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The '''unified atomic mass unit''' ('''u'''), or '''dalton''' ('''Da'''), is a unit of atomic and molecular [[mass]]. By definition it is one twelfth of the mass of an unbound atom of the [[carbon-12]] [[nuclide]], at rest and in its ground state.
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''See also [[Atomic mass]].''


The '''unified atomic mass unit''' ('''''u'''''), or '''dalton''' ('''''Da'''''), is a unit of atomic and molecular mass. By definition it is one twelfth of the mass of an unbound  [[carbon]]-12 (<sup>12</sup>C) [[atom]], at rest and in its ground state.


<!--
The relationship of the unified atomic mass unit to the macroscopic [[SI]] base unit of mass, the [[kilogram]], is given by [[Avogadro's number]] ''N<sub>A</sub>''. By the definition of Avogadro's number, the mass of  ''N<sub>A</sub>'' carbon-12 atoms, at rest and in their ground state, is 12 gram ( = 12&times;10<sup>&minus;3</sup> kg). The latest value of ''N<sub>A</sub>'' is the same numerical value as the Avagadro constant, the number of "elementary entities" in a mole of substance:<ref name=NISTav>
:1 u =  1/''N''<sub>A</sub> [[gram]] = 1/ (1000 ''N''<sub>A</sub>) [[kilogram|kg]] &nbsp;&nbsp;(where ''N''<sub>A</sub> is [[Avogadro's number]])
:1 u ≈ 1.660538782(83) × 10<sup>−27</sup> kg ≈ 931.494028(23) MeV/c<sup>2</sup>


See [[1 E-27 kg]] for a list of objects which have a mass of about 1 u.
{{cite web |title= Fundamental physical constants: Avogadro constant ''N<sub>A</sub>, L'' |publisher=[[NIST]] |accessdate=2011-09-09 |url=http://physics.nist.gov/cgi-bin/cuu/Value?na}}


The symbol '''amu''' for '''atomic mass unit''' is not a symbol for the unified atomic mass unit. Its use is  an historical artifact (written during the time when the amu scales were used), an error (possibly deriving from confusion about historical usage), or correctly referring to the historical scales that used it (see [[#History|History]]). Atomic masses are often written without any unit and then the unified atomic mass unit is implied.
</ref>
In [[biochemistry]] and [[molecular biology]] literature (particularly in reference to [[protein]]s), the term "dalton" is used, with the symbol '''Da'''.  Because proteins are large [[molecule]]s, they are typically referred to in kilodaltons, or "kDa", with one kilodalton being equal to 1000 daltons. 
The unified atomic mass unit, or dalton, is not an [[SI]] unit of mass, although it is accepted for use with SI under either name.


The unit is convenient because one [[hydrogen atom]] has a mass of approximately 1 u, and more generally an [[atom]] or [[molecule]] that contains ''n'' [[proton]]s and [[neutron]]s will have a mass approximately equal to ''n'' u. (The reason is that a carbon-12 atom contains 6 protons, 6 neutrons and 6 electrons, with the protons and neutrons having about the same mass and the [[electron]] mass being negligible in comparison.The mass of the electron is approximately 1/1836 of the mass of the proton) This is an approximation, since it does not account for the mass contained in the [[binding energy]] of an atom's [[atomic nucleus|nucleus]]; this binding energy mass is not a fixed fraction of an atom's total mass. The differences which result from nuclear binding are generally less than 0.01 u, however. Chemical element masses, as expressed in u, would therefore all be close to whole number values (within 2% and usually within 1%) were it not for the fact that atomic weights of chemical elements are averaged values of the various stable isotope masses in the abundances which they naturally occur.<ref>http://www.sisweb.com/referenc/source/exactmaa.htm</ref> For example, [[chlorine]] has an atomic weight of 35.45 u because it is composed of 76% <sup>35</sup>Cl (34.96 u) and 24% <sup>37</sup>Cl (36.97 u). 
:''N<sub>A</sub>'' =  6.022 141 29(27) × 10<sup>23</sup> / mol,


Another reason the unit is used is that it is experimentally much easier and more precise to ''compare'' masses of atoms and molecules (determine ''relative'' masses) than to measure their ''absolute'' masses. Masses are compared with a [[mass spectrometer]] (see below).
where the symbol ''mol'' represents the [[mole]], which can be defined for any substance as a sample containing the same number of "elementary entities" (atoms or molecules, for example) as there are atoms of <sup>12</sup>C in 0.012 kg of carbon-12.


