is:
This was the value used in the calculation of g/Da, the traditional definition of theAvogadro number. This resulted in the valueg/Da = 6.022 140 7620(18) × 1023, which was thenrounded to 9 significant figures (thus guaranteeing continuity, to the precision indicated) and fixed at exactly that value for the 2019 redefinition of the mole.
The value serves as aconversion factor of mass from daltons to kilograms, which can easily be converted tograms and other metric units of mass. The2019 revision of the SI redefined the kilogram by fixing the value of thePlanck constant (h), improving the precision of the atomic mass constant expressed in SI units by anchoring it to fixedphysical constants. Although the dalton remains defined via carbon-12, the revision enhances traceability and accuracy in atomic mass measurements.
Themole is a unit ofamount of substance used inchemistry andphysics, such that the mass of one mole of a substance expressed ingrams (i.e., themolar mass in g/mol or kg/kmol) is numerically equal to the average mass of anelementary entity of the substance (atom,molecule, orformula unit) expressed in daltons. For example, the average mass of one molecule ofwater is about 18.0153 Da, and the mass of one mole of water is about 18.0153 g. A protein whose molecule has an average mass of64 kDa would have a molar mass of64 kg/mol. However, while this equality can be assumed for practical purposes, it is only approximate, because of the2019 redefinition of the mole.[8][1]
The dalton is commonly used inphysics andchemistry to express themass of atomic-scale objects, such asatoms,molecules, andelementary particles, both for discrete instances and multiple types of ensemble averages. For example, an atom ofhelium-4 has a mass of4.0026 Da. This is an intrinsic property of theisotope and all helium-4 atoms have the same mass. Acetylsalicylic acid (aspirin),C 9H 8O 4, has an average mass of about180.157 Da. However, there are no acetylsalicylic acid molecules with this mass. The two most common masses of individual acetylsalicylic acid molecules are180.0423 Da, having the most common isotopes, and181.0456 Da, in which one carbon iscarbon-13.
In general, the mass in daltons of an atom is numerically close but not exactly equal to thenumber of nucleons in itsnucleus. It follows that the molar mass of a compound (grams permole) is numerically close to the average number of nucleons contained in each molecule. By definition, the mass of an atom ofcarbon-12 is 12 daltons, which corresponds with the number of nucleons that it has (6 protons and 6 neutrons). However, the mass of an atomic-scale object is affected by thebinding energy of the nucleons in its atomic nuclei, as well as the mass and binding energy of itselectrons. Therefore, this equality holds only for the carbon-12 atom in the stated conditions, and will vary for other substances. For example, the mass of an unbound atom of the commonhydrogenisotope (hydrogen-1, protium) is1.007825032241(94) Da,[a] the mass of a proton is1.0072764665789(83) Da,[11] the mass of a free neutron is1.00866491606(40) Da,[12] and the mass of ahydrogen-2 (deuterium) atom is2.014101778114(122) Da.[13] In general, the difference (absolutemass excess) is less than 0.1%; exceptions include hydrogen-1 (about 0.8%),helium-3 (0.5%),lithium-6 (0.25%) andberyllium (0.14%).
The mass-equivalent is commonly used in place of a unit of mass inparticle physics, and these values are also important for the practical determination of relative atomic masses.
The interpretation of thelaw of definite proportions in terms of theatomic theory of matter implied that the masses of atoms of various elements had definite ratios that depended on the elements. While the actual masses were unknown, the relative masses could be deduced from that law. In 1803John Dalton proposed to use the (still unknown) atomic mass of the lightest atom, hydrogen, as the natural unit of atomic mass. This was the basis of theatomic weight scale.[16]
For technical reasons, in 1898, chemistWilhelm Ostwald and others proposed to redefine the unit of atomic mass as1/16 the mass of an oxygen atom.[4] That proposal was formally adopted by theInternational Committee on Atomic Weights (ICAW) in 1903. That was approximately the mass of one hydrogen atom, but oxygen was more amenable to experimental determination. This suggestion was made before the discovery of isotopes in 1912.[16] PhysicistJean Perrin had adopted the same definition in 1909 during his experiments to determine the atomic masses and theAvogadro constant.[17] This definition remained unchanged until 1961.[18][19] Perrin also defined the "mole" as an amount of a compound that contained as many molecules as 32 grams of oxygen (O 2). He called that number theAvogadro number in honor of physicistAmedeo Avogadro.
