atomic mass unit
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The dalton or unified atomic mass unit (symbols: Da or u) is a
unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * Unit (album), ' ...
of
mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change of velocity) when a net force is applied. An object's mass ...
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 more abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of the element carbon; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 is of ...
in its nuclear and electronic
ground state The ground state of a quantum mechanics, quantum-mechanical system is its lowest-energy stationary state, state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than ...
and at rest. The atomic mass constant, denoted ''m''u is defined identically, giving . A unit dalton is also approximately numerically equal to the molar mass of the same expressed in grams per mole (). Prior to the
2019 redefinition of the SI base units upright=1.35, The International System of Units, SI system after 1983, but before the 2019 redefinition: Dependence of SI base unit, base unit definitions on other base units (for example, the metre is defined as the distance travelled by light ...
these were numerically identical by definition () and are still treated as such for most purposes. This unit is commonly used in
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...

physics
and
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms, molecules and i ...
to express the mass of atomic-scale objects, such as
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

atom
s,
molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral group of two or more atoms held together by chemical bo ...

molecule
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 the fundamental fermions (quarks, leptons, antiquarks, and an ...
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 consists ...

helium-4
has a mass of . This is an intrinsic property of the isotope and all helium-4 atoms have the same mass. , , 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 dalton (unit), daltons (Da or u). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The r ...
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 metabol ...

protein
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. T ...

nucleic acid
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, or macromolecules, composed of many Repeat unit, repeating subunits. Due to their ...

polymer
s are often expressed with the units
kilo KILO (94.3 FM, 94.3 KILO) is a radio station broadcasting in Colorado Springs The City of Colorado Springs is the List of cities and towns in Colorado#Home rule municipality, Home Rule Municipality that is the county seat and the List of ci ...
daltons (kDa),
mega Mega or MEGA may refer to: Science * mega-, the SI prefix for one million (106, symbol M) * Mega (number), a certain very large integer in Steinhaus–Moser notation * "mega-" a prefix meaning "large" that is List of commonly used taxonomic affi ...
daltons (MDa), etc.
Titin Titin , also known as connectin, is a protein Proteins are large biomolecules or macromolecules that are comprised of one or more long chains of amino acid residue (biochemistry), residues. Proteins perform a vast array of functions within ...
, 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 metabol ...

protein
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 pairs, which are ...

chromosome 1
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 se ...

human genome
has about 249 million
base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids Nucleic acids are biopolymer Biopolymers are natural polymers produced by the cells of Organism, living organisms. Biopolymers consist of monomeric units that are Covalent_b ...
s, each with an average mass of about , or total. The
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
is a unit of
amount of substance In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms, mo ...
, 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 in that sample, measured in mole (unit), moles. The molar mass is a bulk, not molecular, property of a subst ...
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 H2O) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts ...

water
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 ''A'' 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 more abundant of the two stable isotopes of carbon (carbon-13 being the other), amounting to 98.93% of the element carbon; its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 is of ...
is 12 daltons, which corresponds with the number of nucleons that it has (6
proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

proton
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 nuclei of atoms. Since protons and neutrons behav ...

neutron
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 is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has ma ...
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 Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

hydrogen
isotope Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom. The term ...
(
hydrogen-1 Hydrogen (1H) has three naturally occurring isotopes, sometimes denoted 1H, 2H, and 3H. The first two of these are stable, while 3H has a half-life of 12.32 years. There are also heavier isotopes, which are all synthetic and have a half-life l ...

hydrogen-1
, protium) is , the mass of one free neutron is and the mass of one
hydrogen-2 Deuterium (or hydrogen-2, symbol or , also known as heavy hydrogen) is one of two stable isotopes of hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. With a standard atomic weight o ...

hydrogen-2
(deuterium) atom is . In general, the difference (
mass defect Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said thing. In the context of this article, it is one or mo ...
) 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#Hydroge ...

helium-3
(0.5%),
lithium Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the Symbol (chemistry), symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard temperature and pressure, standard conditions, it ...

lithium
(0.25%) and
beryllium Beryllium is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

beryllium
(0.15%). The unified atomic mass unit and the dalton should not be confused with the unit of mass in the atomic units systems, which is instead the
electron rest mass The electron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has ma ...
(''m''e).


Energy equivalents

The atomic mass constant can also be expressed as its energy equivalent, that is ''m''u''c''2. The 2018 CODATA recommended values are: The
megaelectronvolt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the amount of kinetic energy gained by a single electron accelerating from rest through an Voltage, electric potential difference of one volt in vacuum. When ...
(MeV) is commonly used as a unit of mass in
particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that ...
, 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 Atomic theory is the scientific theory that matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed o ...
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 (; 6 September 1766 – 27 July 1844) was an English chemist, physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...

John Dalton
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, ...

Wilhelm Ostwald
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 Jean Baptiste Perrin (30 September 1870 – 17 April 1942) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids, verified Albert Einstein’s explanation of this phenomenon and thereby confirme ...
had adopted the same definition in 1909 during his experiments to determine the atomic masses and Avogadro's 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 (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
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 scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branche ...

Amedeo Avogadro
.