[[Avogadro's number]] (''N''<sub>A</sub>) and the [[mole (unit)|mole]] are defined so that one mole of a substance with atomic or molecular mass 1 u will have a mass of precisely 1 [[gram]].  
From this value for ''N<sub>A</sub>'' follows the latest value of the unified atomic mass unit:<ref name=NISTu>
For example, the molecular mass of a [[Water (molecule)|water molecule]] containing one <sup>16</sup>O isotope and two <sup>1</sup>H isotopes is 18.0106 u, and this means that one mole of this monoisotopic water has a mass of 18.0106 grams. Water and most molecules consist of a mixture of molecular masses due to naturally occurring isotopes. For this reason these sort of comparisons are more meaningful and practical using [[molar mass]]es which are generally expressed in g/mol, not u. In other words the one-to-one relationship between daltons and g/mol is true but in order to be used accurately for any practical purpose any calculations must be with isotopically pure substances or involve much more complicated statistical averaging of multiple isotopic compositions.
 
{{cite web |title= Fundamental physical constants: atomic mass unit-kilogram relationship 1 ''u'' |publisher=[[NIST]] |accessdate=2011-09-09 |url=http://physics.nist.gov/cgi-bin/cuu/Value?ukg}}
 
</ref>
:1 ''u'' ≈ 1.660 538 921(73) × 10<sup>&minus;27</sup> kg
     
Future refinements in Avogadro's number by future improvements in counting large (on the order of 10<sup>27</sup>) numbers  of atoms, will give better accuracy of ''u''. It is hoped that in the future the experimental accuracy of Avogadro's constant will improve so much that the unified atomic mass unit may replace the kilogram as the SI base unit. For instance, there is a proposal under consideration to define the kilogram in terms of a specified number of free [[carbon]]-12 (<sup>12</sup>C) [[atom]]s, at rest and in their ground state, thereby fixing the Avagadro constant, and making an experimental determination unnecessary.<ref name=Richard>
 
{{cite book |title=Metrology and fundamental constants: Volume 166 of Proceedings of the International School of Physics "Enrico Fermi" |url=http://books.google.com/books?id=37HD1iIxlH0C&pg=PA511 |pages=p. 511 |author=P. Richard |editor=Theo W. Hänsch, ed |year=2007|publisher=IOS Press |isbn=1586037846}}
 
</ref> See the article [[kilogram]].
 
The unit ''u'' is convenient because one [[hydrogen]] atom has a mass of approximately 1 ''u'', and more generally an [[atom]] or [[molecule]] that contains ''p'' [[proton]]s and ''n'' [[neutron]]s will have a mass approximately equal to (''p'' + ''n'') ''u''. The mass of a nucleus is not exactly equal to ''p'' + ''n'', because the [[nuclear binding energy]] gives rise to a relativistic [[mass defect]].
 
==Confusions==
In the system of [[atomic units]], the "atomic unit of mass" is the mass of the electron ''m<sub>e</sub>''.<ref name=NISTe>
 
{{cite web |title= Fundamental physical constants: atomic unit of mass ''m<sub>e</sub>'' |publisher=[[NIST]] |accessdate=2011-09-09 |url=http://physics.nist.gov/cgi-bin/cuu/Value?ttme}}
 
</ref> But further confusion prevails:
 
In the literature one still finds the obsolete unit ''amu'' (atomic mass unit). This antiquated usage is deplorable, not only because the ''amu'' is <u>not</u> a unit accepted for use with the [[SI]], but also because two ''different'' standard masses are denoted by ''amu''. There is the physicist's ''amu'' ( = 1/1.000&thinsp;317&thinsp;9 ''u'') and there is the chemist's ''amu'' ( = 1/1.000&thinsp;043 ''u''). Because chemists and physicists now use the same atomic mass unit, today it is referred to as ''unified''.  It is a non-[[SI]] unit accepted for use with the SI, whose value in SI units is obtained experimentally.


==History==
==History==
The [[chemist]] [[John Dalton]] was the first to suggest the mass of one atom of [[hydrogen]] as the atomic mass unit. [[Francis Aston]], inventor of the mass spectrometer, later used {{frac|1|16}} of the mass of one atom of [[oxygen]]-16 as his unit.


