Dalton Unit

Let us know about Dalton Unit. The Dalton or unified atomic mass unit (symbol: Da or U ) is a unit of mass widely used in physics and chemistry. It is defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its atomic and electronic ground state and at rest . [1] [2] The atomic mass constant , denoted m u is defined exactly, giving m u = m ( 12C) / 12 = 1 . [3]A unit dalton is also roughly numerically equal to its molar mass, expressed in g/mol (1 Da 1 g/mol). Before the 2019 redefinition of SI base units these were numerically identical by definition (1 Da = 1 g/mol) and are still considered as such for most purposes.

(Unified Atomic Mass Unit)
unit systemphysical constant
( accepted for use with SI )
unit ofMass
Signda or u
After namesJohn Dalton
1 da or in you…… Is equal to …
   Kilogram   1.660 539 066 60 (50) × 10 −27
   meter u   1
   M.E _1822 .888 486 209 (53)
   MEV C2   931.494 102 42 (28)
Dalton Unit

This unit is commonly used in physics and chemistry to express the mass of atomic-scale objects, such as atoms , molecules , and elementary particles , for both discrete instances and for many types of ensemble averages. For example, the mass of an atom of helium-4 is4.0026 d . This is an intrinsic property of the isotope and all helium-4 atoms have the same mass. acetylsalicylic acid (aspirin) , C9H8O4, the average mass of approx. Is180.157 d . However, there are no acetylsalicylic acid molecules with this mass. The two most common masses of individual acetylsalicylic acid molecules are:180.0423 Da , which has the most common isotopes, and181.0456 Da , in which one carbon is carbon-13.The molecular masses of proteins , nucleic acids , and other large polymers are often expressed with units kilo – dalton (kDa), mega – dalton (Mda), etc. [4] Titin is a molecular mass of one of the largest known proteins . Between 3 and 3.7 megadaltons. [5] The DNA of chromosome 1 in the human genome contains approximately 249 million base pairs , each with an average mass of approximately 249 million.650 of , or156 GDA Total.

The mole is a unit of quantity of matter , widely used in chemistry and physics, which originally defined that the mass of a mole of a substance, measured in grams, is numerically its constituent particles. will be equal to the average mass of one of , measured in daltons. That is, the molar mass of a chemical compound must be numerically equal to its average molecular mass. For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water is about 18.0153 grams. a protein whose molecule has an average mass ofThe molar mass of 64 kDa will be64 kg/mol . However, while this analogy can be assumed for almost all practical purposes, it is now only approximate, because of the way the mole was redefined on 20 May 2019 .

In general, the atom’s dalton has a mass numerically close, but the nucleon a in its nucleus isis not equal to the number of It follows that the molar mass (gram per mole) of a compound is numerically close to the average number of nucleons contained in each molecule. By definition, an atom of carbon-12 has a mass of 12 daltons, which corresponds to the number of nucleons it has (6 protons and 6 neutrons). However, the mass of an atomic-scale object is affected by the binding energy of the nucleons in its atomic nucleus, as well as the mass and binding energy of its electrons. Therefore, this similarity is only for the carbon-12 atom in the stated positions, and will be different for other substances. For example, the mass of an unbound atom of a common hydrogen isotope (hydrogen-1, protium) is1.007 825 032 241 (94) Da , the mass of a free neutron is1.008 664 915 95 (49) Da , [7] and the mass of a hydrogen-2 (deuterium) atom is2.014 101 778 114 (122) da . [8] In general, the difference (mass defect) is less than 0.1%; Exceptions include hydrogen-1 (about 0.8%), helium-3 (0.5%), lithium (0.25%) and beryllium (0.15%).

The unified atomic mass unit and dalton should not be confused with the unit of mass in atomic unit systems, which is instead the electron resting mass ( e ).

energy equivalent

The atomic mass constant can also be expressed as its energy equivalent, which is 2 . The 2018 CODATA recommended values ​​are:

muc2 = 1.49241808560(45)×10−10 J = 931.49410242(28) MeV

Megaelectronvolt (MeV) is commonly used as a unit of mass in particle physics and these values ​​are also important for practical determination of relative atomic mass.


origin of the concept

An explanation of the law of definite proportions in the context of the atomic theory of matter implied that the atoms of different elements have a definite ratio of mass which depends on the elements. While the actual masses were unknown, the relativistic masses could be deduced from that law. In 1803, John Dalton proposed using the (still unknown) atomic mass of the lightest atom of hydrogen as the natural unit of atomic mass. This was the basis of the atomic mass scale. [11 1]

