View source for Physics:Relative atomic mass

{{Short description|Type of atomic measurement}}

'''Relative atomic mass''' (symbol: '''''A''{{sub|r}}'''; sometimes abbreviated '''RAM''' or '''r.a.m.'''), also known by the [[Deprecation|deprecated]] synonym '''atomic weight''', is a dimensionless [[Physics:Physical quantity|physical quantity]] defined as the ratio of the average [[Physics:Mass|mass]] of [[Physics:Atom|atom]]s of a [[Chemistry:Chemical element|chemical element]] in a given sample to the [[Physics:Atomic mass constant|atomic mass constant]]. The atomic mass constant (symbol: ''m''{{sub|u}}) is defined as being {{sfrac|1|12}} of the mass of a [[Physics:Carbon-12|carbon-12]] atom.<ref name="IUPAC1979">{{cite journal | author = International Union of Pure and Applied Chemistry | title = Atomic Weights of the Elements 1979 | url = http://publications.iupac.org/pac-2007/1980/pdf/5210x2349.pdf | doi = 10.1351/pac198052102349 | journal = [[Chemistry:Pure and Applied Chemistry|Pure Appl. Chem.]] | year = 1980 | volume = 52 | pages = 2349–84 | issue = 10 |  doi-access = free }}</ref><ref name="GreenBook">{{GreenBookRef2nd|page=41}}</ref> Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid<ref name="SIBrochure9thEd">{{citation |title=The International System of Units (SI) |author=International Bureau of Weights and Measures |author-link=New SI |date=20 May 2019  |edition=9th |isbn=978-92-822-2272-0 |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf| archive-url = https://web.archive.org/web/20211018184555/https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 |archive-date=18 October 2021 |url-status=live}}</ref>{{rp|page=134}} even after the [[2019 redefinition of the SI base units|2019 redefinition of the SI base units]].{{efn|There are only two consequences of the redefinition that are relevant to the present article. First, the [[Physics:Molar mass|molar mass]] of carbon-12, ''M''(<sup>12</sup>C), is no longer exactly equal to 12 g/mol by definition, but instead has to be determined experimentally and thus has an uncertainty. Its current best value<ref name="NIST MC12">{{cite web |url=https://physics.nist.gov/cgi-bin/cuu/Value?mm12c |title=2018 CODATA Value: molar mass of carbon-12 |date=20 May 2019 |work=The NIST Reference on Constants, Units, and Uncertainty |publisher=[[Organization:National Institute of Standards and Technology|NIST]] |access-date=2023-08-30}}</ref><ref name="CODATA 2018">{{cite journal |last1=Tiesinga |first1=Eite |last2=Mohr |first2=Peter J. |last3=Newell |first3=David B. |last4=Taylor |first4=Barry N. |title=CODATA recommended values of the fundamental physical constants: 2018 |journal=Reviews of Modern Physics |date=30 June 2021 |volume=93 |issue=2 |doi=10.1103/RevModPhys.93.025010|pmc=9890581 }}</ref>{{rp|page=49}} is {{val|11.9999999958}}(36) g/mol. Here the “(36)” is a measure of the uncertainty; basically, the “58” (the last two digits in {{val|11.9999999958}}) should be understood as “58 ± 36”, as explained [[Physics:Uncertainty#In measurements|here]]. However, this is so close to the old value of 12 g/mol (the relative difference is 3.5 × 10<sup>-10</sup>) that, in a vast majority of applications, ''M''(<sup>12</sup>C) may still be taken to be exactly 12 g/mol; this is of course so by design. Second, the [[Physics:Avogadro constant|Avogadro constant]] ''N''<sub>A</sub> is now exactly equal to {{val|6.02214076|e=23|u=reciprocal moles}} by definition, whereas previously it had to be determined experimentally and thus had an uncertainty.<ref name="SIBrochure9thEd"/>{{rp|page=134}}}}{{efn|Immediately following the 2019 redefinition, ''M''(<sup>12</sup>C) was equal to {{val|12.0000000000}}(54) g/mol, corresponding to a relative standard uncertainty<ref>{{cite web|url=http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html|title=Standard Uncertainty and Relative Standard Uncertainty|work=CODATA reference|publisher=NIST|access-date=30 August 2023|url-status=live|archive-url=https://web.archive.org/web/20230724175742/https://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html|archive-date=24 July 2023}}</ref> of 4.5 × 10<sup>-10</sup>. This uncertainty was “inherited” from the relative standard uncertainty that the product ''h N''<sub>A</sub> had immediately prior to the redefinition: also  4.5 × 10<sup>-10</sup>. (Here ''h'' is the [[Physics:Planck constant|Planck constant]]. Following the redefinition, the product ''h N''<sub>A</sub> has an exact value by definition.)<ref name="CODATA 2017 Special Adjustment">{{cite journal |last1=Mohr |first1=Peter J |last2=Newell |first2=David B |last3=Taylor |first3=Barry N |last4=Tiesinga |first4=Eite |title=Data and analysis for the CODATA 2017 special fundamental constants adjustment |journal=Metrologia |date=1 February 2018 |volume=55 |issue=1 |pages=125–146 |doi=10.1088/1681-7575/aa99bc |doi-access=free}}</ref>{{rp|page=143}} Conversely, immediately prior to the redefinition, the Avogadro constant ''N''<sub>A</sub> had a measured value of {{val| 6.022140758|}}(62) × {{val| |e=23|u=reciprocal moles}}, corresponding to a relative standard uncertainty of 1.0 × 10<sup>-8</sup>.
Note that immediately prior to the redefinition, the product ''h N''<sub>A</sub> was known far more precisely than either ''h'' or ''N''<sub>A</sub> individually<ref name="CODATA 2017 Special Adjustment"/>{{rp|page=139}}).}}

