Atomic mass unit

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The unified atomic mass unit (symbol “u”) or dalton (symbol “Da”) is a standard unit of mass defined as one twelfth (1/12) the mass of an unbonded, neutral carbon-12 atom in its electrical and nuclear ground state, and is equal to 1.660 5402(10)×10⁻²⁷ kg (value recommended by CODATA). The mass of one mole of atomic mass units (NA) is equal to one g.

Used to express the mass of atoms and molecules (atomic mass and molecular mass).

The International Committee of Weights and Measures has categorized it as a unit not compatible with the use of the International System of Units, and whose value in SI units must be obtained experimentally.

In the International System of Magnitudes (ISO 80000-1), the "dalton" is given as the only name and the "unified atomic mass unit" is discouraged, since this can take two different values and, also, it does not support multiplicative prefixes (it is not possible to use "ku" but "kDa" can).

Not to be confused with atomic units.

Equivalent energy

The atomic mass constant can also be expressed as its equivalence between mass and energy, which is m_uc². The values recommended by CODATA in 2018 are:

1 uma = 1,66053886 x 10^-27 kg

1 g = 6,0221415 x 10²³ Uma

History

Origin of the concept

Jean Perrin in 1926

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 proportions that depended on the elements. Although the actual masses were unknown, the relative masses could be deduced from that law. In 1803 John Dalton proposed using the atomic mass (still unknown) of the lightest atom, 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 and others proposed redefining the atomic mass unit as ¹⁄₁₆ of the mass of an oxygen atom. This proposal was formally adopted by the International Committee on Atomic Weights (ICAW) in 1903. That was approximately the mass of a hydrogen atom, but oxygen was more susceptible to experimental determination. This suggestion was made before the discovery of the existence of elementary isotopes, which occurred in 1912. The physicist Jean Perrin had adopted the same definition in 1909 during his experiments to determine atomic masses and Avogadro's constant. This definition remained unchanged until 1961. Perrin also defined the "mol" as an amount of a compound containing as many molecules as 32 grams of oxygen (O
2). He named that number Avogadro's number after the physicist Amedeo Avogadro.

Isotopic variation

The discovery of oxygen isotopes in 1929 required a more precise definition of the unit. Unfortunately, two different definitions were used. Chemists choose to define the AMU as 1 ⁄ 16 of the average mass of an oxygen atom 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 1 ⁄ 16 the mass of an atom of the isotope oxygen-16 (¹⁶O).

IUPAC definition

The existence of two distinct units with the same name was confusing, and the difference (about 1.000282 in relative terms) was large enough to affect high-precision measurements. In addition, oxygen isotopes were found to have different natural abundances in water and in air. For these and other reasons, in 1961 the International Union of Pure and Applied Chemistry (IUPAC), which had absorbed the ICAW, adopted a new definition of the atomic mass unit for use in both physics and chemistry; namely, ¹⁄₁₂ of the mass of a carbon-12 atom. This new value was intermediate between the two previous definitions, but closer to that used by chemists (who would be most affected by the change).

The new unit was called the "unified atomic mass unit" and was given a new symbol "u", to replace the old "amu" which had been used for units based on oxygen. However, the old symbol "amu" it has been used sometimes, after 1961, to refer to the new unit, especially in profane and preparatory contexts.

With this new definition, the standard atomic weight of carbon is approximately 12,011 Da, and that of oxygen is approximately 15,999 Da. These values, generally used in chemistry, are based on averages of many samples of the Earth's crust, its atmosphere, and organic materials.

Adoption by the BIPM

The 1961 IUPAC definition of the unified atomic mass unit, by that name and symbol "u", was adopted by the International Bureau of Weights and Measures (BIPM) in 1971 as a Unit not SI accepted for use with the SI.

The Dalton

In 1993, IUPAC proposed the shorter name of "dalton" (with the symbol "Da") for the unified atomic mass unit. Like other unit names such as watt and newton, "dalton" It is not capitalized in English, but its symbol, "Da", is. The name was approved 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 of Units, part of the CIPM, since "it is shorter and works better with the prefixes of the [[International System of Units| YES]".

In 2006, BIPM included the dalton in its 8th edition of the formal definition of SI.

The name was also included as an alternative to the "unified atomic mass unit" by the International Organization for Standardization in 2009. It is currently recommended by several scientific publishers, some of which consider "atomic mass unit" and "amu" obsolete. In 2019, the BIPM retained the color blind in its 9th edition formal definition of the SI, while removing the unified atomic mass unit from its table of non-SI units accepted for use with the SI, but secondarily noting that the color-ton (Da) and the unified atomic mass unit (u) are alternate names (and symbols) for the same unit.