Before [[1961]], the ''physical atomic mass unit'' (amu) was defined as {{frac|1|16}} of the mass of one atom of oxygen-16, while the ''chemical atomic mass unit'' (amu) was defined as {{frac|1|16}} of the ''average'' mass of an oxygen atom (taking the natural abundance of the different oxygen [[isotope]]s into account). Both units are slightly smaller than the '''unified atomic mass unit''', which was adopted by the [[International Union of Pure and Applied Physics]] in 1960 and by the [[International Union of Pure and Applied Chemistry]] in 1961. Hence, before 1961 physicists as well as chemists used the symbol '''amu''' for their respective (and slightly different) atomic mass units. One still sometimes finds this usage in the scientific literature today. However, the accepted standard is now the unified atomic mass unit (symbol u), with: 1 u = 1.000 317 9 amu (physical scale) = 1.000 043  amu (chemical scale).
The different interpretations of the ''amu'' arose historically. Before 1960, in physics the amu was defined as 1/16 of the mass of one atom of oxygen-16, while in chemistry the amu was defined as 1/16 of the ''average'' mass of an oxygen atom (averaged over the natural abundance of the different oxygen [[isotope]]s). Both units are slightly smaller than the ''unified atomic mass unit'', symbol ''u'', that was adopted by the [[International Union of Pure and Applied Physics]] in 1960 and by the [[International Union of Pure and Applied Chemistry]] in 1961.  
 
Much earlier, the first standardization of atomic mass was made by the chemist [[John Dalton]] in the early nineteenth century, who introduced the mass of one atom of [[hydrogen]] as the atomic mass unit. Later [[Francis Aston]], inventor of the [[mass spectrometer]], replace it by one sixteenth of the mass of one atom of [[oxygen]]-16.
 
==Examples==
In the numerical values below, the numbers in parentheses refer to measurement uncertainties.
 
The atomic mass unit in MeV is (1 ''u'') [[speed of light|''c<sub>0</sub>''<sup>2</sup>]]:
 
:1 ''u'' = 931.494 061(21) MeV.<ref name=NIST2>
 
{{cite web |title=Fundamental physical constants: atomic mass unit-electron volt relationship 1 ''u'' (''c<sub>0</sub>''<sup>2</sup>)|url=http://physics.nist.gov/cgi-bin/cuu/Value?uev |publisher=NIST |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-09-04}}
 
</ref>
 
The proton mass is:
:''m<sub>p</sub>'' = 1.007 276 466 812(90) ''u''.<ref name=mpu>
{{cite web |title=Fundamental physical constants: proton mass in ''u'': ''m<sub>p</sub>'' |url=http://physics.nist.gov/cgi-bin/cuu/Value?mpu |publisher=NIST |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-09-04}}
 
</ref>
 
The neutron mass is:
:''m<sub>n</sub>'' = 1.008 664 916 00(43) ''u''.<ref name=mnu>
{{cite web |title=Fundamental physical constants: neutron mass in ''u'': ''m<sub>n</sub>'' |url=http://physics.nist.gov/cgi-bin/cuu/Value?mnu |publisher=NIST |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-09-09}}
 
</ref>
 
The electron mass is:


== References ==
:''m<sub>e</sub>'' = 5.485 799 0946(22) × 10<sup>-4</sup> ''u''.<ref name=meu>
{{reflist}}
{{cite web |title=Fundamental physical constants: electron mass in ''u'': ''m<sub>e</sub>'' |url=http://physics.nist.gov/cgi-bin/cuu/Value?meu |publisher=NIST |work=The NIST reference on constants, units, and uncertainty |accessdate=2011-09-04}}


== See also ==
</ref>
* [[Molecular mass]]


==External links==
==References==
*[http://www1.bipm.org/en/si/si_brochure/chapter4/table7.html SI website on acceptable non-SI units]
<references />
*[http://physics.nist.gov/cgi-bin/cuu/Value?ukg Accepted value of 1u as of 2006]
-->

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See also Atomic mass.

The unified atomic mass unit (u), or dalton (Da), is a unit of atomic and molecular mass. By definition it is one twelfth of the mass of an unbound carbon-12 (12C) atom, at rest and in its ground state.