For a single given sample, the relative atomic mass of a given element is the [[Weighted arithmetic mean|weighted arithmetic mean]] of the masses of the individual atoms (including all its [[Physics:Isotope|isotope]]s) that are present in the sample. This quantity can vary significantly between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced combinations of isotopic [[Chemistry:Natural abundance|abundances]] in varying ratios. For example, due to a different mixture of stable carbon-12 and [[Physics:Carbon-13|carbon-13]] isotopes, a sample of elemental carbon from volcanic [[Chemistry:Methane|methane]] will have a different relative atomic mass than one collected from plant or animal tissues.

The more common, and more specific quantity known as [[Physics:Standard atomic weight|standard atomic weight]] (''A''{{sub|r,standard}}) is an application of the relative atomic mass values obtained from many different samples. It is sometimes interpreted as the ''expected range'' of the relative atomic mass values for the atoms of a given element from all terrestrial sources, with the various sources being [[Chemistry:Isotope geochemistry|taken from Earth]].<ref>[http://goldbook.iupac.org/S05907.html Definition of element sample]</ref> "Atomic weight" is often loosely and incorrectly used as a synonym for standard atomic weight (incorrectly because standard atomic weights are not from a single sample). Standard atomic weight is nevertheless the most widely published variant of relative atomic mass.

Additionally, the continued use of the term "atomic weight" (for any element) as opposed to "relative atomic mass" has attracted considerable controversy since at least the 1960s, mainly due to the technical difference between [[Physics:Weight|weight]] and mass in physics.<ref name="IUPAChist">{{AtomicWeightHistory}}</ref> Still, both terms are officially sanctioned by the IUPAC. The term "relative atomic mass" now seems to be replacing "atomic weight" as the preferred term, although the term "''standard'' atomic weight" (as opposed to the more correct "''standard'' relative atomic mass") continues to be used.

==Definition==

Relative atomic mass is determined by the average atomic mass, or the weighted mean of the atomic masses of all the atoms of a particular chemical element found in a particular sample, which is then compared to the atomic mass of carbon-12.<ref>{{GoldBookRef|file=R05258|title=relative atomic mass}}</ref> This comparison is the quotient of the two weights, which makes the value dimensionless (having no unit). This quotient also explains the word ''relative'': the sample mass value is considered relative to that of carbon-12.

It is a synonym for atomic weight, though it is not to be confused with relative isotopic mass. Relative atomic mass is also frequently used as a synonym for [[Physics:Standard atomic weight|standard atomic weight]] and these quantities may have overlapping values if the relative atomic mass used is that for an element from Earth under defined conditions. However, relative atomic mass (atomic weight) is still technically distinct from standard atomic weight because of its application only to the atoms obtained from a single sample; it is also not restricted to terrestrial samples, whereas standard atomic weight averages multiple samples but only from terrestrial sources. Relative atomic mass is therefore a more general term that can more broadly refer to samples taken from non-terrestrial environments or highly specific terrestrial environments which may differ substantially from Earth-average or reflect different degrees of [[Measurement uncertainty|certainty]] (e.g., in number of [[Significant figures|significant figures]]) than those reflected in standard atomic weights.