For technical reasons, in 1898, chemist Wilhelm Ostwald and others proposed redefining the unit of atomic mass as 1/16 of the mass of an oxygen atom. [12] That resolution was formally adopted by the International Committee on Atomic Weights (ICAW) in 1903. It was approximately the mass of a hydrogen atom, but oxygen was more amenable to experimental determination. This suggestion was made prior to the discovery of the existence of elemental isotopes, which occurred in 1912. [11] Physicist Jean Perrin adopted this definition in 1909 during his experiments to determine the atomic mass and Avogadro’s constant. [13] This definition remained unchanged until 1961. [14] [15]Perrin also defined “mole” as the amount of a compound containing 32 grams of oxygen ( O ).2) He called that number the Avogadro number in honor of 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 came into use. 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 known isotopes, weighted by their natural abundance. Physicists, on the other hand, defined it as 1/16 of the mass of an atom of the isotope oxygen-16 ( 16 O). [12]

Definition by IUPAC

The existence of two separate units with the same name was confusing, and the difference (approx.)1.000 in 282 relative terms) was large enough to affect high precision measurements. In addition, it turned out that oxygen isotopes had 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; That is, 1/12 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 most affected by the change). [11] [12]

The new unit was given the name “Unified Atomic Mass Unit” and a new symbol “U” was given to replace the old “Amu” which was used for oxygen-based units. [16] However, after 1961 the old symbol “amu” is sometimes used to refer to the new entity, especially in general and early contexts.

With this new definition, the standard atomic weight of carbon is approximately12.011 Da , and oxygen is approx.15.999 d . These values, commonly used in chemistry, are based on the average of several samples of the Earth’s crust, its atmosphere, and organic matter.

Adoption by BIPM

The IUPAC 1961 definition of a unified atomic mass unit, with that name and symbol “u”, was adopted by the International Bureau of Weights and Measures (BIPM) in 1971 as a non-SI unit accepted for use with the SI. [17]


In 1993, IUPAC proposed the shortened name “Dalton” (with the symbol “Da”) for the unified atomic mass unit. [18] [19] As with other unit names such as the watt and the newton, in English “dalton” is not capitalized, but its symbol “da” is capitalized. The name was endorsed by the International Union of Pure and Applied Physics (IUPAP) in 2005. [20]

The name was recommended to BIPM in 2003 by the Advisory Committee for Units, part of the CIPM, because it “is shorter and works better with [SI] prefixes”. [21] In 2006, the BIPM included Dalton in its 8th edition of the formal definition of SI. [22] The name was also listed by the International Organization for Standardization in 2009 as an alternative to the “unified atomic mass unit”. [23] [24] It is now recommended by many scientific publishers, [25] and few of them consider it. “Atomic Mass Unit” and “Amu” deprecated. [26]In 2019, the BIPM retained the Dalton in its 9th edition of the formal definition of SI, while removing the unified atomic mass unit from its table of accepted non-SI units for use with the SI, but secondly it notes states that the dalton (Da) and the unified atomic mass unit (U) are alternative names (and symbols) for the same unit. [1]

A proposal

In 2012, American engineer Brian Leonard proposed redefining the Dalton (and possibly the unified atomic mass unit) as 1/ N gram, breaking the relationship with 12 C. [27] This would mean a change in the atomic mass of all elements when expressed in Daltons, but the change would be too small to have practical effect.

2019 SI Redefinition of Base Units

Dalton’s definition was not affected by the 2019 redefinition of SI base units, [28] [29] [1] i.e., 1 Da in SI is still 1/12 of the mass of a carbon-12 atom, a quantity referred to as SI units. The context should be determined experimentally. However, the definition of a mole was changed to be the amount of substance containing exactly6.022 140 76 × 10 23 units and the definition of the kilogram was also changed. 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 equal to the number of Daltons in its average molecular mass.


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 electrons removed to form ions, and The electron binding energy, also equal to the mass, b / 2 . The total binding energy of the six electrons in the carbon-12 atom is 1030.1089 eV = 1.650 4163 × 10 −16 J : b / 2  = 1.105 8674 × 10 −6 Or roughly one part in 10 million. atomic mass. Before the 2019 redefinition of SI units, the purpose of experiments was to determine the value of the Avogadro constant, to find the value of the unified atomic mass unit.

joseph loschmidt

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

Jean Perrin

Perrin estimated the Avogadro number in various ways at the turn of the 20th century. For this work he was largely awarded the 1926 Nobel Prize in Physics.


The electric charge per mole of electrons is a constant called the Faraday constant, the value of which was essentially known since 1834 when Michael Faraday 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 Avogadro’s number.

The classic experiment is that of Bower and Davis at NIST, [35] and relies on dissolving silver metal away from the anode of an electrolysis cell, while passing a constant electric current I for a known time t . If the mass of silver lost from the anode is m and the atomic weight of silver is r , then the Faraday constant is given by:

F={\frac {A_{{{\rm {r}}}}M_{{{\rm {u}}}}It}{m}}.