The discovery of isotopes of oxygen in 1929 required a more precise definition of the unit. Two distinct definitions came into use. Chemists choose to define the AMU as1/16 of the average mass of an oxygen atom as found in nature; that is, the average of the masses of the known isotopes, weighted by their natural abundance. Physicists, on the other hand, defined it as1/16 of the mass of an atom of the isotope oxygen-16 (16O).[4]
The existence of two distinct units with the same name was confusing, and the difference (about1.000282 in relative terms) was large enough to affect high-precision measurements. Moreover, it was discovered that the isotopes of oxygen had different natural abundances in water and in air.
In April 1957Alfred O. C. Nier suggested toJosef Mattauch that thecarbon-12 be adopted as mass scale because of carbon's use as a secondary standard inmass spectrometry. Also, carbon-12 implied acceptable relative changes in the atomic weight scale, i.e., 42 parts-per-million (ppm) compared to 275 ppm foroxygen-16 which would not be acceptable to chemists.
The new unit was named the "unified atomic mass unit" and given a new symbol "u", to replace the old "amu" that had been used for the oxygen-based unit.[20] However, the old symbol "amu" has sometimes been used, after 1961, to refer to the new unit, particularly in lay and preparatory contexts.
In 1993, the IUPAC proposed the shorter name "dalton" (with symbol "Da") for the unified atomic mass unit.[22][23] As with other unit names such as watt and newton, "dalton" is not capitalized in English, but its symbol, "Da", is capitalized. The name was endorsed by theInternational Union of Pure and Applied Physics (IUPAP) in 2005.[24]
In 2003 the name was recommended to the BIPM by theConsultative Committee for Units, part of theCIPM, as it "is shorter and works better with [SI] prefixes".[25] In 2006, the BIPM included the dalton in its 8th edition of theSI brochure of formal definitions as anon-SI unit accepted for use with the SI.[26] The name was also listed as an alternative to "unified atomic mass unit" by theInternational Organization for Standardization in 2009.[27][3] It is now recommended by several scientific publishers,[28] and some of them consider "atomic mass unit" and "amu" deprecated.[29] In 2019, the BIPM retained the dalton in its 9th edition of theSI brochure, while dropping the unified atomic mass unit from its table of non-SI units accepted for use with the SI, but secondarily notes that the dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit.[1]
The definition of the dalton was not affected by the2019 revision of the SI,[30][31][1] that is, 1 Da in the SI is still1/12 of the mass of acarbon-12 atom, a quantity that must be determined experimentally in terms of SI units. However, the definition of amole was changed to be the amount of substance consisting of exactly6.02214076×1023 entities, and the definition of thekilogram was changed as well. As a consequence, themolar mass constant (Mu) remains close to but no longer exactly 1 g/mol, meaning that the mass ingrams of one mole of any substance remains nearly but no longer exactly numerically equal to the average mass of an entity in daltons,[32] although the relative standard uncertainty of4.5×10−10 at the time of the redefinition is insignificant for all practical purposes.[1] Lettingent denote oneentity, the smallest amount of any substance (retaining its chemical properties), one mole is an aggregate of anAvogadro number of entities, i.e.1 mol = N0 ent ≈ (g/Da) ent. This means that the appropriate atomic-scale unit for molar mass is dalton per entity (Da/ent), equal to the constantMu, very nearly equal to 1 g/mol. For Da/ent to be exactly equal to g/mol, the dalton would need to be redefined exactly in terms of the (fixed-h) kilogram and the Avogadro number so that 1 Da = (1/N0) g, satisfying the relationshipsN0 = g/Da and1 mol = N0 ent = (g/Da) ent, thus conforming to the original mole concept—that the Avogadro number is the gram-to-dalton mass unit ratio.