===Current definition===

The prevailing IUPAC definitions (as taken from the "Gold Book") are:
:''atomic weight'' — See: relative atomic mass<ref>[http://goldbook.iupac.org/A00505.html IUPAC Gold Book - atomic weight]</ref>
and
:''relative atomic mass (atomic weight)'' — The ratio of the average mass of the atom to the unified atomic mass unit.<ref>[http://goldbook.iupac.org/R05258.html IUPAC Gold Book - relative atomic mass (atomic weight), A r]</ref>
Here the "unified atomic mass unit" refers to {{frac|1|12}} of the mass of an atom of {{sup|12}}C ''in its ground state''.<ref>[http://goldbook.iupac.org/U06554.html IUPAC Gold Book - unified atomic mass unit]</ref>

The IUPAC definition<ref name="IUPAC1979"/> of relative atomic mass is:
:An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of {{sup|12}}C.

The definition deliberately specifies "'''''An''''' atomic weight…", as an element will have different relative atomic masses depending on the source. For example, [[Chemistry:Boron|boron]] from [[Place:Turkey|Turkey]] has a lower relative atomic mass than boron from {{wipe|California}}, because of its different [[Physics:Isotope|isotopic composition]].<ref>{{Greenwood&Earnshaw1st|pages=21, 160}}</ref><ref name="Rev2000">{{cite journal | author = International Union of Pure and Applied Chemistry | title = Atomic Weights of the Elements: Review 2000 | url = https://media.iupac.org/publications/pac/2003/pdf/7506x0683.pdf | journal = [[Chemistry:Pure and Applied Chemistry|Pure Appl. Chem.]] | volume = 75 | issue = 6 | pages = 683–800 | year = 2003 | doi = 10.1351/pac200375060683 | s2cid = 96800435 | author-link = International Union of Pure and Applied Chemistry }}</ref> Nevertheless, given the cost and difficulty of [[Physics:Isotope analysis|isotope analysis]], it is common practice to instead substitute the tabulated values of [[Physics:Standard atomic weight|standard atomic weights]], which are ubiquitous in chemical laboratories and which are revised biennially by the IUPAC's [[Organization:Commission on Isotopic Abundances and Atomic Weights|Commission on Isotopic Abundances and Atomic Weights]] (CIAAW).<ref>[http://goldbook.iupac.org/html/S/S05907.html IUPAC Gold Book - standard atomic weights]</ref>

===Historical usage===

Older (pre-1961) historical relative scales based on the atomic mass unit (symbol: ''a.m.u.'' or ''amu'') used either the [[Physics:Oxygen-16|oxygen-16]] relative isotopic mass or else the oxygen relative atomic mass (i.e., atomic weight) for reference. See the article on the history of the modern [[Physics:Unified atomic mass unit|unified atomic mass unit]] for the resolution of these problems.

==Standard atomic weight==
{{main|Physics:Standard atomic weight}}

The IUPAC commission CIAAW maintains an expectation-interval value for relative atomic mass (or atomic weight) on Earth named standard atomic weight. Standard atomic weight requires the sources be terrestrial, natural, and stable with regard to radioactivity. Also, there are requirements for the research process. For 84 stable elements, CIAAW has determined this standard atomic weight. These values are widely published and referred to loosely as 'the' atomic weight of elements for real-life substances like pharmaceuticals and commercial trade. 

Also, CIAAW has published abridged (rounded) values and simplified values (for when the Earthly sources vary systematically).

== Other measures of the mass of atoms ==

'''[[Physics:Atomic mass|Atomic mass]]''' (''m''<sub>a</sub>) is the mass of a single atom. It defines the mass of a specific isotope, which is an input value for the determination of the relative atomic mass. An example for three [[Chemistry:Silicon|silicon]] isotopes is given below. A convenient unit of mass for atomic mass is the [[Dalton (unit)|dalton]] (Da), which is also called the unified atomic mass unit (u).

The '''relative ''isotopic'' mass''' is the ''ratio of'' the mass of a single atom to the [[Physics:Atomic mass constant|atomic mass constant]] ({{nowrap|1=''m''<sub>u</sub> = 1&nbsp;Da}}). This ratio is dimensionless.

==Determination of relative atomic mass==
{{main|Chemistry:Isotope geochemistry}}

Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each [[Physics:Nuclide|nuclide]]) and [[Physics:Isotope|isotopic composition]] of a sample. Highly accurate atomic masses are available<ref name="NIST">[[Organization:National Institute of Standards and Technology|National Institute of Standards and Technology]]. [http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&ascii=html&isotype=some Atomic Weights and Isotopic Compositions for All Elements].</ref><ref name="AME2003">{{AME 2003}}</ref> for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples.<ref name="TICE1997">{{AtWt TICE 1997}}</ref><ref name="IAvar">{{AtWt IAV}}</ref> For this reason, the relative atomic masses of the 22 [[Mononuclidic element|mononuclidic element]]s (which are the same as the isotopic masses for each of the single naturally occurring nuclides of these elements) are known to especially high accuracy. For example, there is an uncertainty of only one part in 38 million for the relative atomic mass of [[Chemistry:Fluorine|fluorine]], a precision which is greater than the current best value for the [[Physics:Avogadro constant|Avogadro constant]] (one part in 20 million).

