unified atomic mass unit

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The dalton or unified atomic mass unit (symbols: Da or u) is a non-SI unit of
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
widely used in physics and chemistry. It is defined as of the mass of an unbound neutral atom of
carbon-12 Carbon-12 (12C) is the most abundant of the two Stable isotope, stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of Periodic table, element carbon on Earth; its abundance is due to the triple-alpha process by which it is ...
in its nuclear and electronic
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical qu ...
and at rest. The atomic mass constant, denoted ''m''u, is defined identically, giving . This unit is commonly used in
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
and
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...
to express the mass of atomic-scale objects, such as
atom Every atom is composed of a atomic nucleus, nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, l ...
s,
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
s, and
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiqu ...
s, both for discrete instances and multiple types of ensemble averages. For example, an atom of
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
has a mass of . This is an intrinsic property of the isotope and all helium-4 atoms have the same mass. Acetylsalicylic acid (aspirin), , has an average mass of approximately . However, there are no acetylsalicylic acid molecules with this mass. The two most common masses of individual acetylsalicylic acid molecules are , having the most common isotopes, and , in which one carbon is carbon-13. The
molecular mass The molecular mass (''m'') is the mass of a given molecule: it is measured in daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotope Isotopes are two or more ty ...
es of
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metabo ...
s,
nucleic acid Nucleic acids are biopolymers, macromolecules, essential to all Organism, known forms of life. They are composed of nucleotides, which are the monomers made of three components: a pentose, 5-carbon sugar, a phosphate group and a nitrogenous base. ...
s, and other large
polymer A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules called macromolecules, composed of many Repeat unit, repeating subunits. Due to t ...
s are often expressed with the units kilodaltons (kDa), megadaltons (MDa), etc. Titin, one of the largest known
protein Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within organisms, including Enzyme catalysis, catalysing metabo ...
s, has a molecular mass of between 3 and 3.7 megadaltons. The DNA of
chromosome 1 Chromosome 1 is the designation for the largest human chromosome. Humans have two copies of chromosome 1, as they do with all of the autosomes, which are the non- sex chromosomes. Chromosome 1 spans about 249 million nucleotide base pair A ba ...
in the
human genome The human genome is a complete set of nucleic acid sequences for humans, encoded as DNA within the 23 chromosome pairs in cell nuclei and in a small DNA molecule found within individual Mitochondrial DNA, mitochondria. These are usually treated s ...
base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both ...
s, each with an average mass of about , or total. The mole is a unit of
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the countable quantity, quantity or particle number, number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or ent ...
, widely used in chemistry and physics, which was originally defined so that the mass of one mole of a substance, measured in grams, would be numerically equal to the average mass of one of its constituent particles, measured in daltons. That is, the
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in mole (unit), moles. The molar mass is a bulk, not ...
of a chemical compound was meant to be numerically equal to its average molecular mass. For example, the average mass of one molecule of
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
is about 18.0153 daltons, and one mole of water is about 18.0153 grams. A protein whose molecule has an average mass of would have a molar mass of . However, while this equality can be assumed for almost all practical purposes, it is now only approximate, because of the way mole was redefined on 20 May 2019. In general, the mass in daltons of an atom is numerically close but not exactly equal to the number of nucleons contained in its
nucleus Nucleus (plural, : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA ...
. It follows that the molar mass of a compound (grams per mole) is numerically close to the average number of nucleons contained in each molecule. By definition, the mass of an atom of
carbon-12 Carbon-12 (12C) is the most abundant of the two Stable isotope, stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of Periodic table, element carbon on Earth; its abundance is due to the triple-alpha process by which it is ...
is 12 daltons, which corresponds with the number of nucleons that it has (6
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s and 6
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
s). However, the mass of an atomic-scale object is affected by the
binding energy In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly use ...
of the nucleons in its atomic nuclei, as well as the mass and binding energy of its
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
s. 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 one unbound atom of the common
hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the chemical ...
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbe ...
(
hydrogen-1 Hydrogen (1H) has three naturally occurring Isotope, isotopes, sometimes denoted , , and . and are stable, while has a half-life of years. Heavier isotopes also exist, all of which are synthetic and have a half-life of less than one Orders o ...
, protium) is , the mass of the proton is , the mass of one free neutron is and the mass of one hydrogen-2 (deuterium) atom is . In general, the difference (absolute mass excess) is less than 0.1%; exceptions include hydrogen-1 (about 0.8%),
helium-3 Helium-3 (3He see also helion (chemistry), helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than Isotopes of hydrogen#Hydrog ...
(0.5%), lithium-6 (0.25%) and
beryllium Beryllium is a chemical element with the Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other ...
(0.14%). The dalton differs from the unit of mass in the atomic units systems, which is the electron rest mass (''m''e).

# Energy equivalents

The atomic mass constant can also be expressed as its energy-equivalent, ''m''u''c''2. The 2018 CODATA recommended values are: The megaelectronvolt mass-equivalent (MeV/''c''2) is commonly used as a unit of mass in
particle physics Particle physics or high energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standa ...
, and these values are also important for the practical determination of relative atomic masses.