NIST scientists devised a method to replenish the silver lost from the anode due to mechanical reasons, and performed an isotope analysis of the silver used to determine its atomic weight. Their value for the conventional Faraday constant is 90  = . was96 485 .39(13) C/mol , which corresponds to the value of Avogadro’s constant6.022 1449 (78) × 10 23  mol -1 : In both values ​​. is the relative standard uncertainty of1.3 × 10 −6 ।

electron mass measurement

In practice, the atomic mass constant is determined by the electron’s rest mass e and the electron relative atomic mass r (e) (that is, 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 remaining mass of the electron can be obtained 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}})c\alpha ^{2}}},}
{\displaystyle m_{\rm {u}}={\frac {M_{\rm {u}}}{N_{\rm {A}}}},}
N_{{{\rm {A}}}}={\frac {M_{{{\rm {u}}}}A_{{{\rm {r}}}}({{\rm {e}}})}{m_{{{\rm {e}}}}}}={\frac {M_{{{\rm {u}}}}A_{{{\rm {r}}}}({{\rm {e}}})c\alpha ^{2}}{2R_{\infty }h}}

where c is the speed of light, h is the Planck 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 in the accuracy of the Avogadro constant was the uncertainty in the value of the Planck constant, as all other constants that contributed to the calculation were known more precisely. goes.

ContinuouslySign2014 Codata Valuesrelative standard uncertaintyCorrelation Coefficientn with a
Proton-Electron Mass RatioMP / ME _1836.152 673 89(17)9.5 × 10 -11-0.0003
molar mass constantu0.001 kg/mole = 1 g/mole0 (defined) –
Rydberg constant_10 973 731.568 508 (65) m −15.9 × 10 -12-0.0002
planck constanth6,626 070 040 (81) × 10 -34 J s1.2 × 10 -8−0.99993
speed of lightC299 792 458 m/s0 (defined) –
fine structure constanta7.297 352 5664(17) × 10 -32.3 × 10 -100.0193
Avogadro constanta6.022 140 857(74) × 10 23 mol -11.2 × 10 -81

The power of the currently defined values ​​of the universal constant can be understood from the table below (2018 CODATA).

ContinuouslySign2018 Codata Values ​​[37]relative standard uncertaintyA. correlation
coefficient with
Proton-Electron Mass RatioMP / ME _1836.152 673 43(11)6.0 × 10 -11 –
molar mass constantu0.999 999 999 65(30) × 10 -3 kg/mol3.0 × 10 -10 –
Rydberg constant_10 973 731.568 160(21) m −11.9 × 10 -12 –
planck constanth6.626 070 15 × 10 -34 J s0 (defined) –
speed of lightC299 792 458 m/s0 (defined) –
fine structure constanta7.297 352 5693(11) × 10 -31.5 × 10 -10 –
Avogadro constanta6.022 140 76 × 10 23 mol -10 (defined) –

X-ray crystal density methods

Silicon single crystals can be produced today in commercial facilities with extremely high purity and few lattice defects. This method defined the Avogadro constant as the ratio of the molar volume, m , to the atomic volume atom :

N_{{{\rm {A}}}}={\frac {V_{{{\rm {m}}}}}{V_{{{\rm {atom}}}}}}where , is and n is the number of atoms per unit cell of the volume cell .V_{{{\rm {atom}}}}={\frac {V_{{{\rm {cell}}}}}{n}}

The unit cell of silicon is a cubic packing arrangement of 8 atoms, and the unit cell volume can be measured by determining a single unit cell parameter, the length of one of the sides of a cube. [38] The 2018 CODATA value of a for silicon is5.431 020 511 (89) × 10 -10  m . [39]

In practice, measurements are made at a distance known as 220 (Si), which is the distance between the planes represented by the Miller indices {220}, and is equal to a / 8 .

The isotope proportional composition of the sample used should be measured and taken into account. Silicon occurs in three stable isotopes ( 28 Si, 29 Si, 30 Si), and the natural variation in their ratio outweighs the other uncertainties in the measurement. The atomic weight for an R sample crystal can be calculated as the standard atomic weight of three known nuclides with considerable accuracy. This allows the sample density measured together with the molar volume V m to be determined:

V_{{{\rm {m}}}}={\frac {A_{{{\rm {r}}}}M_{{{\rm {u}}}}}{\rho }}

where u is the molar mass constant. The 2018 CODATA value for Molar Volume of Silicon isWith a relative standard uncertainty of 1.205 883 199 (60) × 10 −5  m 3 mol −1 ,4.9 × 10 −8 । [40]