Editing Relative atomic mass (section)

== Determination of relative atomic mass ==
{{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 [[isotope|isotopic composition]] of a sample. Highly accurate atomic masses are available<ref name="NIST">[[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]]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 [[fluorine]], a precision which is greater than the current best value for the [[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 [[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&nbsp;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 [[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 {{val|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>