# History

## Origin of the concept

The interpretation of the law of definite proportions in terms of the atomic 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 1803
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...
proposed to use the (still unknown) atomic mass of the lightest atom, that of hydrogen, as the natural unit of atomic mass. This was the basis of the atomic weight scale. For technical reasons, in 1898, chemist
Wilhelm Ostwald Friedrich Wilhelm Ostwald (; 4 April 1932) was a Baltic German chemist and German philosophy, philosopher. Ostwald is credited with being one of the founders of the field of physical chemistry, with Jacobus Henricus van 't Hoff, Walther Nernst, ...
and others proposed to redefine the unit of atomic mass as of the mass of an oxygen atom. That proposal was formally adopted by the International 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 the existence of elemental isotopes, which occurred in 1912. The physicist Jean Perrin had adopted the same definition in 1909 during his experiments to determine the atomic masses and the Avogadro constant. This definition remained unchanged until 1961. Perrin also defined the "mole" as an amount of a compound that contained as many molecules as 32 grams of oxygen (). He called that number the
Avogadro number The Avogadro constant, commonly denoted or , is the proportionality factor that relates the particle number, number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an I ...
in honor of physicist
Amedeo Avogadro Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (, also , ; 9 August 17769 July 1856) was an Italian people, Italian scientist, most noted for his contribution to molecular theory now known as Avogadro's law, which states th ...
.

## Isotopic variation

The discovery of isotopes of oxygen in 1929 required a more precise definition of the unit. Unfortunately, two distinct definitions came into use. Chemists choose to define the AMU as 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 as of the mass of an atom of the isotope oxygen-16 (16O).

## Definition by the IUPAC

The existence of two distinct units with the same name was confusing, and the difference (about 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. For these and other reasons, in 1961 the
International Union of Pure and Applied Chemistry The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
(IUPAC), which had absorbed the ICAW, adopted a new definition of the atomic mass unit for use in both physics and chemistry; namely, of the mass of a carbon-12 atom. This new value was intermediate between the two earlier definitions, but closer to the one used by chemists (who would be affected the most by the change). 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 units. However, the old symbol "amu" has sometimes been used, after 1961, to refer to the new unit, particularly in lay and preparatory contexts. With this new definition, the standard atomic weight of
carbon Carbon () is a chemical element with the chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—its atom making four electrons available to form covalent bond, covalent chemical bonds. It belongs to gro ...
is approximately , and that of oxygen is approximately . These values, generally used in chemistry, are based on averages of many samples from
Earth's crust Earth's crust is Earth's thin outer shell of Rock (geology), rock, referring to less than 1% of Earth's radius and volume. It is the top component of the lithosphere, a division of Earth's layers that includes the Crust (geology), crust and the ...
, its
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
, and organic materials.

The IUPAC 1961 definition of the unified atomic mass unit, with that name and symbol "u", was adopted by the International Bureau for Weights and Measures (BIPM) in 1971 as a non-SI unit accepted for use with the SI.

## Unit name

In 1993, the IUPAC proposed the shorter name "dalton" (with symbol "Da") for the unified atomic mass unit. 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 the International Union of Pure and Applied Physics (IUPAP) in 2005. In 2003 the name was recommended to the BIPM by the Consultative Committee for Units, part of the CIPM, as it "is shorter and works better with he SIprefixes". In 2006, the BIPM included the dalton in its 8th edition of the formal definition of SI. The name was also listed as an alternative to "unified atomic mass unit" by the
International Organization for Standardization The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Art ...
in 2009. It is now recommended by several scientific publishers, and some of them consider "atomic mass unit" and "amu" deprecated. In 2019, the BIPM retained the dalton in its 9th edition of the formal definition of SI 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.

## 2019 redefinition of the SI base units

The definition of the dalton was not affected by the 2019 redefinition of SI base units, that is, 1 Da in the SI is still of the mass of a carbon-12 atom, a quantity that must be determined experimentally in terms of SI units. However, the definition of a mole was changed to be the amount of substance consisting of exactly entities and the definition of the kilogram was changed as well. As a consequence, the molar mass constant is no longer exactly 1 g/mol, meaning that the number of grams in the mass of one mole of any substance is no longer exactly equal to the number of daltons in its average molecular mass.

# Measurement

Although relative atomic masses are defined for neutral atoms, they are measured (by
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is us ...
) 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 the
electron binding energy The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
, ''E''b/''m''u''c''2. The total binding energy of the six electrons in a carbon-12 atom is  = : ''E''b/''m''u''c''2 = , or about one part in 10 million of the mass of the atom. Before the 2019 redefinition of SI units, experiments were aimed to determine the value of the Avogadro constant for finding the value of the unified atomic mass unit.

## Josef Loschmidt

A reasonably accurate value of the atomic mass unit was first obtained indirectly by Josef Loschmidt in 1865, by estimating the number of particles in a given volume of gas.