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 that represents chemists in individual countries. It is a member of the International Science Council (ISC). IUPAC i ...
(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 The standard atomic weight (''A''r, standard(E)) of a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting ...
of
carbon Carbon (from la, carbo "coal") is a chemical element with the Symbol (chemistry), symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—making four electrons available to form covalent bond, covalent chemical bonds. ...

carbon
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 350px, Plates in the crust of Earth Earth's crust is a thin shell on the outside of Earth, accounting for less than 1% of Earth's volume. It is the top component of the lithosphere, a division of Earth's layers that includes the Crust (geology), ...
, its
atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' or 'sphere') is a layer or a set of layers of gases surrounding a planet or other material body, that is held in ...

atmosphere
, and .


Adoption by the BIPM

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.


The dalton

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 The International Union of Pure and Applied Physics (IUPAP ) is an international non-governmental organization whose mission is to assist in the worldwide development of physics, to foster international cooperation in physics, and to help in the a ...
(IUPAP) in 2005. In 2003 the name was recommended to the BIPM by the Consultative Committee for Units, part of the
CIPM The General Conference on Weights and Measures (French language, French: ''Conférence Générale des Poids et Mesures'', abbreviated CGPM and sometimes referred to as the GCWM) is the supreme authority of the International Bureau of Weights and Me ...
, as it "is shorter and works better with
he SI He or HE may refer to: Language * He (pronoun) In Modern English, ''he'' is a Grammatical number, singular, Grammatical gender, masculine, Grammatical person, third-person personal pronoun, pronoun. Morphology In Standard English, Standard ...
prefixes". In 2006, the BIPM included the dalton in its 8th edition of the formal definition of . 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-setting body composed of representatives from various national standards organizations. Founded on 23 February 1947, the organization develops and publishe ...
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 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 upright=1.35, The SI system after 1983, but before the 2019 redefinition: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second The ...
, 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 The molar mass constant, usually denoted by ''M''u, is a physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and hav ...
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 used i ...
) 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 In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior throug ...
, ''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 The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
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 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 "M ...
, largely for this work.


Coulometry

The electric charge per
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpidae ...
of electrons 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 of one mole (unit), mole of electrons. It can be thought of as the conversion factor between the mole (used in chemistry) and ...
, whose value had been essentially known since 1834 when
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest. In clas ...

Michael Faraday
published his works on electrolysis. In 1910,
Robert Millikan Robert Andrews Millikan (March 22, 1868 – December 19, 1953) was an American experimental physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branch ...
obtained the first measurement of the charge on an electron, ''e''. The quotient ''F''/''e'' provided an estimate of Avogadro's number. The classic experiment is that of Bower and Davis at
NIST The National Institute of Standards and Technology (NIST) is a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, ea ...

NIST
, and relies on dissolving
silver Silver is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same n ...

silver
metal away from the
anode An anode is an electrode An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor A semiconductor material has an Electrical resistivity and conductivity, electrical conductivit ...

anode
of an
electrolysis In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms ...

electrolysis
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 part ...
''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, the abundance of certain stable isotopes and chemical elements within organic and inorganic compounds. Isotopic analysis can be used to understand the flow of energy through a food w ...
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 The electron is a subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has ma ...
''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 . The magnet is painted yellow. A cyclotron is a type of particle accelerator , a synchrotron collider type particle accelerator at Fermi National Accelerator Laboratory (Fermilab), Batavia, Illinois, USA. Shut down in 2011, until 2007 it wa ...

cyclotron
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 A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure m ...
, ''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
, ''α'' is the
fine-structure constant In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...
, and ''R'' is the
Rydberg constant In spectroscopy Spectroscopy is the study of the interaction between matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched ar ...
. 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 A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature an ...
, 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

200px, Ball-and-stick_model_of_the_unit_cell_of_silicon.html" ;"title="unit_cell.html" ;"title="Ball-and-stick model of the unit cell">Ball-and-stick model of the unit cell of silicon">unit_cell.html" ;"title="Ball-and-stick model of the unit cell">Ball-and-stick model of the unit cell of silicon. 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 the molar volume, ''V'', to the atomic volume ''V'': 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 index, Miller indices , and is equal to ''a''/. The
isotope Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom. The term ...
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 ''A'' for the sample crystal can be calculated, as the
standard atomic weight The standard atomic weight (''A''r, standard(E)) of a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting ...
s of the three nuclides are known with great accuracy. This, together with the measured density ''ρ'' of the sample, allows the molar volume ''V'' to be determined: where ''M'' is the molar mass constant. The 2018 CODATA value for the molar volume of silicon is , with a relative standard uncertainty of .


See also

* Mass (mass spectrometry) ** Kendrick mass ** Monoisotopic mass * Mass-to-charge ratio


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 Confernce Générale des Poids et Mesures
''. Available at th
BIPM website
Carl Wilhelm Oseen, 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 a physical sciences Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, ea ...

NIST
. Accessed on 2019-07-03.
Bureau International des Poids et Mesures (1971):
14th Conference Générale des Poids et Mesures
'' Available at th
BIPM website


External links


Atomic weights and isotopic compositions


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