Though relative atomic masses are defined for neutral atoms, they are measured (bymass spectrometry) for ions: hence, the measured values must be corrected for the mass of the electrons that were removed to form the ions, and also for the mass equivalent of theelectron binding energy,Eb/muc2. The total binding energy of the six electrons in a carbon-12 atom is1030.1089 eV =1.6504163×10−16 J:Eb/muc2 = 1.1058674×10−6, or about one part in 10 million of the mass of the atom.[33]
Before the 2019 revision of the SI, experiments were aimed to determine the value of theAvogadro constant for finding the value of the unified atomic mass unit.
A reasonably accurate value of the atomic mass unit was first obtained indirectly byJosef Loschmidt in 1865, by estimating the number of particles in a given volume of gas.[34]
Perrin estimated the Avogadro number by a variety of methods, at the turn of the 20th century. He was awarded the 1926Nobel Prize in Physics, largely for this work.[35]
The classic experiment is that of Bower and Davis atNIST,[37] and relies on dissolvingsilver metal away from theanode of anelectrolysis cell, while passing a constantelectric currentI for a known timet. Ifm is the mass of silver lost from the anode andAr the atomic weight of silver, then the Faraday constant is given by:
The NIST scientists devised a method to compensate for silver lost from the anode by mechanical causes, and conducted anisotope analysis of the silver used to determine its atomic weight. Their value for the conventional Faraday constant wasF90 = 96485.39(13) C/mol, which corresponds to a value for the Avogadro constant of6.0221449(78)×1023 mol−1: both values have a relative standard uncertainty of1.3×10−6.
In practice, the atomic mass constant is determined from theelectron rest massme and theelectron relative atomic massAr(e) (that is, the mass of electron divided by the atomic mass constant).[38] The relative atomic mass of the electron can be measured incyclotron experiments, while the rest mass of the electron can be derived from other physical constants.
As may be observed from the old values (2014 CODATA) in the table below, the main limiting factor in the precision of the Avogadro constant was the uncertainty in the value of thePlanck constant, as all the other constants that contribute to the calculation were known more precisely.
Ball-and-stick model of theunit cell ofsilicon. X-ray diffraction measures the cell parameter,a, which is used to calculate a value for the Avogadro constant.
Silicon single crystals may be produced today in commercial facilities with extremely high purity and with few lattice defects. This method defined the Avogadro constant as the ratio of themolar volume,Vm, to the atomic volumeVatom:whereVatom =Vcell/n andn is the number of atoms per unit cell of volumeVcell.
The unit cell of silicon has a cubic packing arrangement of 8 atoms, and the unit cell volume may be measured by determining a single unit cell parameter, the lengtha of one of the sides of the cube.[40] The CODATA value ofa for silicon is5.431020511(89)×10−10 m.[41]
In practice,X-ray crystallography measurements are carried out on a distance known asd220(Si), which is the distance between the planes denoted by theMiller indices {220}, and is equal toa/√8.
Theisotope proportional composition of the sample used must be measured and taken into account. Silicon occurs in three stable isotopes (28Si,29Si,30Si), and the natural variation in their proportions is greater than other uncertainties in the measurements. Theatomic weightAr for the sample crystal can be calculated, as thestandard atomic weights of the threenuclides are known with great accuracy. This, together with the measureddensityρ of the sample, allows the molar volumeVm to be determined:whereMu is the molar mass constant. The CODATA value for the molar volume of silicon is1.205883199(60)×10−5 m3⋅mol−1, with a relative standard uncertainty of4.9×10−8.[42]
^abInternational Standard ISO 80000-10:2019 – Quantities and units – Part 10: Atomic and nuclear physics, International Organization for Standardization, 2019
^Loschmidt, J. (1865). "Zur Grösse der Luftmoleküle".Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien.52 (2):395–413.English translation.