## Jean Perrin

Perrin estimated the Avogadro number by a variety of methods, at the turn of the 20th century. He was awarded the 1926
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
, largely for this work.

## Coulometry

The electric charge per mole of
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
s is a constant called the
Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole (unit), mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefi ...
, ''F'', whose value had been essentially known since 1834 when
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, ...
published his works on electrolysis. In 1910, Robert Millikan obtained the first measurement of the charge on an electron, −''e''. The quotient ''F''/''e'' provided an estimate of the Avogadro constant. The classic experiment is that of Bower and Davis at
NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
, and relies on dissolving
silver Silver is a chemical element with the Symbol (chemistry), symbol Ag (from the Latin ', derived from the Proto-Indo-European wikt:Reconstruction:Proto-Indo-European/h₂erǵ-, ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, whi ...
metal away from the
anode An anode is an electrode of a polarized electrical device through which conventional current enters the device. This contrasts with a cathode, an electrode of the device through which conventional current leaves the device. A common mnemonic is ...
of an
electrolysis In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, str ...
cell, while passing a constant
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
''I'' for a known time ''t''. If ''m'' is the mass of silver lost from the anode and ''A'' 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 an
isotope analysis Isotope analysis is the identification of isotopic signature, abundance of certain stable isotopes of chemical Chemical element, elements within Organic compound, organic and Inorganic compound, inorganic compounds. Isotopic analysis can be used ...
of the silver used to determine its atomic weight. Their value for the conventional Faraday constant was ''F'' = , which corresponds to a value for the Avogadro constant of : both values have a relative standard uncertainty of .

## Electron mass measurement

In practice, the atomic mass constant is determined from the electron rest mass ''m''e and the electron relative atomic mass ''A''r(e) (that is, the mass of electron divided by the atomic mass constant). The relative atomic mass of the electron can be measured in
cyclotron A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Janu ...
experiments, while the rest mass of the electron can be derived from other physical constants. where ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
, ''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
, ''α'' is the fine-structure constant, and ''R'' is the Rydberg constant. 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 the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
, as all the other constants that contribute to the calculation were known more precisely. The power of the presently defined values of universal constants can be understood from the table below (2018 CODATA).

## X-ray crystal density methods

Silicon Silicon is a chemical element with the Symbol (chemistry), symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a Tetravalence, tetravalent metalloid and semiconductor. It is a member ...
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 the
molar volume In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...
, ''V'', to the atomic volume ''V'': $N_ = \frac,$ where $V_ = \frac$ and ''n'' is the number of atoms per unit cell of volume ''V''cell. 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 length ''a'' of one of the sides of the cube. The 2018 CODATA value of ''a'' for silicon is . In practice, measurements are carried out on a distance known as ''d''(Si), which is the distance between the planes denoted by the Miller indices , and is equal to . The
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbe ...
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. The
atomic weight Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecation, deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical elem ...
''A'' for the sample crystal can be calculated, as the standard atomic weights of the three
nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...
s are known with great accuracy. This, together with the measured
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...
''ρ'' of the sample, allows the molar volume ''V'' to be determined: $V_ = \frac,$ where ''M'' is the molar mass constant. The 2018 CODATA value for the molar volume of silicon is , with a relative standard uncertainty of .

* Mass (mass spectrometry) ** Kendrick mass ** Monoisotopic mass *
Mass-to-charge ratio The mass-to-charge ratio (''m''/''Q'') is a physical quantity Ratio, relating the ''mass'' (quantity of matter) and the ''electric charge'' of a given particle, expressed in Physical unit, units of kilograms per coulomb (kg/C). It is most widely ...

# References

Meng Wang, G. Audi, F.G. Kondev, W.J. Huang, S. Naimi, and Xing Xu (2017): "The Ame2016 atomic mass evaluation (II). Tables, graphs and references". ''Chinese Physics C'', volume 41, issue 3, article 030003, pages 1-441. Integrated DNA Technologies (2011):
Molecular Facts and Figures
". Article on th
IDT website, Support & Education section
, accessed on 2019-07-08.

Bureau International des Poids et Mesures (2019):
The International System of Units (SI)
', 9th edition, English version, page 146. Available at th
BIPM website
International Bureau for Weights and Measures (2017):
Proceedings of the 106th meeting of the International Committee for Weights and Measures (CIPM), 16-17 and 20 October 2017
', page 23. Available at th

.
International Bureau for Weights and Measures (2018):
Resolutions Adopted - 26th Conference Générale des Poids et Mesures
''. Available at th
BIPM website
Oseen, C.W. (December 10, 1926).
Presentation Speech for the 1926 Nobel Prize in Physics
'.

(1974):

' From the ''Encyclopaedia Britannica'', 15th edition; reproduced by
NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
. Accessed on 2019-07-03.
Bureau International des Poids et Mesures (1971):
14th Conference Générale des Poids et Mesures
'' Available at th
BIPM website