# Atomic mass unit

Physical unit
Unit name Atomic mass unit
Unit symbol ${\ displaystyle \ mathrm {u}}$(or ) ${\ displaystyle \ mathrm {Da}}$
Physical quantity (s) Dimensions
Formula symbol ${\ displaystyle m}$
dimension ${\ displaystyle {\ mathsf {M}}}$
system Approved for use with the SI
In SI units ${\ displaystyle \ mathrm {1 \, u = 1 {,} 660 \, 539 \, 066 \, 60 (50) \ cdot 10 ^ {- 27} \; kg}}$

The atomic mass unit (unit symbol: u for u nified atomic mass unit, outdated amu for a Tomic m ass u nit ) is a unit of mass . Its value is to 1 / 12 the mass of an atom of the carbon - isotope 12 defined C. The atomic mass unit is approved for use with the International System of Units (SI) and is a legal unit of measurement .

It is used when specifying not only atomic but also molecular masses . In biochemistry , and in the USA also in organic chemistry , the atomic mass unit is also known as the Dalton (unit symbol: Da ), named after the English naturalist John Dalton .

The atomic mass unit chosen in this way has the practically useful property that all known nuclear and atomic masses are close to integer multiples of u; the deviations are in all cases less than 0.1 u. The whole number in question is called the mass number of the nucleus or atom and is equal to the number of nucleons in the nucleus.

In addition, the atomic or molecular mass in the unit u (or Da) has the same numerical value as the mass of a mole of this substance in grams. The mass of large molecules such as proteins , DNA and other biomolecules is often characterized in kilodaltons, as there are no numerical differences between the values ​​given in kg / mol.

## definition

1 u is defined as one twelfth of the mass of an isolated atom of the carbon isotope 12 C in the ground state . The currently recommended value is

${\ displaystyle 1 \, \ mathrm {u} = 1 {,} 660 \, 539 \, 066 \, 60 (50) \ cdot 10 ^ {- 27} \, \ mathrm {kg}}$or because of the mass-energy equivalence
${\ displaystyle 1 \, \ mathrm {u} = 931 {,} 494 \, 102 \, 42 (28) \, \ mathrm {MeV} / \ mathrm {c} ^ {2}}$.

The conversion into the SI unit of kilograms gives

${\ displaystyle 1 \, \ mathrm {kg} = 6 {,} 022 \, 140 \, 7621 (18) \ cdot 10 ^ {26} \, \ mathrm {u}}$ or.
${\ displaystyle 1 \; \; \, \ mathrm {g} = 6 {,} 022 \, 140 \, 7621 (18) \ cdot 10 ^ {23} \, \ mathrm {u}}$.

Since the nucleus of the 12 carbon atom contains 12 nucleons , the unit u is approximately equal to the mass of a nucleon, i.e. a proton or a neutron . Therefore the numerical value of the atomic mass in u roughly corresponds to the mass number or nucleon number, i.e. the number of heavy core components of the atom.

## Relationship to molar mass

Until the redefinition of the SI units in 2019, the mole was defined as the amount of substance that consists of as many individual particles as there are atoms in 12 g of 12 C. The atomic mass unit and the mole were thus defined by the same atom 12 C. This resulted in exactly the same numerical value for the mass of a particle in u and its molar mass in g / mol. In other words: 1 u ·  N A  = 1 g / mol. The Avogadro constant N A , i.e. the number of particles per mole, had to be determined experimentally according to this definition and was subject to a measurement uncertainty.

Since 2019, N A is no longer determined by the mass of the 12 C atom, but is precisely determined by definition. Therefore the mass of a particle in u and the molar mass in g no longer have exactly the same numerical value. However, the deviation is extremely small and irrelevant in practice:

${\ displaystyle M _ {\ text {u}} = 1 \, {\ text {u}} \ cdot N _ {\ text {A}} = 0 {,} 999 \, 999 \, 999 \, 65 (30) \, {\ text {g}} / {\ text {mol}}}$

## Earlier definitions

Until 1960 the atomic mass unit was defined as 116 of the mass of an oxygen atom. The chemists referred to the average mass of an atom in the naturally occurring isotope mixture of the element O, while the physicists referred to the mass of the atom of the main isotope 16 O.