A proposal

In 2012, Australian aerospace engineer B P Leonard proposed redefining the dalton exactly in terms of the kilogram, thus breaking the link with ¹²C. This would cause very slight changes in the atomic masses of all elements when expressed in daltons, but the changes would be too small to have any practical effect in stoichiometric calculations. However, this ensures that the 2019 redefinition of Avogadro's number as an exact integer is equivalent to its traditional definition as g/Da, without the need for a correction factor. The mole, traditionally defined as Avogadro's number of entities, can then be written as mol = g/Da ent, where an entity, ent, is proposed by Leonard as the unit of quantity of substance on an atomic scale. The atomic and macroscopic scale units for molar mass are then related by dimensionally consistent formulas: Da/ent = g/mol = kg/kmol, exactly.

Redefinition of the SI base units in 2019

The definition of the dalton was not affected by the redefinition of SI units, that is, 1 Da in the SI is still ¹⁄₁₂ of the mass of a carbon atom- 12, 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, which means 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) for ions: therefore, 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 binding energy of the electron, E_b/m_uc². The total binding energy of the six electrons in a carbon-12 atom is 1030.1089 eV = 1.6504163 e=−16 J: E_b/m_uc² = 1.1058674 e⁻⁶, or about one part in 10 million of the mass of the atom.

Prior to the redefinition of SI units in 2019, experiments aimed to determine the value of Avogadro's constant to find 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 Avogadro's number using various methods, in the early 20th century. He was awarded the 1926 Nobel Prize in Physics, largely for this work.

Coulometry

Main article: Culombime

The electric charge per mole of electrons is a constant called Faraday's constant, whose value has been known essentially since 1834 when Michael Faraday published his papers on electrolysis. In 1910, Robert Millikan obtained the first measurement of the charge on an electron, e. The ratio F/e provided an estimate of Avogadro's number.

The classic experiment is that of Bower and Davis on the NIST, and is based on the dissolution of silver metal away from the anode of an electrolysis cell, while a constant electric current is passed I for a known time t. Yeah. m is the silver dough lost by the anode and A _r the atomic weight of silver, then the constant of Faraday is given by: ${displaystyle F={frac {A_{rm {r}}M_{rm {u}}It}{m}}.}$ NIST scientists devised a method to compensate for the lost silver of the anode for mechanical causes, and performed an isotopic analysis of the silver used to determine its atomic weight. Its value for Faraday's conventional constant was F ₉₀= 96485,39(13) Cmol, which corresponds to a value for the Avogadro constant of 6,0221449(78)x10²³mol^-1: both values have a relative standard uncertainty of 1.3x10^-6.

Measurement of Electron Mass

In practice, the atomic mass constant is determined from the rest mass of the electron m_e and the relative atomic mass of the electron A _r(e) (ie, the mass of the electron divided by the atomic mass constant). [36] The relative atomic mass of the electron can be measured in cyclotron experiments, while the rest mass of the electron can be derived from other physical constants.

${displaystyle m_{rm {u}}={frac {m_{rm {e}}}{A_{rm {r}}({rm {e}})}}={frac {2R_{infty }h}{A_{rm {r}}({rm {e}})calpha ^{2}}},}$
${displaystyle m_{rm {u}}={frac {M_{rm {u}}}{N_{rm {A}}}},}$
${displaystyle N_{rm {A}}={frac {M_{rm {u}}A_{rm {r}}({rm {e}})}{m_{rm {e}}}}={frac {M_{rm {u}}A_{rm {r}}({rm {e}})calpha ^{2}}{2R_{infty }h}}}$

where c is the speed of light, h is Planck's constant, α is the fine structure constant, and R _∞ is the Rydberg constant.

As can be seen from the old values (2014 CODATA) in the table below, the main limiting factor for the precision of Avogadro's constant was the uncertainty in the value of Planck's constant, since all other constants that contribute to the calculation were known with greater precision.

Examples

A hydrogen-1 atom (nucleus formed by a single proton) has a mass of 1,007 825 0 u (1,007 825 0 Da), while deuterium (hydrogen-2, also has a neutron) one of 2,014 101 78 u.
By definition, a carbon-12 atom has a mass of 12 or (12 Da).
An acetylsalicylic acid molecule (aspirin) has a mass of 180.16 u (.

The values recommended by CODATA in 2018 are: 180.16 Da).

Beta-actine, one of the most common proteins in eukaryotic organisms, has a mass of 42 kDa (41737 Da).
Titin, the largest known protein, has a molecular mass of 3-3.7 megadaltons (3 000 000 Da).

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