Standard atomic weight

Among various variants of the notion of atomic weight (A_r, also known as relative atomic mass) used by scientists, the standard atomic weight (A_r°) is the most common and practical. The standard atomic weight of each chemical element is determined and published by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) based on natural, stable, terrestrial sources of the element. The definition specifies the use of samples from many representative sources from the Earth, so that the value can widely be used as the atomic weight for substances as they are encountered in reality—for example, in pharmaceuticals and scientific research. Non-standardized atomic weights of an element are specific to sources and samples, such as the atomic weight of carbon in a particular bone from a particular archaeological site. Standard atomic weight averages such values to the range of atomic weights that a chemist might expect to derive from many random samples from Earth. This range is the rationale for the interval notation given for some standard atomic weight values.

Of the 118 known chemical elements, 84 have this Earth-environment based value, all but 4 of which have stable isotopes. Typically, such a value is, for example helium: A_r°(He) = 4.002602(2). The "(2)" indicates the uncertainty in the last digit shown, to read 4.002602±0.000002. IUPAC also publishes abridged values, rounded to five significant figures. For helium, A_{r, abridged}°(He) = 4.0026.

For fourteen elements the samples diverge on this value, because their sample sources have had a different decay history. For example, thallium (Tl) in sedimentary rocks has a different isotopic composition than in igneous rocks and volcanic gases. For these elements, the standard atomic weight is noted as an interval: A_r°(Tl) = [204.38, 204.39]. With such an interval, for less demanding situations, IUPAC also publishes a conventional value. For thallium, A_{r, conventional}°(Tl) = 204.38.

Definition

The standard atomic weight is a special value of the relative atomic mass. It is defined as the "recommended values" of relative atomic masses of sources in the local environment of the Earth's crust and atmosphere as determined by the IUPAC Commission on Atomic Weights and Isotopic Abundances (CIAAW). In general, values from different sources are subject to natural variation due to a different radioactive history of sources. Thus, standard atomic weights are an expectation range of atomic weights from a range of samples or sources. By limiting the sources to terrestrial origin only, the CIAAW-determined values have less variance, and are a more precise value for relative atomic masses (atomic weights) actually found and used in worldly materials.

The CIAAW-published values are used and sometimes lawfully required in mass calculations. The values have an uncertainty (noted in brackets), or are an expectation interval (see example in illustration immediately above). This uncertainty reflects natural variability in isotopic distribution for an element, rather than uncertainty in measurement (which is much smaller with quality instruments).

Although there is an attempt to cover the range of variability on Earth with standard atomic weight figures, there are known cases of mineral samples which contain elements with atomic weights that are outliers from the standard atomic weight range.

For synthetic elements the isotope formed depends on the means of synthesis, so the concept of natural isotope abundance has no meaning. Therefore, for synthetic elements the total nucleon count of the most stable isotope (i.e., the isotope with the longest half-life) is listed in brackets, in place of the standard atomic weight.

When the term "atomic weight" is used in chemistry, usually it is the more specific standard atomic weight that is implied. It is standard atomic weights that are used in periodic tables and many standard references in ordinary terrestrial chemistry.

Lithium represents a unique case where the natural abundances of the isotopes have in some cases been found to have been perturbed by human isotopic separation activities to the point of affecting the uncertainty in its standard atomic weight, even in samples obtained from natural sources, such as rivers.

Terrestrial definition

An example of why "conventional terrestrial sources" must be specified in giving standard atomic weight values is the element argon. Between locations in the Solar System, the atomic weight of argon varies as much as 10%, due to extreme variance in isotopic composition. Where the major source of argon is the decay of ⁴⁰
K in rocks, ⁴⁰
Ar will be the dominant isotope. Such locations include the planets Mercury and Mars, and the moon Titan. On Earth, the ratios of the three isotopes ³⁶Ar : ³⁸Ar : ⁴⁰Ar are approximately 5 : 1 : 1600, giving terrestrial argon a standard atomic weight of 39.948(1).

However, such is not the case in the rest of the universe. Argon produced directly, by stellar nucleosynthesis, is dominated by the alpha-process nuclide ³⁶
Ar. Correspondingly, solar argon contains 84.6% ³⁶
Ar (according to solar wind measurements), and the ratio of the three isotopes ³⁶Ar : ³⁸Ar : ⁴⁰Ar in the atmospheres of the outer planets is 8400 : 1600 : 1. The atomic weight of argon in the Sun and most of the universe, therefore, would be only approximately 36.3.

Causes of uncertainty on Earth

Famously, the published atomic weight value comes with an uncertainty. This uncertainty (and related: precision) follows from its definition, the source being "terrestrial and stable". Systematic causes for uncertainty are:

1. Measurement limits. As always, the physical measurement is never finite. There is always more detail to be found and read. This applies to every single, pure isotope found. For example, today the mass of the main natural fluorine isotope (fluorine-19) can be measured to the accuracy of eleven decimal places: 18.998403163(6). But a still more precise measurement system could become available, producing more decimals.
2. Imperfect mixtures of isotopes. In the samples taken and measured the mix (relative abundance) of those isotopes may vary. For example, copper. While in general its two isotopes make out 69.15% and 30.85% each of all copper found, the natural sample being measured can have had an incomplete 'stirring' and so the percentages are different. The precision is improved by measuring more samples of course, but there remains this cause of uncertainty. (Example: lead samples vary so much, it can not be noted more precise than four figures: 207.2)
3. Earthly sources with a different history. A source is the greater area being researched, for example 'ocean water' or 'volcanic rock' (as opposed to a 'sample': the single heap of material being investigated). It appears that some elements have a different isotopic mix per source. For example, thallium in igneous rock has more lighter isotopes, while in sedimentary rock it has more heavy isotopes. There is no Earthly mean number. These elements show the interval notation: A_r°(Tl) = [204.38, 204.39]. For practical reasons, a simplified 'conventional' number is published too (for Tl: 204.38).

These three uncertainties are accumulative. The published value is a result of all these.