The difference between the “chemical” definition and the “physical” definition was the reason to introduce a unified definition. About the negotiations in the responsible committees it is reported that the chemists were initially not prepared to agree to the definition of the physicists with 16 O, as this would have resulted in considerable losses in the sale of chemical substances. Finally, the physicists convinced the chemists with the suggestion to use 12 C as a basis, which not only made the difference to the chemical definition much smaller, but also went in the “right direction” and would have a positive effect on sales revenues.

The relationship applies between the new and the two obsolete values ​​of the unit

${\ displaystyle 1 \, \ mathrm {u _ {(since 1961)}} = 1 {,} 000 \, 317 \, 9 \, \ mathrm {amu _ {(old, physical)}} = 1 {,} 000 \, 043 \, \ mathrm {amu _ {(old, chemical)}}}$

The difference between the old physical and today's definition is due to the mass defect , which is higher at 16 O than at 12 C.

## use

In the International Bureau of Weights and Measures brochure (“SI Brochure”) the atomic unit of mass is included in the list of “Non-SI Units Approved for Use with the SI”. In the 8th edition (2006) the unit name "Dalton" was added for the first time, as a synonym for u. The 9th edition (2019) only mentions the dalton and indicates in a footnote that the "atomic mass unit (u)" is an alternative designation for the same unit. The term "Dalton" does not appear in the legal regulations of EU Directive 80/181 / EEC for the states of the EU and in the Federal Law on Metrology in Switzerland.

The use of prefixes for decimal multiples and parts is permitted for both the atomic mass unit and the dalton . Commonly used are the kilodalton, 1 kDa = 1000 Da, and the megadalton, 1 MDa = 1,000,000 Da.

## Examples

• By definition, a carbon atom of isotope 12 C has a mass of 12 u.
• A hydrogen atom of the isotope 1 H has the mass 1.007 825 0 u.
• One molecule of the well-known active ingredient acetylsalicylic acid (aspirin) has a mass of 180.16 u.
• One molecule of the small peptide hormone insulin has a mass of 5808 u.
• One molecule of the protein actin (one of the most common proteins in eukaryotes ) has a mass of approximately 42 ku.

## Individual evidence

1. a b The International System of Units (SI) . German translation of the BIPM brochure "Le Système international d'unités / The International System of Units (8e édition, 2006)". In: PTB-Mitteilungen . tape 117 , no. 2 , 2007 ( Online [PDF; 1.4 MB ]).
2. a b Le Système international d'unités . 9e édition, 2019 (the so-called "SI brochure", French and English).
3. on the basis of EU Directive 80/181 / EEC in the states of the EU or the Federal Law on Metrology in Switzerland.
4. ^ Josef Mattauch: Units of measurement for atomic weights and nuclide masses. In: Journal of Nature Research A . 13, 1958, pp. 572-596 ( online ).
5. CODATA Recommended Values. National Institute of Standards and Technology, accessed May 20, 2019 . Value for u in the unit kg. The numbers in brackets denote the uncertainty in the last digits of the value; this uncertainty is given as the estimated standard deviation of the specified numerical value from the actual value.
6. CODATA Recommended Values. National Institute of Standards and Technology, accessed May 20, 2019 . Value for u in the unit MeV / c 2 . The numbers in brackets denote the uncertainty in the last digits of the value; this uncertainty is given as the estimated standard deviation of the specified numerical value from the actual value.
7. CODATA Recommended Values. National Institute of Standards and Technology, accessed August 24, 2019 .
8. Aaldert Wapstra , quoted from G. Audi, The History of Nuclidic Masses and of their Evaluation, Int.J. Mass Spectr.Ion Process. 251 (2006) 85-94, arxiv