The relationship of the unified atomic mass unit to the macroscopic SI base unit of mass, the kilogram, is given by Avogadro's number NA. By the definition of Avogadro's number, the mass of NA carbon-12 atoms, at rest and in their ground state, is 12 gram ( = 12×10−3 kg). The latest value of NA is the same numerical value as the Avagadro constant, the number of "elementary entities" in a mole of substance:[1]

NA = 6.022 141 29(27) × 1023 / mol,

where the symbol mol represents the mole, which can be defined for any substance as a sample containing the same number of "elementary entities" (atoms or molecules, for example) as there are atoms of 12C in 0.012 kg of carbon-12.

From this value for NA follows the latest value of the unified atomic mass unit:[2]

1 u ≈ 1.660 538 921(73) × 10−27 kg

Future refinements in Avogadro's number by future improvements in counting large (on the order of 1027) numbers of atoms, will give better accuracy of u. It is hoped that in the future the experimental accuracy of Avogadro's constant will improve so much that the unified atomic mass unit may replace the kilogram as the SI base unit. For instance, there is a proposal under consideration to define the kilogram in terms of a specified number of free carbon-12 (12C) atoms, at rest and in their ground state, thereby fixing the Avagadro constant, and making an experimental determination unnecessary.[3] See the article kilogram.

The unit u is convenient because one hydrogen atom has a mass of approximately 1 u, and more generally an atom or molecule that contains p protons and n neutrons will have a mass approximately equal to (p + n) u. The mass of a nucleus is not exactly equal to p + n, because the nuclear binding energy gives rise to a relativistic mass defect.

Confusions

In the system of atomic units, the "atomic unit of mass" is the mass of the electron me.[4] But further confusion prevails:

In the literature one still finds the obsolete unit amu (atomic mass unit). This antiquated usage is deplorable, not only because the amu is not a unit accepted for use with the SI, but also because two different standard masses are denoted by amu. There is the physicist's amu ( = 1/1.000 317 9 u) and there is the chemist's amu ( = 1/1.000 043 u). Because chemists and physicists now use the same atomic mass unit, today it is referred to as unified. It is a non-SI unit accepted for use with the SI, whose value in SI units is obtained experimentally.

History

The different interpretations of the amu arose historically. Before 1960, in physics the amu was defined as 1/16 of the mass of one atom of oxygen-16, while in chemistry the amu was defined as 1/16 of the average mass of an oxygen atom (averaged over the natural abundance of the different oxygen isotopes). Both units are slightly smaller than the unified atomic mass unit, symbol u, that was adopted by the International Union of Pure and Applied Physics in 1960 and by the International Union of Pure and Applied Chemistry in 1961.

Much earlier, the first standardization of atomic mass was made by the chemist John Dalton in the early nineteenth century, who introduced the mass of one atom of hydrogen as the atomic mass unit. Later Francis Aston, inventor of the mass spectrometer, replace it by one sixteenth of the mass of one atom of oxygen-16.

Examples

In the numerical values below, the numbers in parentheses refer to measurement uncertainties.

The atomic mass unit in MeV is (1 u) c02:

1 u = 931.494 061(21) MeV.[5]

The proton mass is:

mp = 1.007 276 466 812(90) u.[6]

The neutron mass is:

mn = 1.008 664 916 00(43) u.[7]

The electron mass is:

me = 5.485 799 0946(22) × 10-4 u.[8]

References

  1. ↑ Fundamental physical constants: Avogadro constant NA, L. NIST. Retrieved on 2011-09-09.
  2. ↑ Fundamental physical constants: atomic mass unit-kilogram relationship 1 u. NIST. Retrieved on 2011-09-09.
  3. ↑ P. Richard (2007). Theo W. Hänsch, ed: Metrology and fundamental constants: Volume 166 of Proceedings of the International School of Physics "Enrico Fermi". IOS Press, p. 511. ISBN 1586037846. 
  4. ↑ Fundamental physical constants: atomic unit of mass me. NIST. Retrieved on 2011-09-09.
  5. ↑ Fundamental physical constants: atomic mass unit-electron volt relationship 1 u (c02). The NIST reference on constants, units, and uncertainty. NIST. Retrieved on 2011-09-04.
  6. ↑ Fundamental physical constants: proton mass in u: mp. The NIST reference on constants, units, and uncertainty. NIST. Retrieved on 2011-09-04.
  7. ↑ Fundamental physical constants: neutron mass in u: mn. The NIST reference on constants, units, and uncertainty. NIST. Retrieved on 2011-09-09.
  8. ↑ Fundamental physical constants: electron mass in u: me. The NIST reference on constants, units, and uncertainty. NIST. Retrieved on 2011-09-04.
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