Relative atomic mass

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.{{GoldBookRef|file=R05258|title=relative atomic mass}} 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 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 certainty (e.g., in number of significant figures) than those reflected in standard atomic weights.

The prevailing IUPAC definitions (as taken from the "Gold Book") are:

: atomic weight – See: relative atomic mass[http://goldbook.iupac.org/A00505.html IUPAC Gold Book – atomic weight]

and

: relative atomic mass (atomic weight) – The ratio of the average mass of the atom to the unified atomic mass unit.[http://goldbook.iupac.org/R05258.html IUPAC Gold Book – relative atomic mass (atomic weight), A r]

Here the "unified atomic mass unit" refers to 1/12 of the mass of an atom of {{sup|12}}C in its ground state.[http://goldbook.iupac.org/U06554.html IUPAC Gold Book – unified atomic mass unit]

The IUPAC definition 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, boron from Turkey has a lower relative atomic mass than boron from California, because of its different isotopic composition.{{Greenwood&Earnshaw1st|pages=21, 160}}{{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 = 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 }} Nevertheless, given the cost and difficulty of isotope analysis, it is common practice to instead substitute the tabulated values of standard atomic weights, which are ubiquitous in chemical laboratories and which are revised biennially by the IUPAC's Commission on Isotopic Abundances and Atomic Weights (CIAAW).[http://goldbook.iupac.org/html/S/S05907.html IUPAC Gold Book – standard atomic weights]

Older (pre-1961) historical relative scales based on the atomic mass unit (symbol: a.m.u. or amu) used either the 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 unified atomic mass unit for the resolution of these problems.

{{main|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).

Atomic mass (m_a) 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 silicon isotopes is given below. A convenient unit of mass for atomic mass is the 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 atomic mass constant ({{nowrap|1=m_u = 1 Da}}). This ratio is dimensionless.

{{main|Isotope geochemistry}}

Modern relative atomic masses (a term specific to a given element sample) are calculated from measured values of atomic mass (for each nuclide) and isotopic composition of a sample. Highly accurate atomic masses are availableNational 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].{{AME 2003}} for virtually all non-radioactive nuclides, but isotopic compositions are both harder to measure to high precision and more subject to variation between samples.{{AtWt TICE 1997}}{{AtWt IAV}} For this reason, the relative atomic masses of the 22 mononuclidic elements (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 fluorine, a precision which is greater than the current best value for the Avogadro constant (one part in 20 million).

The calculation is exemplified for silicon, whose relative atomic mass is especially important in 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 billion for {{sup|28}}Si and about one part in one billion for the others. However, the range of 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}} × {{val|0.922297}}) + ({{val|28.97649}} × {{val|0.046832}}) + ({{val|29.97377}} × {{val|0.030872}}) = {{val|28.0854}}

The estimation of the uncertainty is complicated,{{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 }} especially as the sample distribution is not necessarily symmetrical: the IUPAC standard relative atomic masses are quoted with estimated symmetrical uncertainties,{{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 }} and the value for silicon is 28.0855(3). The relative standard uncertainty in this value is {{val|e=-5}} or 10 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.{{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}}

• International Union of Pure and Applied Chemistry (IUPAC)
• Commission on Isotopic Abundances and Atomic Weights (CIAAW)

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• {{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}}

• [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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