{| class="wikitable" align="right"
|-
! rowspan=2 | Isotope
! rowspan=2 | Atomic mass<ref name="AME2003" />
! colspan=2 | Abundance<ref name="TICE1997" />
|-
! Standard
! Range
|-
| align="center" | {{sup|28}}Si
| {{val|27.97692653246|(194)}}
| 92.2297(7)%
| 92.21–92.25%
|-
| align="center" | {{sup|29}}Si
| {{val|28.976494700|(22)}}
| 4.6832(5)%
| 4.67–4.69%
|-
| align="center" | {{sup|30}}Si
| {{val|29.973770171|(32)}}
| 3.0872(5)%
| 3.08–3.10%
|-
|}

The calculation is exemplified for [[Chemistry:Silicon|silicon]], whose relative atomic mass is especially important in [[Metrology|metrology]]. Silicon exists in nature as a mixture of three isotopes: {{sup|28}}Si, {{sup|29}}Si and {{sup|30}}Si. The atomic masses of these nuclides are known to a precision of one part in 14&nbsp;billion for {{sup|28}}Si and about one part in one billion for the others. However, the range of [[Chemistry:Natural abundance|natural abundance]] for the isotopes is such that the standard abundance can only be given to about ±0.001% (see table).

The calculation is as follows:
:''A''{{sub|r}}(Si) = ({{val|27.97693}} × 0.922297) + ({{val|28.97649}} × 0.046832) + ({{val|29.97377}} × 0.030872) = 28.0854

The estimation of the [[Measurement uncertainty|uncertainty]] is complicated,<ref name="Meija">{{cite journal | last1 = Meija | first1 = Juris | journal = Metrologia | year = 2008 | title = Uncertainty propagation of atomic weight measurement results | volume = 45 | pages = 53–62 | doi = 10.1088/0026-1394/45/1/008 | last2 = Mester | first2 = Zoltán| issue = 1 |bibcode = 2008Metro..45...53M | s2cid = 122229901 }}</ref> especially as the sample distribution is not necessarily symmetrical: the IUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties,<ref name="Holden">{{cite journal | last = Holden | first = Norman E. | url = https://media.iupac.org/publications/ci/2004/2601/1_holden.html | journal = Chemistry International | year = 2004 | issue = 1 | title = Atomic Weights and the International Committee—A Historical Review | volume = 26 | pages = 4–7 }}</ref> and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is 1{{e|–5}} or 10&nbsp;ppm. 

Apart from this uncertainty by measurement, some elements have variation over sources. That is, different sources (ocean water, rocks) have a different radioactive history and so different isotopic composition. To reflect this natural variability, the IUPAC made the decision in 2010 to list the standard relative atomic masses of 10 elements as an interval rather than a fixed number.<ref>{{cite web |title=Changes to the Periodic Table |url= https://ucalgary.ca/news/utoday/december16-2010/periodictable |archive-url= https://web.archive.org/web/20190715104320/https://ucalgary.ca/news/utoday/december16-2010/periodictable |archive-date=2019-07-15}}</ref>

== See also ==
* [[Organization:International Union of Pure and Applied Chemistry|International Union of Pure and Applied Chemistry]] (IUPAC)
* [[Organization:Commission on Isotopic Abundances and Atomic Weights|Commission on Isotopic Abundances and Atomic Weights]] (CIAAW)

== Notes ==
{{notelist}}

== References ==
{{reflist|2}}

== Further reading ==
* {{cite journal|url=https://www.degruyter.com/view/j/pac.2018.90.issue-2/pac-2016-0402/pac-2016-0402.xml|access-date=2019-02-08|date=2018-01-04|title=Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)|first1=Antonio|last1=Possolo|first2=Adriaan M.H.|last2=van der Veen|first3=Juris|last3=Meija|first4=D.|last4=Brynn Hibbert|journal=Pure and Applied Chemistry|volume=90|issue=2|pages=395–424|doi=10.1515/pac-2016-0402|s2cid=145931362|doi-access=free}}

== External links ==
*[http://www.ciaaw.org IUPAC Commission on Isotopic Abundances and Atomic Weights]
*[http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&ascii=html&isotype=some NIST relative atomic masses of all isotopes and the standard atomic weights of the elements]
*[https://www.ciaaw.org/atomic-weights.htm Standard Atomic Weights]

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[[Category:Chemical properties]]
[[Category:Stoichiometry]]
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{{Sourceattribution|Relative atomic mass}}